# A Misleading Gallery of Fluid Motion by Generative Artificial Intelligence

Ali Kashefi
Department of Civil & Environmental Engineering
Stanford University, Stanford, CA 94305, USA
<EMAIL_ADDRESS>
Corresponding author.

###### Abstract

In this technical report, we extensively investigate the accuracy of outputs
from well-known generative artificial intelligence (AI) applications in
response to prompts describing common fluid motion phenomena familiar to the
fluid mechanics community. We examine a range of applications, including
Midjourney, Dall·E, Runway ML, Microsoft Designer, Gemini, Meta AI, and
Leonardo AI, introduced by prominent companies such as Google, OpenAI, Meta,
and Microsoft. Our text prompts for generating images or videos include
examples such as “Von Kármán vortex street”, “flow past an airfoil”, “Kelvin-
Helmholtz instability”, “shock waves on a sharp-nosed supersonic body”, etc.
We compare the images generated by these applications with real images from
laboratory experiments and numerical software. Our findings indicate that
these generative AI models are not adequately trained in fluid dynamics
imagery, leading to potentially misleading outputs. Beyond text-to-image/video
generation, we further explore the transition from image/video to text
generation using these AI tools, aiming to investigate the accuracy of their
descriptions of fluid motion phenomena. This report serves as a cautionary
note for educators in academic institutions, highlighting the potential for
these tools to mislead students. It also aims to inform researchers at these
renowned companies, encouraging them to address this issue. We conjecture that
a primary reason for this shortcoming is the limited access to copyright-
protected fluid motion images from scientific journals.

_Keywords_ AI-generated fluid imagery $\cdot$ AI in education $\cdot$ Prompt
engineering $\cdot$ Midjourney $\cdot$ Dall·E $\cdot$ Meta AI $\cdot$ Gemini

##  1 Introduction and motivation

Generative AI models (Gozalo-Brizuela and Garrido-Merchan, 2023; Feuerriegel
et al., 2024; Lim et al., 2023; Cao et al., 2023; Epstein et al., 2023;
Kashefi and Mukerji, 2023; Brynjolfsson et al., 2023; Fui-Hoon Nah et al.,
2023) are nowadays popular and are used in various applications with
transforming text, images, video, and sounds based on diverse input prompts. A
subset of generative models is Large Language Models (LLMs) (Xu et al., 2022;
Hoffmann et al., 2022; Thirunavukarasu et al., 2023; Kasneci et al., 2023;
Chang et al., 2023; Chen et al., 2021; Kojima et al., 2022; Yang et al., 2023;
Touvron et al., 2023; Roziere et al., 2023; Çelen et al., 2024), which have
seen substantial development from famous tech companies such as Google,
Microsoft, Open AI, Midjourney, and Runway ML.

One specific task of these models is to generate images from text prompts. As
researchers in the fluid mechanics and applied mathematics communities, we are
interested in investigating the capability of these generative AI models to
produce accurate images based on textual prompts describing fluid mechanics
phenomena. For our investigation, we use common textual prompts that are
almost universally known in the community for a fair assessment.

Image generation using textual prompts can be assessed on two levels. At the
first level, the question is whether the generative AI models can generate at
least a relevant image. A relevant image can be thought of as something that
first comes to mind for a fluid mechanics expert. For instance, if the prompt
is “Von-Karmann Vortex Street”, (Tritton, 1959; Kashefi and Staples, 2018;
Kashefi, 2020a, 2022) an image similar to the cover of the “An Album of Fluid
Motion” book (Van Dyke and Van Dyke, 1982) might be expected. At a deeper
level, the images should not only be relevant but also accurately describe the
characteristic features of fluid motion. For example, for the prompt “Flow
over a backward-facing step at Reynolds number of 400”, (Kim and Moin, 1985;
Armaly et al., 1983; Le et al., 1997; Kashefi and Staples, 2018; Kashefi,
2020b) it is crucial to assess whether the reattachment length in the
generated image is correct. This technical report focuses on the first level.
We compare generative images with those found in open-source articles from the
Journal of Fluid Mechanics, which are derived from lab experiments or
numerical software.

The remainder of this technical report is organized as follows. Sect. 2 offers
a brief review of the governing equations of fluid motion along with two
special cases of compressible and incompressible flow. Sect. 3, which is the
main part of this report, focuses on text-to-image generation for fluid motion
using well-known AI tools. In Sect. 4, an example of text-to-video generation
relevant to fluid motion is provided. Image-to-text and video-to-text
generation, as applied to fluid dynamic motion, are investigated in Sect. 5
and Sect. 6, respectively. Lastly, we provide a summary and concluding remarks
of our technical report in Sect. 7.

##  2 Brief overview of fluid dynamic motion

In this subsection, we briefly review the governing equations for fluids at
the most general level. The two main principles are the continuity equation
and the Cauchy momentum equation (Euler, 1757; Łukaszewicz and Kalita, 2016;
Constantin and Foiaş, 1988; Chorin et al., 1990; Batchelor, 1967) and can be
written respectively as

$\frac{D\rho}{Dt}+\rho\left(\nabla\cdot\bm{\mathit{u}}\right)=0,$ (1)

$\rho\frac{D\bm{\mathit{u}}}{Dt}=\rho\bm{\mathit{f}}+\nabla\cdot\bm{\mathit{T}},$
(2)

where $\rho$ represents the fluid density, and $\bm{\mathit{u}}$ represents
the velocity vector. The total derivative with respect to time is denoted by
$\frac{D}{Dt}$. The body force is represented by $\bm{\mathit{f}}$.
$\bm{\mathit{T}}$ represents the most general form of the stress tensor. Under
different assumptions, these two equations (Eqs. 1–2) can be simplified. For
instance, in the case of compressible flow (Feistauer et al., 2003; Novotny
and Straskraba, 2004), the stress tensor is expressed as

$\bm{\mathit{T}}=-p\bm{\mathit{I}}+\lambda\left(\nabla\cdot\bm{\mathit{u}}\right)\bm{\mathit{I}}+\mu\left(\nabla\bm{\mathit{u}}+\nabla\bm{\mathit{u}}^{T}\right),$
(3)

where $p$ indicates the fluid pressure. Dynamic viscosity and the second
viscosity are respectively shown by $\mu$ and $\lambda$. $\bm{\mathit{I}}$ is
the identity tensor. As another simplification, in the case of incompressible
flow (Majda et al., 2002; Panton, 2024), the velocity vector is divergence-
free, which is mathematically represented as

$\nabla\cdot\bm{\mathit{u}}=0,$ (4)

leading to further simplification of Eq. 3. These equations (Eqs. 1–2), which
may be coupled with others, describe the behavior of fluid motion in an
Eulerian system. Similarly, fluid motion can be described in a Lagrangian
system. In a specified time-space domain, along with boundary and initial
conditions, the equations can be solved numerically, and the results are
illustrated using visualization software (Matsson, 2023; Squillacote et al.,
2007; Ayachit, 2015; Yang et al., 2020; Jasak, 2009; Jasak et al., 2007;
Heidbach et al., 2020; Pryor, 2009; Flaischlen and Wehinger, 2019; Mullen,
2011). In this technical report, we consider images of fluid motions obtained
by both experimental (Huang et al., 1997; Westerweel et al., 1997; Willert and
Gharib, 1991; Van Dyke and Van Dyke, 1982; Adrian, 1991; Tropea et al., 2007;
Raffel et al., 2018) and numerical tools (Hirsch, 2007; Patankar, 2018; Osher
and Fedkiw, 2004; Anderson and Wendt, 1995; Reddy and Gartling, 2010).

##  3 Text to image

In this subsection, we first briefly introduce different generative
applications and then compare their outputs for eleven different text prompts
related to fluid dynamics motion. Specifically, we consider Midjourney
111https://www.midjourney.com/home (Sect. 3.1), ChatGPT-4
222https://chat.openai.com and Microsoft Designer
333https://designer.microsoft.com with DALL·E 3 (Sect. 3.2), Runway ML
444https://runwayml.com/ (Sect. 3.3), Gemini 555https://gemini.google.com/app
(Sect. 3.4), Meta AI 666https://ai.meta.com/meta-ai/ (Sect. 3.5), and Leonardo
AI 777https://leonardo.ai (Sect. 3.6).

###  3.1 Midjourney

Midjourney (Borji, 2022; Hanna, 2023; Huang et al., 2023; Henderson et al.,
2023) was released in July 2022 by the research lab Midjourney. Its primary
goal is to generate images from users’ textual prompts. The platform offers
different plans, with the basic one priced at $10 per month. Access to this AI
platform is provided through Discord. Additionally, users can view the prompts
and images generated by others. The capabilities of Midjourney have been
investigated by other researchers in areas such as graphic design (Mansour,
2023), architecture (Jaruga-Rozdolska, 2022), industrial design (Yin et al.,
2023), etc.

###  3.2 DALL·E (embedded in ChatGPT 4, ChatGPT 4o, and Microsoft Designer)

DALL·E was developed and released by OpenAI in 2021 (Kang and Yi, 2023;
Leivada et al., 2023; Borji, 2022; Marcus et al., 2022; Betker et al., 2023;
Adams et al., 2023; Hwang and Oh, 2023; Henderson et al., 2023; Ajmera et al.,
2024). The most recent version, DALL·E 3, is now integrated with ChatGPT 4,
and recently ChatGPT 4o. As a result, users of ChatGPT 4 and ChatGPT 4o can
generate images using textual prompts. Currently, the basic plan for ChatGPT 4
and ChatGPT 4o is priced at $20 per month, with a limit of 40 messages every
three hours.

It is noted that Microsoft Designer currently uses DALL·E 3 for generating
images as well. Microsoft Designer (Hwang and Oh, 2023; Henderson et al.,
2023; Pearson, 2023) was launched by Microsoft and is currently still in its
experimental phase. This AI tool generates photos based on user-generated
textual prompts, and the platform is currently available for free to users.

###  3.3 Runway ML

Runway ML (Hales, 2021; Othman, 2023; Gupta, 2021) was launched in 2018 by
Runway AI, Inc. This platform has a variety of applications, but we
specifically explore its capabilities in text-to-image and text-to-video
generation, particularly in the context of fluid motion. The current version
of Runway operates based on the deep learning model of Stable Diffusion
(Rombach et al., 2022; Esser et al., 2024; Meng et al., 2023; Ho et al.,
2022). Notably, researchers from Runway AI, Inc. contributed to the
development of the Stable Diffusion algorithm (Borji, 2022). It is worth
noting that Stability AI is another notable company that contributed to the
development of the Stable Diffusion algorithm (Esser et al., 2024). However,
in this work, our examination is focused on Runway ML. Note that Runway ML
offers different styles for generating images. In the current article, we use
the None style.

###  3.4 Gemini Advanced

Gemini, a large language model developed by Google DeepMind, originally known
as Bard, can generate images from textual descriptions and describe image
content in text (Masalkhi et al., 2024; McIntosh et al., 2023; Singh et al.,
2023; Aydin, 2023; Campesato, 2024; Carlà et al., 2024; Buscemi and Proverbio,
2024; Lu et al., 2024). This report explores both capabilities of Gemini:
text-to-image in this subsection and image-to-text in Sect. 5.3. The basic
version of Gemini is free, while its advanced version is free for two months
and then costs $20 per month. We use the advanced version (i.e., Gemini
Advanced) for the current study.

###  3.5 Meta AI (built on Meta LLaMA 3)

Meta AI, released by Meta, is a large language model built on the Meta LLaMA 3
architecture (Touvron et al., 2023; Bhatt et al., 2024; Li et al., 2024a;
Harper, 2024). The model is currently available for free, but only in specific
countries. The model has the capability to generate images based on text
prompts.

###  3.6 Leonardo Ai

Leonardo Ai is another tool that operates using deep learning models (Ruiz-
Rojas et al., 2023; Wang and Utama, 2023; Moreno-Sánchez et al., 2023). For
the purposes of this technical report, we examine its capabilities for text-
to-image generation. Additionally, we utilize the paid version of the service
($12 per month) for this exploration. Note that Leonardo Ai offers different
models with different modes. In this study, we use the model of “Leonardo
Lightning XL” with the “Dynamics" mode.

###  3.7 Comparison

In this subsection, we compare the performance of these six different
generative models. As a general structure for this subsection, we present
images generated by these generative models, along with a sub-figure in part
(g) of Figs. 1–11 that shows an accurate image (as ground truth) associated
with the prompt relevant to that fluid dynamics phenomenon.

(a) Midjourney

(b) Gemini

(c) DALL·E 3

(d) Meta AI

(e) Runway

(f) Leonardo Ai

(g) Von Kármán vortex street behind an oscillating circular cylinder in a lab
experimental setup; this image is taken from part (c) of Fig. 25 in Khan et
al. (2023), published as open access under a Creative Commons license in the
Journal of Fluid Mechanics, allowing readers to distribute the content freely.

Figure 1: A comparison between the AI-generated images and the lap
experimental result (i.e., ground truth) for the prompt “Von Kármán vortex
street”

####  3.7.1 Von Kármán vortex street

The first textual prompt we investigate in this subsection is “Von Kármán
vortex street”. Before analyzing the outputs from the generative models, we
highlight a few aspects of this fluid dynamics problem, specifically by
mentioning the Reynolds number ($Re$). An important dimensionless number in
fluid mechanics is the Reynolds number (see e.g., (Rott, 1990; Johnson and
Patel, 1999; Purcell, 2014; Smits et al., 2011; Drela, 1989; Kashefi et al.,
2021; Kashefi, 2020c)). Depending on the context of the problem, it can be
written in different forms. For instance, for the problem of flow past a
circular cylinder, which can be seen in part (g) of Fig. 1 and part (g) of
Fig. 2, it can be expressed as follows:

$Re=\frac{\rho dU_{\infty}}{\mu},$ (5)

where $\rho$ and $\mu$ are respectively the density and the dynamic viscosity
of the fluid. The free stream velocity and the cylinder diameter are shown by
$U_{\infty}$ and $d$, respectively. The Reynolds number ($Re$) is used to
characterize other important fluid motion problems, such as flow over an
airfoil (see part (g) of Fig. 8), flow over an airplane wing (see part (g) of
Fig. 11), and Kelvin–Helmholtz instability (see part (g) of Fig. 4), among
others.

One of the dimensionless numbers relevant to the Von Kármán vortex street (see
e.g., (Von Kármán, 2004)), which can be seen in part (g) of Fig. 1, is the
Strouhal number (see e.g., (Okajima, 1982)), which is formulated as follows:

$St=\frac{f_{s}d}{u_{\infty}},$ (6)

where $f_{s}$ represents the shedding frequency, $d$ is the cylinder diameter
similar to what we define in Eq. 5, and $u_{\infty}$ is the free stream
velocity of the fluid.

Figure 1 depicts responses to the prompt “Von Kármán vortex street”. In images
generated by Midjourney and Leonardo Ai, a street is visible, indicating that
these generative models are misled by the term “street” in the prompt. The
concept of “vortex” is observed in images generated by Midjourney, Gemini
Advanced, DALL·E 3, Meta AI, and Runway; however, none of these
representations acceptably depict the vortex in a Von Kármán vortex street.

The image generated by Meta AI is interesting in that it depicts water
circulation in a pipe within a laboratory environment. Although this image
does not represent the Von Kármán vortex street, it is relevant to fluid
mechanics. Interestingly, the image generated by DALL·E 3 could be considered
relevant to the rotating disk problem or the Von Kármán swirling flow problem
(Cochran, 1934; Kármán, 1921).

As a general observation, it seems that these generative models do not
interpret “Von Kármán vortex street” as a cohesive expression. Instead, they
treat it as a combination of the individual words “vortex” and “street”,
attempting to generate images that merge these two concepts.

(a) Midjourney

(b) Gemini

(c) DALL·E 3

(d) Meta AI

(e) Runway

(f) Leonardo Ai

(g) Flow past a three-dimensional circular cylinder at a Reynolds number of
$Re=3900$; this image, showing vorticity and produced by a numerical
simulation, serves as the abstract photo in Lu et al. (2023), published as
open access under a Creative Commons license in the Journal of Fluid
Mechanics, allowing readers to distribute the content freely.

Figure 2: A comparison between the AI-generated images and the numerical
simulation result (i.e., ground truth) for the prompt “Flow past a circular
cylinder”

####  3.7.2 Flow past a circular cylinder

Figure 2 presents images generated in response to the prompt “flow past a
circular cylinder”. None of the generative models under investigation
accurately captures the phenomenon. Among the generated images, the result
from Midjourney is notable as it features fluid rotating in a hollow cylinder.

In the fluid mechanics community, the term “flow” typically implies fluid
flow, such as water or air. Bearing this in mind, although some types of flow
are visible in the images generated by DALL·E 3 and Meta AI, they do not
depict actual fluid flow, perhaps due to the fact that the term “fluid” is not
included in the prompt “flow past a circular cylinder”. In all of these
generated images, we can observe the presence of a cylinder as an object.
Interestingly, each generative model depicts the cylinder from a unique
perspective and angle.

The image generated by Gemini Advanced is interesting because, although it is
not directly relevant to “flow past a circular cylinder”, it depicts a
schematic of flow inside an inclined cylinder. Additionally, this image
includes some written letters. This type of figure can often be found in fluid
mechanics textbooks (see, for example, Fig. P5.131 of (Munson et al., 2013)).
A similar observation applies to the image generated by Runway, which can be
interpreted as showing the cross-section of a cylinder. The figure generated
by Leonardo Ai is remarkable because it exhibits flow evolving on the outer
surface of a cylinder, perhaps the closest representation to what we expected,
yet it remains significantly distant from the actual phenomenon.

(a) Midjourney

(b) Gemini

(c) DALL·E 3

(d) Meta AI

(e) Runway

(f) Leonardo Ai

(g) Hydraulic jump in a lab experimental setup; a series of Kelvin–Helmholtz
billows is also observable. This image is taken from part (b) of Fig. 9 in
Lawrence and Armi (2022), published as open access under a Creative Commons
license in the Journal of Fluid Mechanics, allowing readers to distribute the
content freely.

Figure 3: A comparison between the AI-generated images and the lap
experimental result (i.e., ground truth) for the prompt “Hydraulic jump”

####  3.7.3 Hydraulic jump

The next prompt considered in this technical report is “hydraulic jump”, with
the corresponding images displayed in Fig. 3. The occurrence of the hydraulic
jump, as observed in part (g) of Fig. 3 and part (g) of Fig. 9, can be
identified using the dimensionless Froude number (see e.g., (Hornung et al.,
1995)), defined as:

$Fr=\frac{U_{u}^{2}}{gh_{u}},$ (7)

where $U_{u}$ and $h_{u}$ respectively represent the upstream velocity and
height of the fluid. For $Fr>1$, a hydraulic jump is expected.

As can be seen from Fig. 3, the images generated by Midjourney, Runway, and
Leonardo Ai are inaccurate. Similar to some results discussed for previous
prompts, these generative models interpret “hydraulic jump” as two separate
words, “hydraulic” and “jump”. Consequently, they depict unrelated objects
such as motorcycles, minibus, or even humans jumping over a river.

On the other hand, the results by Gemini Advanced and Meta AI could be
considered moderately relevant. These two generative models produce images
that are partially accurate, as they depict water exiting a dam and a step in
a river, two scenarios in nature where a hydraulic jump can occur, based on
our knowledge. The image generated by DALL·E 3, however, does not seem
informative and is difficult to judge.

(a) Midjourney

(b) Gemini

(c) DALL·E 3

(d) Meta AI

(e) Runway

(f) Leonardo Ai

(g) Kelvin–Helmholtz instability; this image, showing a density contour and
produced by a numerical simulation, serves as the abstract photo in Lewin and
Caulfield (2022), published as open access under a Creative Commons license in
the Journal of Fluid Mechanics, allowing readers to freely distribute the
content.

Figure 4: A comparison between the AI-generated images and the numerical
simulation result (i.e., ground truth) for the prompt “Kelvin–Helmholtz
instability”

####  3.7.4 Kelvin-Helmholtz instability

Figure 4 displays the collective images generated in response to the prompt
“Kelvin-Helmholtz instability”. Surprisingly, all of the images are relevant
to this phenomenon. Images generated by Gemini Advanced, DALL·E 3, and
Leonardo Ai attempt to depict the Kelvin-Helmholtz instability in clouds in
the sky, which is a common manifestation of this instability in nature (see
e.g., (Baumgarten and Fritts, 2014)). Images produced by Midjourney, Meta AI,
and Runway depict the mixing of different liquids with varying colors, a
phenomenon characteristic of Kelvin-Helmholtz instability, as shown in part
(g) of Fig. 4, which serves as a ground truth example. It is worth mentioning
that the images generated by Runway differ slightly from the others in terms
of context.

(a) Midjourney

(b) Gemini

(c) DALL·E 3

(d) Meta AI

(e) Runway

(f) Leonardo Ai

(g) Shock wave around a cone at a Mach number of $M_{\infty}=2.05$; This
image, produced by a numerical simulation, is taken from the top part of Fig.
4 in Zuo et al. (2023), published as open access under a Creative Commons
license in the Journal of Fluid Mechanics, allowing readers to distribute the
content freely.

Figure 5: A comparison between the AI-generated images and the numerical
simulation result (i.e., ground truth) for the prompt “shock waves on a sharp-
nosed supersonic body”

####  3.7.5 Shock waves on a sharp-nosed supersonic body

Figure 5 exhibits a collection of images generated in response to the prompt
“shock waves on a sharp-nosed supersonic body”. A shock can be categorized
using the dimensionless number known as the Mach number (see e.g., (Davis and
Chyu, 1966; Howe, 1979)), formulated as:

$M_{\infty}=\frac{V_{\infty}}{c},$ (8)

where $V_{\infty}$ represents the free stream velocity and $c$ is the sound
speed. A Mach number of $M_{\infty}=2.05$ indicates a supersonic flow
accompanied by shock waves, as illustrated in part (g) of Fig. 5.

Based on observations from Fig. 5, the images produced by Gemini Advanced and
DALL·E 3 can be considered the most relevant, especially when compared to a
ground truth figure shown in part (g) of Fig. 5. The picture produced by
Leonardo Ai is also interesting as it depicts shock boundaries, although it
lacks a sharp-nosed body. The result by Runway is difficult to judge. It
illustrates an educational poster with text printed below that reads, “Shock
Waes aver Srpeouoc Edoy”, closely mirroring the prompt “shock waves on a
sharp-nosed supersonic body”. Midjourney and Meta AI generate images that
feature warplanes as sharp-nosed supersonic bodies, representing shock waves
in an artistic rather than a scientific manner.

(a) Midjourney

(b) Gemini

(c) DALL·E 3

(d) Meta AI

(e) Runway

(f) Leonardo Ai

(g) Rayleigh-Taylor instability in a lap experimental setup; the picture is
taken from part (a) of Fig. 5 in Suchandra and Ranjan (2023), published as
open access under a Creative Commons license in the Journal of Fluid
Mechanics, allowing readers to distribute the content freely.

Figure 6: A comparison between the AI-generated images and the lap
experimental result (i.e., ground truth) for the prompt “Rayleigh-Taylor
instability”

####  3.7.6 Rayleigh-Taylor instability

The next prompt is “Rayleigh-Taylor instability”, with the generated images
displayed in Fig. 6. An important dimensionless number for investigating
Rayleigh-Taylor instability, which can be observed in Fig. 6, is the Atwood
number (see e.g., (Luo et al., 2020; Ker, 1988; Andrews and Dalziel, 2010)),
expressed as:

$A=\frac{\rho_{1}-\rho_{2}}{\rho_{1}+\rho_{2}},$ (9)

where $\rho_{1}$ and $\rho_{2}$ are the densities of the heavier and lighter
fluids, respectively.

According to observations from Fig. 6, the image produced by DALL·E 3 is
particularly interesting as it suggests the interaction between heavy and
light fluids. The result from Gemini Advanced is noteworthy because it
displays the interaction of two fluids. The outputs from Midjourney and
Leonardo Ai are somewhat similar to the images generated for the “Kelvin-
Helmholtz instability” prompt, as shown in Fig. 4. Conversely, the outputs
from Meta AI and Runway are not accurate and largely irrelevant.

(a) Midjourney

(b) Gemini

(c) DALL·E 3

(d) Meta AI

(e) Runway

(f) Leonardo Ai

(g) Capillary wave: A small water droplet, approximately 0.4 mm in radius,
rebounds from the same fluid bath in a lab experimental setup; this image is
Fig. 1 in Alventosa et al. (2023), published as open access under a Creative
Commons license in the Journal of Fluid Mechanics, allowing readers to
distribute the content freely.

Figure 7: A comparison between the AI-generated images and the numerical
simulation result (i.e., ground truth) for the prompt “capillary wave”

####  3.7.7 Capillary wave

“Capillary wave” is the next prompt, and the generated images are collected in
Fig. 7. The most accurate result is generated by Gemini Advanced. One possible
question is whether Gemini Advanced uses online information simultaneously for
generating images or if it only uses a predefined dataset. Following Gemini
Advanced, the output from Meta AI is also relatively accurate and contextually
relevant. In contrast, the images generated by Midjourney, Runway, and
Leonardo Ai are misleading, as they depict general waves, such as sea waves.
Meanwhile, the result from DALL·E 3, while artistic, does not pertain to
capillary waves.

(a) Midjourney

(b) Gemini

(c) DALL·E 3

(d) Meta AI

(e) Runway

(f) Leonardo Ai

(g) Streamwise vorticity over an airfoil; this image, produced by a numerical
simulation, is taken from part (a) of Fig. 1 in Turner and Kim (2022),
published as open access under a Creative Commons license in the Journal of
Fluid Mechanics, allowing readers to distribute the content freely.

Figure 8: A comparison between the AI-generated images and the numerical
simulation result (i.e., ground truth) for the prompt “Flow over an airfoil”

####  3.7.8 Flow over an airfoil

In Fig. 8, we present a collection of generated images for the prompt “Flow
over an airfoil”. Gemini Advanced produces the most relevant image and it
depicts an airplane wing. This wing might resemble NACA airfoils (Abbott et
al., 1945), where the cross-section of the wing can be considered as an
airfoil.

The image generated by DALL·E 3 depicts an airplane turbine, while Meta AI
produces an image of an airplane in a room. The image generated by Runway is
conceptually similar to those produced by Runway in Fig. 2 and Fig. 5.
Additionally, the letters “Flow over m Ain Afirol” can be seen in that image.
Images generated by Midjourney and Leonardo Ai are artistically similar to
each other, yet they do not accurately represent the fluid mechanics concept
of flow over an airfoil. Similar to our discussion on the prompt “Flow past a
circular cylinder” in Sect. 3.7.2, the term “flow” may not be understood as
“fluid flow” by these generative models.

(a) Midjourney

(b) Gemini

(c) DALL·E 3

(d) Meta AI

(e) Runway

(f) Leonardo Ai

(g) Free-surface flow in a channel around a square cylinder at a Froude number
of $Fr=2.5$; a hydraulic jump is observed. The picture, produced by a
numerical simulation, is taken from part (c) of Fig. 3 in Eames and Robinson
(2024), published as open access under a Creative Commons license in the
Journal of Fluid Mechanics, allowing readers to distribute the content freely.

Figure 9: A comparison between the AI-generated images and the numerical
simulation result (i.e., ground truth) for the prompt “Free-surface flow”

####  3.7.9 Free-surface channel flow

The images generated in response to the prompt “Free-surface channel flow” are
displayed in Fig. 9. This prompt is intriguing because it is a common term in
everyday life and simultaneously a scientific term in fluid dynamics.
Interestingly, this phenomenon shares features in both contexts. As
illustrated in Fig. 9, all the generated images depict free surface flow in
nature, resembling everyday photos. Conversely, part (g) of Fig. 9 presents a
scientific picture associated with this phenomenon.

This simple experiment with prompts suggests the idea of allowing users to
choose the context in generative models, particularly those available as
applications. This feature would be beneficial when a prompt is common across
different contexts or domains of knowledge, enabling users to select the
specific context for which they want to generate images. For instance,
Leonardo Ai currently allows users to specify a domain of interest for
generating images, such as cinematic, environment, general, photography, etc.
However, an academic option is not yet available.

(a) Midjourney

(b) Gemini

(c) DALL·E 3

(d) Meta AI

(e) Runway

(f) Leonardo Ai

(g) Bénard cells resulting from Rayleigh–Bénard convection in a porous medium.
This image, produced by a numerical simulation, is taken from part (b) of Fig.
9 in De Paoli et al. (2022), published as open access under a Creative Commons
license in the Journal of Fluid Mechanics, allowing readers to distribute the
content freely.

Figure 10: A comparison between the AI-generated images and the numerical
simulation result (i.e., ground truth) for the prompt “Bénard cells”

####  3.7.10 Bénard cells

In Fig. 10, we examine the images generated by the models in response to the
prompt “Bénard cells”. Except for the image produced by Gemini Advanced, the
rest are irrelevant. Similar to what we discussed in the previous part, this
accuracy from Gemini Advanced may suggest it has access to online information.
The other models display images of cells, likely reflecting contexts such as
biology or medicine, indicating a misunderstanding of “Bénard cells” as a
technical term in fluid mechanics.

####  3.7.11 Flow over an airplane wing

The last prompt investigated in this technical report is “Flow over an
airplane wing”, with the outputs from the generative models displayed in Fig.
11. Midjourney, Gemini Advanced, Runway, and Leonardo Ai each generate an
image of an airplane wing. These images are very similar to each other,
displaying a similar perspective and angle of view. They depict wings of
airplanes flying in the sky above clouds. However, it is not clear how the
term “flow” in our textual prompt is reflected in these images, as can be seen
in Fig. 11.

According to Fig. 11, the generated image by Meta AI is notable because it
shows an airplane moving downward, with water flowing around the wing. The
photo appears artistic; however, it can be considered an alternative
interpretation of the textual prompt. Indeed, although we did not initially
expect to see this image in response to the prompt “flow over an airplane
wing”, the image effectively illustrates the action of an object falling into
water, capturing a realistic sense in the context of fluid dynamics.

From what we observe in Fig. 11, the image generated by DALL·E 3 is moderately
similar to what DALL·E 3 produced for the prompt “flow over an airfoil”, shown
in Fig. 8. Again, we see a turbine attached to an airplane wing. However, this
time the wing is depicted in a very cinematic style.

(a) Midjourney

(b) Gemini

(c) DALL·E 3

(d) Meta AI

(e) Runway

(f) Leonardo Ai

(g) Normalized wall shear stress (left) and confidence map (right) displayed
over the NASA Common Research Model High-lift
(https://commonresearchmodel.larc.nasa.gov/high-lift-crm/). This image,
produced by a numerical simulation, is Fig. 16 in Lozano-Durán and Bae (2023),
published as open access under a Creative Commons license in the Journal of
Fluid Mechanics, allowing readers to distribute the content freely.

Figure 11: A comparison between the AI-generated images and the numerical
simulation result (i.e., ground truth) for the prompt “Flow over an airplane
wing”

##  4 Text to video

###  4.1 Meta AI

In Sect. 3.5, we used Meta AI to generate images of fluid motion from text
descriptions. In this subsection, we investigate Meta AI’s capability to
generate videos from text prompts. It should be noted that Meta AI does not
directly create videos from text prompts. Instead, it first generates images,
and then users can animate these images by pressing the “animate” button. Meta
AI automatically animates the images, producing animations approximately three
seconds in length.

###  4.2 Runway ML

In Sect. 5.2, we used Runway ML for generating images from text, specifically
depicting fluid dynamic motion. In this subsection, we shift to exploring
Runway ML’s text-to-video capabilities, focusing on creating short videos that
visually represent fluid dynamic motion based on textual descriptions. Similar
to Meta AI, Runway ML first generates a picture and then animates it. However,
compared to Meta AI, Runway ML produces images of higher quality.

###  4.3 Comparison

To compare the performance of Meta AI and Runway ML, we use the textual prompt
“water past a circular cylinder”. The generated videos are available in the
repository mentioned in the data availability section. To illustrate the
outputs, we display several sequential frames from the generated videos by
Meta AI and Runway ML respectively in Fig. 12 and Fig. 13. The result from
Runway ML could be aesthetically valuable. It appears that the cylinder is
fixed while water flows around it before entering a river. The interaction
between this water and the river water is interesting, as it creates waves.
These waves could be considered similar to capillary waves. The image
generated by Meta AI is striking, as it appears that the cylinder rotates,
causing the water inside to also rotate. Furthermore, the cylinder is
partially submerged in pond water, and the interaction between the rotating
cylinder and the water surface is displayed. Overall, the generated videos do
not deliver the expected and relevant results for the prompt “water past a
circular cylinder”; however, they do generate other interesting fluid dynamics
phenomena. Finally, it should be noted that the reason for using the term
“water” instead of “flow” or “fluid flow” is intentional, as these generative
models have issues interpreting “flow” in the context of fluid dynamics. This
issue was discussed in detail in Sect. 3.7.

Figure 12: Several sequential frames from the generated video by Meta AI for
the prompt “water past a circular cylinder”. The full generated video is
available at this GitHub repository: https://github.com/Ali-
Stanford/MisleadingGalleryOfFluidMotionByAI.

Figure 13: Several sequential frames from the generated video by Runway ML for
the prompt “water past a circular cylinder”. The full generated video is
available at this GitHub repository: https://github.com/Ali-
Stanford/MisleadingGalleryOfFluidMotionByAI.

##  5 Image to text

###  5.1 LLaVA

LLaVA 888https://llava.hliu.cc was primarily developed by researchers at
Microsoft and the University of Wisconsin-Madison (Liu et al., 2023a; Lin et
al., 2023; Buscemi and Proverbio, 2024). It is designed to generate textual
descriptions from input images and videos. LLaVA is open-source and free to
use, and it has been widely applied in various fields such as biomedicine (Li
et al., 2023), AI agents (Liu et al., 2023b), and solving mathematical
geometric problems (Gao et al., 2023). In this subsection, we utilize image-
to-text generation, while in Sect. 6.1, we employ the video-to-text generation
capability of LLaVA.

###  5.2 ChatGPT 4

Beyond the capability of generating images from textual descriptions, ChatGPT
4 is also capable of describing the content of a given image in text (Ren et
al., 2024; Lu et al., 2024; Zhu et al., 2023; Johnson et al., 2023). In this
subsection, we analyze this aspect of ChatGPT 4, focusing on fluid dynamic
motion images.

###  5.3 Gemini

In Sect. 3.5, we explored Gemini’s capability for generating textual
descriptions of images depicting fluid motion. In this subsection, we assess
Gemini’s performance in providing textual descriptions for an image
illustrating fluid motion.

###  5.4 Comparison

In this section, we explore the capabilities of three different generative
models: ChatGPT-4, Gemini Advanced, and LLaVA, in generating textual
descriptions of images depicting fluid motion. We upload a photo of fluid
motion to these applications and then ask each to describe the image. To
compare these models, we consider two different images. The first image is the
Von Karman vortex street shown in part (g) of Fig. 1. The generated textual
descriptions are provided in the following box.

ChatGPT-4
The image appears to capture a fluid dynamic phenomenon known as a Karman
vortex street. This occurs when a fluid flows around a cylindrical object,
causing the flow to separate and form vortices on the downstream side. The
photograph shows several swirling patterns with bright yellow lines on a dark
background, indicating the path of the fluid flow and the vortices created.
The yellow lines could be a dye or some form of visual aid to show the flow
pattern in the fluid, often used in fluid dynamics studies to visualize the
motion. There’s a sequence of alternating vortices that create a somewhat
symmetric pattern across the image. The overall aesthetic is quite artistic
and mesmerizing, capturing both the beauty and complexity of fluid motion.
Gemini Advanced
The image you sent me is a close-up of a lemon peel. The peel is a bright
yellow color, and it has a rough, textured surface. The black background makes
the yellow of the peel stand out. There is a small white letter “C” in the
bottom right corner of the image. LLaVA
The image appears to be a close-up photograph of a substance with a flowing,
swirling pattern. The substance has a yellowish hue and is captured in motion,
creating a dynamic, abstract shape that resembles a snake or a ribbon. The
background is dark, which contrasts with the bright yellow of the substance,
making the swirling pattern stand out. The image has a shallow depth of field,
with the focus on the swirling substance, causing the background to be
blurred. There is a letter "C" in the top right corner, which might be a
watermark or a part of a logo. The overall effect is quite mesmerizing and
could be interpreted as a representation of movement or fluid dynamics.

As indicated in the above box, ChatGPT-4 provides the best description
compared to Gemini Advanced and LLaVA. ChatGPT-4 clearly mentions the “Karman
vortex street” and describes the phenomenon by addressing keywords such as
“vortex” and “flow past a cylinder”. It also recognizes the colors yellow and
black in the image. More importantly, ChatGPT-4 notes the yellow color as
indicative of an experimental technique used to visualize the vortex.

While the LLaVA description is not entirely accurate, it contains
significantly more accurate information compared to Gemini Advanced. For
instance, LLaVA addresses the swirling pattern and includes terms such as
“movement of fluid dynamics” in its description. On the other hand, the Gemini
Advanced response is almost unrelated. Interestingly, both Gemini Advanced and
LLaVA refer to the letter “C” in the picture. Note that as mentioned earlier,
LLaVA is free, whereas Gemini Advanced costs $12 per month.

Another interesting and important point is that when we ask DALL·E 3, embedded
in ChatGPT-4, to generate a picture of the Von Kármán vortex street in Sect.
3, the result is inaccurate, as exhibited in part (c) of Fig. 1. However, it
provides an accurate textual description when it analyzes an actual picture of
the Von Kármán vortex street.

The second image depicts another relatively famous phenomenon in fluid
dynamics: the corona splash, which occurs at the moment a droplet impacts a
liquid surface, as shown in Fig. 14. The textual descriptions by ChatGPT-4,
Gemini Advanced, and LLaVA are provided in the following box.

ChatGPT-4
This image captures a moment of fluid dynamics beautifully. It’s a black and
white photograph showing a crown-like splash of water. The base of the splash
is broad and relatively calm, which suggests that it is probably the surface
of water in a container. From this base, several columns of water rise and arc
outwards, with droplets separating from the tips of these arcs, forming a
pattern that resembles a tiara or a crown. The splash is symmetric, and the
physics behind this phenomenon involve the surface tension of the water and
the forces exerted upon the initial impact, likely from a droplet falling into
the water. The clarity and sharpness of the image suggest a high-speed
photograph to freeze the motion. Gemini Advanced
The image you sent is a black and white photo of a crown made of water
droplets. The water droplets are arranged in a circular pattern, with some
droplets larger than others. The background is dark and blurry. The overall
effect is one of fragility and impermanence, as the water droplets appear to
be on the verge of falling apart. LLaVA
The image shows a glass of water with water droplets being poured into it. The
droplets are captured in mid-air, creating a dynamic and splashy effect. The
water appears to be clear, and the glass is transparent, allowing us to see
the water inside. The background is a plain, light color, which contrasts with
the dark tones of the water and the droplets, emphasizing the action of the
pouring. The image is in black and white, which adds a timeless and artistic
quality to the scene.

Similar to the previous investigation, and now focusing on the image shown in
Fig. 14, the output from ChatGPT-4 is significantly more accurate and
informative than those generated by Gemini Advanced and LLaVA. ChatGPT-4
clearly mentions the term “splash”. More interestingly, it addresses the
physics of surface tension and accurately recognizes that the photo was taken
with a high-speed camera. Both Gemini Advanced and LLaVA describe the water
splashing and droplets, and their results are more relevant compared to the
image of the Von Karman vortex street.

Figure 14: Corona splash in a lab experimental setup; this image is taken from
part (c) of Fig. 2 in Burzynski et al. (2020), published as open access under
a Creative Commons license in the Journal of Fluid Mechanics, allowing readers
to distribute the content freely. Figure 15: Breaking wave in a lab
experimental setup: The corresponding movie is available as a “supplementary
movie” at https://doi.org/10.1017/jfm.2021.841. This image is Fig. 3 in Steer
et al. (2021), published as open access under a Creative Commons license in
the Journal of Fluid Mechanics, allowing readers to distribute the content
freely. Figure 16: Drops and bubbles around a sphere showing nucleation
effects on cavitation in a lab experimental setup: The corresponding movie is
available as “supplementary movie 2” at https://doi.org/10.1017/jfm.2022.511.
This image is taken from parts (a)–(h) of Fig. 6 in Brandner et al. (2022),
published as open access under a Creative Commons license in the Journal of
Fluid Mechanics, allowing readers to distribute the content freely.

##  6 Video to text

###  6.1 Video-LLaMA

In this subsection, we evaluate the performance of Video-LLaMA
999https://huggingface.co/spaces/DAMO-NLP-SG/Video-LLaMA (Zhang et al., 2023)
in providing textual descriptions for a short movie that shows fluid motion.
We consider two short movies, both of which are taken from laboratory
experimental studies published in the Journal of Fluid Mechanics. These movies
are available as supplementary materials on the website of each journal paper.
Therefore, potential audiences can refer to these websites to watch the
movies. Additionally, we have included frames from the movies in Figures 13
and 14, as presented in the associated journal papers. The first movie depicts
breaking waves, as illustrated by the frames shown in Fig. 15. The
accompanying textual description from Video-LLaMA is provided in the box
below.

Video-LLaMA
In this video, we see a black and white photograph of a room with water
pouring on a table or floor. We see a variety of objects in the room,
including a table, glasses, and a toilet. There is also a skateboard in the
room and a clock in the background. We see different angles and views of the
pouring water as it covers the table or floor.

The only accurate information in the textual description by Video-LLaMA is
relevant to water being poured on a table or the floor. Video-LLaMA also
attempts to identify objects, and the only accurately identified object is a
table. However, it fails to address the main phenomenon depicted in the movie,
which is wave breaking.

The second movie depicts drops and bubbles around a sphere, and some of its
frames can be observed in Fig. 16. The text describing the movie, generated by
Video-LLaMA, can be read as follows.

Video-LLaMA
The video consists of a black background with various objects and actions
happening around it. The objects in the video include a metal ball on a table,
a metal plate, a black liquid, a bottle of water, a cup, and a black mirror.
The actions in the video include the presence of smoke, water on a mirror, and
various objects moving.

Similar to the previous examination, Video-LLaMA cannot correctly predict and
describe the phenomenon occurring in the movie. The only correct information
it contains pertains to the presence of a ball and water. It seems that Video-
LLaMA views the movies as a sequence of pictures; however, it is unable to
make acceptable reasoning among the frames.

##  7 Summary and conclusion

This technical report comprehensively evaluated the capabilities of several
generative AI models to generate text-to-image, text-to-video, image-to-text,
and video-to-text in the context of fluid dynamics. Specifically, we
investigated prominent models such as Midjourney, Dall·E3, Gemini Advanced,
Meta AI, Runway ML, Leonardo Ai, Video-LLaMA, and LLaVA. Our findings
demonstrated that the outputs generated by these AI models generally exhibited
discrepancies when compared to realistic images obtained from numerical
simulations or laboratory experiments, where fluid dynamics events are
scientifically and accurately represented. The limitations of these generative
models could be concerning in educational contexts, where they might
potentially be used with students. Therefore, it is crucial to be aware of
these models’ shortcomings in handling domain-specific knowledge.

Our conjecture is that these limitations arise because these generative models
have not been trained or refined with empirical data on fluid dynamics
phenomena. This issue likely stems from the fact that such data, including
images and videos, are often copyrighted by scientific journals and
publishers, making them not publicly available. As a potential solution,
educational institutions could request that the corresponding companies
customize and refine these generative models specifically for fluid dynamics
by providing sufficient data. We hope that this technical report serves as a
starting point for further collaboration between AI companies developing these
models and domain-specific experts in the fluid mechanics community to bridge
the existing gap.

Finally, it should be noted that similar assessments have been conducted in
other scientific disciplines for generative models (see e.g., (Meskó and
Topol, 2023; Megahed et al., 2024; Theis et al., 2015; Yang and Lerch, 2020)).
As a future direction, such investigations could be extended to additional
areas of mechanical engineering and engineering mechanics (Xue et al., 2020;
Regenwetter et al., 2022; Kashefi and Mukerji, 2022; Kashefi et al., 2023; Pal
et al., 2024; Ni and Buehler, 2024; Polverini and Gregorcic, 2024; Luu and
Buehler, 2024; Li et al., 2024b). This expansion would provide further
insights into the capabilities and limitations of these generative AI models
across various engineering disciplines.

### Data availability

The generated videos and high-quality images are available at the following
GitHub repository: https://github.com/Ali-
Stanford/MisleadingGalleryOfFluidMotionByAI.

## References

  * Gozalo-Brizuela and Garrido-Merchan [2023] Roberto Gozalo-Brizuela and Eduardo C Garrido-Merchan.  Chatgpt is not all you need. a state of the art review of large generative ai models.  _arXiv preprint arXiv:2301.04655_ , 2023.
  * Feuerriegel et al. [2024] Stefan Feuerriegel, Jochen Hartmann, Christian Janiesch, and Patrick Zschech.  Generative ai.  _Business & Information Systems Engineering_, 66(1):111–126, 2024.
  * Lim et al. [2023] Weng Marc Lim, Asanka Gunasekara, Jessica Leigh Pallant, Jason Ian Pallant, and Ekaterina Pechenkina.  Generative ai and the future of education: Ragnarök or reformation? a paradoxical perspective from management educators.  _The international journal of management education_ , 21(2):100790, 2023.
  * Cao et al. [2023] Yihan Cao, Siyu Li, Yixin Liu, Zhiling Yan, Yutong Dai, Philip S Yu, and Lichao Sun.  A comprehensive survey of ai-generated content (aigc): A history of generative ai from gan to chatgpt.  _arXiv preprint arXiv:2303.04226_ , 2023.
  * Epstein et al. [2023] Ziv Epstein, Aaron Hertzmann, Investigators of Human Creativity, Memo Akten, Hany Farid, Jessica Fjeld, Morgan R Frank, Matthew Groh, Laura Herman, Neil Leach, et al.  Art and the science of generative ai.  _Science_ , 380(6650):1110–1111, 2023.
  * Kashefi and Mukerji [2023] Ali Kashefi and Tapan Mukerji.  Chatgpt for programming numerical methods.  _Journal of Machine Learning for Modeling and Computing_ , 4(2), 2023.
  * Brynjolfsson et al. [2023] Erik Brynjolfsson, Danielle Li, and Lindsey R Raymond.  Generative ai at work.  Technical report, National Bureau of Economic Research, 2023.
  * Fui-Hoon Nah et al. [2023] Fiona Fui-Hoon Nah, Ruilin Zheng, Jingyuan Cai, Keng Siau, and Langtao Chen.  Generative ai and chatgpt: Applications, challenges, and ai-human collaboration, 2023.
  * Xu et al. [2022] Frank F Xu, Uri Alon, Graham Neubig, and Vincent Josua Hellendoorn.  A systematic evaluation of large language models of code.  In _Proceedings of the 6th ACM SIGPLAN International Symposium on Machine Programming_ , pages 1–10, 2022.
  * Hoffmann et al. [2022] Jordan Hoffmann, Sebastian Borgeaud, Arthur Mensch, Elena Buchatskaya, Trevor Cai, Eliza Rutherford, Diego de Las Casas, Lisa Anne Hendricks, Johannes Welbl, Aidan Clark, et al.  Training compute-optimal large language models.  _arXiv preprint arXiv:2203.15556_ , 2022.
  * Thirunavukarasu et al. [2023] Arun James Thirunavukarasu, Darren Shu Jeng Ting, Kabilan Elangovan, Laura Gutierrez, Ting Fang Tan, and Daniel Shu Wei Ting.  Large language models in medicine.  _Nature medicine_ , 29(8):1930–1940, 2023.
  * Kasneci et al. [2023] Enkelejda Kasneci, Kathrin Seßler, Stefan Küchemann, Maria Bannert, Daryna Dementieva, Frank Fischer, Urs Gasser, Georg Groh, Stephan Günnemann, Eyke Hüllermeier, et al.  Chatgpt for good? on opportunities and challenges of large language models for education.  _Learning and individual differences_ , 103:102274, 2023.
  * Chang et al. [2023] Yupeng Chang, Xu Wang, Jindong Wang, Yuan Wu, Linyi Yang, Kaijie Zhu, Hao Chen, Xiaoyuan Yi, Cunxiang Wang, Yidong Wang, et al.  A survey on evaluation of large language models.  _ACM Transactions on Intelligent Systems and Technology_ , 2023.
  * Chen et al. [2021] Mark Chen, Jerry Tworek, Heewoo Jun, Qiming Yuan, Henrique Ponde de Oliveira Pinto, Jared Kaplan, Harri Edwards, Yuri Burda, Nicholas Joseph, Greg Brockman, et al.  Evaluating large language models trained on code.  _arXiv preprint arXiv:2107.03374_ , 2021.
  * Kojima et al. [2022] Takeshi Kojima, Shixiang Shane Gu, Machel Reid, Yutaka Matsuo, and Yusuke Iwasawa.  Large language models are zero-shot reasoners.  _Advances in neural information processing systems_ , 35:22199–22213, 2022.
  * Yang et al. [2023] Liu Yang, Siting Liu, Tingwei Meng, and Stanley J Osher.  In-context operator learning with data prompts for differential equation problems.  _Proceedings of the National Academy of Sciences_ , 120(39):e2310142120, 2023.
  * Touvron et al. [2023] Hugo Touvron, Thibaut Lavril, Gautier Izacard, Xavier Martinet, Marie-Anne Lachaux, Timothée Lacroix, Baptiste Rozière, Naman Goyal, Eric Hambro, Faisal Azhar, et al.  Llama: Open and efficient foundation language models.  _arXiv preprint arXiv:2302.13971_ , 2023.
  * Roziere et al. [2023] Baptiste Roziere, Jonas Gehring, Fabian Gloeckle, Sten Sootla, Itai Gat, Xiaoqing Ellen Tan, Yossi Adi, Jingyu Liu, Tal Remez, Jérémy Rapin, et al.  Code llama: Open foundation models for code.  _arXiv preprint arXiv:2308.12950_ , 2023.
  * Çelen et al. [2024] Ata Çelen, Guo Han, Konrad Schindler, Luc Van Gool, Iro Armeni, Anton Obukhov, and Xi Wang.  I-design: Personalized llm interior designer.  _arXiv preprint arXiv:2404.02838_ , 2024.
  * Tritton [1959] David J Tritton.  Experiments on the flow past a circular cylinder at low reynolds numbers.  _Journal of Fluid Mechanics_ , 6(4):547–567, 1959.
  * Kashefi and Staples [2018] Ali Kashefi and Anne E Staples.  A finite-element coarse-grid projection method for incompressible flow simulations.  _Advances in Computational Mathematics_ , 44:1063–1090, 2018.
  * Kashefi [2020a] Ali Kashefi.  A coarse grid projection method for accelerating free and forced convection heat transfer computations.  _Results in Mathematics_ , 75:1–24, 2020a.
  * Kashefi [2022] Ali Kashefi.  A coarse-grid projection method for accelerating incompressible mhd flow simulations.  _Engineering with Computers_ , 38(Suppl 2):1539–1553, 2022.
  * Van Dyke and Van Dyke [1982] Milton Van Dyke and Milton Van Dyke.  _An album of fluid motion_ , volume 176.  Parabolic Press Stanford, 1982.
  * Kim and Moin [1985] John Kim and Parviz Moin.  Application of a fractional-step method to incompressible navier-stokes equations.  _Journal of computational physics_ , 59(2):308–323, 1985.
  * Armaly et al. [1983] Bassem F Armaly, F Durst, JCF Pereira, and B Schönung.  Experimental and theoretical investigation of backward-facing step flow.  _Journal of fluid Mechanics_ , 127:473–496, 1983.
  * Le et al. [1997] Hung Le, Parviz Moin, and John Kim.  Direct numerical simulation of turbulent flow over a backward-facing step.  _Journal of fluid mechanics_ , 330:349–374, 1997.
  * Kashefi [2020b] Ali Kashefi.  Coarse grid projection methodology: a partial mesh refinement tool for incompressible flow simulations.  _Bulletin of the Iranian Mathematical Society_ , 46:177–181, 2020b.
  * Euler [1757] Leonhard Euler.  Principes généraux du mouvement des fluides.  _Mémoires de l’académie des sciences de Berlin_ , pages 274–315, 1757.
  * Łukaszewicz and Kalita [2016] Grzegorz Łukaszewicz and Piotr Kalita.  _Navier–Stokes Equations: An Introduction with Applications_.  Springer, 2016.
  * Constantin and Foiaş [1988] Peter Constantin and Ciprian Foiaş.  _Navier-stokes equations_.  University of Chicago press, 1988.
  * Chorin et al. [1990] Alexandre Joel Chorin, Jerrold E Marsden, and Jerrold E Marsden.  _A mathematical introduction to fluid mechanics_ , volume 3.  Springer, 1990.
  * Batchelor [1967] George Keith Batchelor.  _An introduction to fluid dynamics_.  Cambridge university press, 1967.
  * Feistauer et al. [2003] Miloslav Feistauer, Jiří Felcman, and Ivan Straškraba.  _Mathematical and computational methods for compressible flow_.  Oxford University Press, USA, 2003.
  * Novotny and Straskraba [2004] Antonin Novotny and Ivan Straskraba.  _Introduction to the mathematical theory of compressible flow_ , volume 27.  OUP Oxford, 2004.
  * Majda et al. [2002] Andrew J Majda, Andrea L Bertozzi, and A Ogawa.  Vorticity and incompressible flow. cambridge texts in applied mathematics.  _Appl. Mech. Rev._ , 55(4):B77–B78, 2002.
  * Panton [2024] Ronald L Panton.  _Incompressible flow_.  John Wiley & Sons, 2024.
  * Matsson [2023] John E Matsson.  _An Introduction to Ansys Fluent 2023_.  Sdc Publications, 2023.
  * Squillacote et al. [2007] Amy Henderson Squillacote, James Ahrens, Charles Law, Berk Geveci, Kenneth Moreland, and Brad King.  _The paraview guide_ , volume 366.  Kitware Clifton Park, NY, 2007.
  * Ayachit [2015] Utkarsh Ayachit.  _The paraview guide: a parallel visualization application_.  Kitware, Inc., 2015.
  * Yang et al. [2020] Won Y Yang, Wenwu Cao, Jaekwon Kim, Kyung W Park, Ho-Hyun Park, Jingon Joung, Jong-Suk Ro, Han L Lee, Cheol-Ho Hong, and Taeho Im.  _Applied numerical methods using MATLAB_.  John Wiley & Sons, 2020.
  * Jasak [2009] Hrvoje Jasak.  Openfoam: Open source cfd in research and industry.  _International Journal of Naval Architecture and Ocean Engineering_ , 1(2):89–94, 2009.
  * Jasak et al. [2007] Hrvoje Jasak, Aleksandar Jemcov, Zeljko Tukovic, et al.  Openfoam: A c++ library for complex physics simulations.  In _International workshop on coupled methods in numerical dynamics_ , volume 1000, pages 1–20, 2007.
  * Heidbach et al. [2020] O Heidbach, M Ziegler, and D Stromeyer.  Manual of the tecplot 360 add-on geostress v2. 0.  2020\.
  * Pryor [2009] Roger W Pryor.  _Multiphysics modeling using COMSOL®: a first principles approach_.  Jones & Bartlett Publishers, 2009.
  * Flaischlen and Wehinger [2019] Steffen Flaischlen and Gregor D Wehinger.  Synthetic packed-bed generation for cfd simulations: Blender vs. star-ccm+.  _ChemEngineering_ , 3(2):52, 2019.
  * Mullen [2011] Tony Mullen.  _Mastering blender_.  John Wiley & Sons, 2011.
  * Huang et al. [1997] H Huang, D Dabiri, and Morteza Gharib.  On errors of digital particle image velocimetry.  _Measurement Science and Technology_ , 8(12):1427, 1997.
  * Westerweel et al. [1997] Jerry Westerweel, D Dabiri, and Morteza Gharib.  The effect of a discrete window offset on the accuracy of cross-correlation analysis of digital piv recordings.  _Experiments in fluids_ , 23(1):20–28, 1997.
  * Willert and Gharib [1991] Christian E Willert and Morteza Gharib.  Digital particle image velocimetry.  _Experiments in fluids_ , 10(4):181–193, 1991.
  * Adrian [1991] Ronald J Adrian.  Particle-imaging techniques for experimental fluid mechanics.  _Annual review of fluid mechanics_ , 23(1):261–304, 1991.
  * Tropea et al. [2007] Cameron Tropea, Alexander L Yarin, John F Foss, et al.  _Springer handbook of experimental fluid mechanics_ , volume 1.  Springer, 2007.
  * Raffel et al. [2018] Markus Raffel, Christian E Willert, Fulvio Scarano, Christian J Kähler, Steve T Wereley, and Jürgen Kompenhans.  _Particle image velocimetry: a practical guide_.  springer, 2018.
  * Hirsch [2007] Charles Hirsch.  _Numerical computation of internal and external flows: The fundamentals of computational fluid dynamics_.  Elsevier, 2007.
  * Patankar [2018] Suhas Patankar.  _Numerical heat transfer and fluid flow_.  CRC press, 2018.
  * Osher and Fedkiw [2004] Stanley Osher and Ronald Fedkiw.  Level set methods and dynamic implicit surfaces.  _Appl. Mech. Rev._ , 57(3):B15–B15, 2004.
  * Anderson and Wendt [1995] John David Anderson and John Wendt.  _Computational fluid dynamics_ , volume 206.  Springer, 1995.
  * Reddy and Gartling [2010] Junuthula Narasimha Reddy and David K Gartling.  _The finite element method in heat transfer and fluid dynamics_.  CRC press, 2010.
  * Khan et al. [2023] Izhar Hussain Khan, Puja Sunil, Soumarup Bhattacharyya, Rahul Yadav, Kamal Poddar, and Sanjay Kumar.  Flow past two rotationally oscillating cylinders.  _Journal of Fluid Mechanics_ , 969:A16, 2023.
  * Lu et al. [2023] Wilson Lu, Daniah Aljubaili, Tony Zahtila, Leon Chan, and Andrew Ooi.  Asymmetric wakes in flows past circular cylinders confined in channels.  _Journal of Fluid Mechanics_ , 958:A8, 2023.
  * Lawrence and Armi [2022] Gregory A Lawrence and Laurence Armi.  Stationary internal hydraulic jumps.  _Journal of Fluid Mechanics_ , 936:A25, 2022.
  * Lewin and Caulfield [2022] SF Lewin and CP Caulfield.  Stratified turbulent mixing in oscillating shear flows.  _Journal of Fluid Mechanics_ , 944:R3, 2022.
  * Zuo et al. [2023] Feng-Yuan Zuo, Antonio Memmolo, and Sergio Pirozzoli.  On wall pressure fluctuations in conical shock wave/turbulent boundary layer interaction.  _Journal of Fluid Mechanics_ , 967:A3, 2023.
  * Suchandra and Ranjan [2023] Prasoon Suchandra and Devesh Ranjan.  Dynamics of multilayer rayleigh–taylor instability at moderately high atwood numbers.  _Journal of Fluid Mechanics_ , 974:A35, 2023.
  * Alventosa et al. [2023] Luke FL Alventosa, Radu Cimpeanu, and Daniel M Harris.  Inertio-capillary rebound of a droplet impacting a fluid bath.  _Journal of Fluid Mechanics_ , 958:A24, 2023.
  * Turner and Kim [2022] Jacob M Turner and Jae Wook Kim.  Quadrupole noise generated from a low-speed aerofoil in near-and full-stall conditions.  _Journal of Fluid Mechanics_ , 936:A34, 2022.
  * Eames and Robinson [2024] Ian Eames and Tristan Robinson.  Free-surface channel flow around a square cylinder.  _Journal of Fluid Mechanics_ , 980:A16, 2024.
  * De Paoli et al. [2022] Marco De Paoli, Sergio Pirozzoli, Francesco Zonta, and Alfredo Soldati.  Strong rayleigh–darcy convection regime in three-dimensional porous media.  _Journal of Fluid Mechanics_ , 943:A51, 2022.
  * Lozano-Durán and Bae [2023] Adrián Lozano-Durán and H Jane Bae.  Machine learning building-block-flow wall model for large-eddy simulation.  _Journal of Fluid Mechanics_ , 963:A35, 2023.
  * Borji [2022] Ali Borji.  Generated faces in the wild: Quantitative comparison of stable diffusion, midjourney and dall-e 2.  _arXiv preprint arXiv:2210.00586_ , 2022.
  * Hanna [2023] Dena Magdy Hanna.  The use of artificial intelligence art generator “midjourney” in artistic and advertising creativity.  _Journal of Design Sciences and Applied Arts_ , 4(2):42–58, 2023.
  * Huang et al. [2023] Jiayang Huang, Yiran Chen, and David Yip.  Crossing of the dream fantasy: Ai technique application for visualizing a fictional character’s dream.  In _2023 IEEE International Conference on Multimedia and Expo Workshops (ICMEW)_ , pages 338–342. IEEE, 2023.
  * Henderson et al. [2023] Peter Henderson, Xuechen Li, Dan Jurafsky, Tatsunori Hashimoto, Mark A Lemley, and Percy Liang.  Foundation models and fair use.  _arXiv preprint arXiv:2303.15715_ , 2023.
  * Mansour [2023] Soha Mansour.  Intelligent graphic design: The effectiveness of midjourney as a participant in a creative brainstorming session.  _International Design Journal_ , 13(5):501–512, 2023.
  * Jaruga-Rozdolska [2022] Anna Jaruga-Rozdolska.  Artificial intelligence as part of future practices in the architect’s work: Midjourney generative tool as part of a process of creating an architectural form.  _Architectus_ , (3 (71), 2022.
  * Yin et al. [2023] Hu Yin, Zipeng Zhang, and Yuanyuan Liu.  The exploration of integrating the midjourney artificial intelligence generated content tool into design systems to direct designers towards future-oriented innovation.  _Systems_ , 11(12):566, 2023.
  * Kang and Yi [2023] Joohoon Kang and Youngjoo Yi.  Beyond chatgpt: Multimodal generative ai for l2 writers.  _Journal of Second Language Writing_ , 62:101070, 2023.
  * Leivada et al. [2023] Evelina Leivada, Elliot Murphy, and Gary Marcus.  Dall· e 2 fails to reliably capture common syntactic processes.  _Social Sciences & Humanities Open_, 8(1):100648, 2023.
  * Marcus et al. [2022] Gary Marcus, Ernest Davis, and Scott Aaronson.  A very preliminary analysis of dall-e 2.  _arXiv preprint arXiv:2204.13807_ , 2022.
  * Betker et al. [2023] James Betker, Gabriel Goh, Li Jing, Tim Brooks, Jianfeng Wang, Linjie Li, Long Ouyang, Juntang Zhuang, Joyce Lee, Yufei Guo, et al.  Improving image generation with better captions.  _Computer Science. https://cdn. openai. com/papers/dall-e-3. pdf_ , 2(3):8, 2023.
  * Adams et al. [2023] Lisa C Adams, Felix Busch, Daniel Truhn, Marcus R Makowski, Hugo JWL Aerts, and Keno K Bressem.  What does dall-e 2 know about radiology?  _Journal of Medical Internet Research_ , 25:e43110, 2023.
  * Hwang and Oh [2023] JaeYoung Hwang and SangHoon Oh.  A brief survey of watermarks in generative ai.  In _2023 14th International Conference on Information and Communication Technology Convergence (ICTC)_ , pages 1157–1160. IEEE, 2023.
  * Ajmera et al. [2024] P Ajmera, N Nischal, S Ariyaratne, B Botchu, KDP Bhamidipaty, KP Iyengar, SR Ajmera, N Jenko, and R Botchu.  Validity of chatgpt-generated musculoskeletal images.  _Skeletal Radiology_ , pages 1–11, 2024.
  * Pearson [2023] Andrew Pearson.  The rise of crealtives: Using ai to enable and speed up the creative process.  _Journal of AI, Robotics & Workplace Automation_, 2(2):101–114, 2023.
  * Hales [2021] Chris Hales.  Artificial intelligence: The latent revolution in filmmaking.  _ADAM ARTS_ , 2, 2021.
  * Othman [2023] Imran Othman.  Ai video editor: A conceptual review in generative arts.  In _Proceedings of the 3rd International Conference on Creative Multimedia 2023 (ICCM 2023)_ , volume 786, page 16. Springer Nature, 2023.
  * Gupta [2021] Sakshi Gupta.  _Agency, Trust, and Interpretability of Generative Adversarial Networks (GANs)_.  PhD thesis, North Carolina State University, 2021.
  * Rombach et al. [2022] Robin Rombach, Andreas Blattmann, Dominik Lorenz, Patrick Esser, and Björn Ommer.  High-resolution image synthesis with latent diffusion models.  In _Proceedings of the IEEE/CVF conference on computer vision and pattern recognition_ , pages 10684–10695, 2022.
  * Esser et al. [2024] Patrick Esser, Sumith Kulal, Andreas Blattmann, Rahim Entezari, Jonas Müller, Harry Saini, Yam Levi, Dominik Lorenz, Axel Sauer, Frederic Boesel, et al.  Scaling rectified flow transformers for high-resolution image synthesis.  _arXiv preprint arXiv:2403.03206_ , 2024.
  * Meng et al. [2023] Chenlin Meng, Robin Rombach, Ruiqi Gao, Diederik Kingma, Stefano Ermon, Jonathan Ho, and Tim Salimans.  On distillation of guided diffusion models.  In _Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition_ , pages 14297–14306, 2023.
  * Ho et al. [2022] Jonathan Ho, William Chan, Chitwan Saharia, Jay Whang, Ruiqi Gao, Alexey Gritsenko, Diederik P Kingma, Ben Poole, Mohammad Norouzi, David J Fleet, et al.  Imagen video: High definition video generation with diffusion models.  _arXiv preprint arXiv:2210.02303_ , 2022.
  * Masalkhi et al. [2024] Mouayad Masalkhi, Joshua Ong, Ethan Waisberg, and Andrew G Lee.  Google deepmind’s gemini ai versus chatgpt: a comparative analysis in ophthalmology.  _Eye_ , pages 1–6, 2024.
  * McIntosh et al. [2023] Timothy R McIntosh, Teo Susnjak, Tong Liu, Paul Watters, and Malka N Halgamuge.  From google gemini to openai q*(q-star): A survey of reshaping the generative artificial intelligence (ai) research landscape.  _arXiv preprint arXiv:2312.10868_ , 2023.
  * Singh et al. [2023] Shashi Kant Singh, Shubham Kumar, and Pawan Singh Mehra.  Chat gpt & google bard ai: A review.  In _2023 International Conference on IoT, Communication and Automation Technology (ICICAT)_ , pages 1–6. IEEE, 2023.
  * Aydin [2023] Ömer Aydin.  Google bard generated literature review: metaverse.  _Journal of AI_ , 7(1):1–14, 2023.
  * Campesato [2024] Oswald Campesato.  _Google Gemini for Python: Coding with Bard_.  Stylus Publishing, LLC, 2024.
  * Carlà et al. [2024] Matteo Mario Carlà, Gloria Gambini, Antonio Baldascino, Federico Giannuzzi, Francesco Boselli, Emanuele Crincoli, Nicola Claudio D’Onofrio, and Stanislao Rizzo.  Exploring ai-chatbots’ capability to suggest surgical planning in ophthalmology: Chatgpt versus google gemini analysis of retinal detachment cases.  _British Journal of Ophthalmology_ , 2024.
  * Buscemi and Proverbio [2024] Alessio Buscemi and Daniele Proverbio.  Chatgpt vs gemini vs llama on multilingual sentiment analysis.  _arXiv preprint arXiv:2402.01715_ , 2024.
  * Lu et al. [2024] Chaochao Lu, Chen Qian, Guodong Zheng, Hongxing Fan, Hongzhi Gao, Jie Zhang, Jing Shao, Jingyi Deng, Jinlan Fu, Kexin Huang, et al.  From gpt-4 to gemini and beyond: Assessing the landscape of mllms on generalizability, trustworthiness and causality through four modalities.  _arXiv preprint arXiv:2401.15071_ , 2024.
  * Bhatt et al. [2024] Manish Bhatt, Sahana Chennabasappa, Yue Li, Cyrus Nikolaidis, Daniel Song, Shengye Wan, Faizan Ahmad, Cornelius Aschermann, Yaohui Chen, Dhaval Kapil, et al.  Cyberseceval 2: A wide-ranging cybersecurity evaluation suite for large language models.  _arXiv preprint arXiv:2404.13161_ , 2024.
  * Li et al. [2024a] Shengrui Li, Xueting Han, and Jing Bai.  Nuteprune: Efficient progressive pruning with numerous teachers for large language models.  _arXiv preprint arXiv:2402.09773_ , 2024a.
  * Harper [2024] Jeremy Harper.  Autogenesisagent: Self-generating multi-agent systems for complex tasks.  _arXiv preprint arXiv:2404.17017_ , 2024.
  * Ruiz-Rojas et al. [2023] Lena Ivannova Ruiz-Rojas, Patricia Acosta-Vargas, Javier De-Moreta-Llovet, and Mario Gonzalez-Rodriguez.  Empowering education with generative artificial intelligence tools: Approach with an instructional design matrix.  _Sustainability_ , 15(15):11524, 2023.
  * Wang and Utama [2023] Hsi Yeh Wang and Surapong Utama.  Investigating the generative-ai evaluation methods and correlation with fashion designers.  In _2023 7th International Conference on Information Technology (InCIT)_ , pages 508–513. IEEE, 2023.
  * Moreno-Sánchez et al. [2023] Daniel Moreno-Sánchez, Daniel Moreno-Nieto, Pedro Burgos-Pintos, and Sergio I Molina.  Artificial intelligence in the design workflow. review of tools with special focus on additive manufacturing.  In _International conference on The Digital Transformation in the Graphic Engineering_ , pages 468–475. Springer, 2023.
  * Rott [1990] Nikolaus Rott.  Note on the history of the reynolds number.  _Annual review of fluid mechanics_ , 22(1):1–12, 1990.
  * Johnson and Patel [1999] TA Johnson and VC Patel.  Flow past a sphere up to a reynolds number of 300.  _Journal of Fluid Mechanics_ , 378:19–70, 1999.
  * Purcell [2014] Edward M Purcell.  Life at low reynolds number.  In _Physics and our world: reissue of the proceedings of a symposium in honor of Victor F Weisskopf_ , pages 47–67. World Scientific, 2014.
  * Smits et al. [2011] Alexander J Smits, Beverley J McKeon, and Ivan Marusic.  High–reynolds number wall turbulence.  _Annual Review of Fluid Mechanics_ , 43:353–375, 2011.
  * Drela [1989] Mark Drela.  Xfoil: An analysis and design system for low reynolds number airfoils.  In _Low Reynolds Number Aerodynamics: Proceedings of the Conference Notre Dame, Indiana, USA, 5–7 June 1989_ , pages 1–12. Springer, 1989.
  * Kashefi et al. [2021] Ali Kashefi, Davis Rempe, and Leonidas J Guibas.  A point-cloud deep learning framework for prediction of fluid flow fields on irregular geometries.  _Physics of Fluids_ , 33(2), 2021.
  * Kashefi [2020c] Ali Kashefi.  A coarse-grid incremental pressure projection method for accelerating low reynolds number incompressible flow simulations.  _Iran Journal of Computer Science_ , 3(1):13–23, 2020c.
  * Von Kármán [2004] Theodore Von Kármán.  _Aerodynamics: selected topics in the light of their historical development_.  Courier Corporation, 2004.
  * Okajima [1982] Atsushi Okajima.  Strouhal numbers of rectangular cylinders.  _Journal of Fluid mechanics_ , 123:379–398, 1982.
  * Cochran [1934] WG Cochran.  The flow due to a rotating disc.  In _Mathematical proceedings of the Cambridge philosophical society_ , volume 30, pages 365–375. Cambridge University Press, 1934.
  * Kármán [1921] Th V Kármán.  Über laminare und turbulente reibung.  _ZAMM-Journal of Applied Mathematics and Mechanics/Zeitschrift für Angewandte Mathematik und Mechanik_ , 1(4):233–252, 1921.
  * Munson et al. [2013] B.R. Munson, T.H. Okiishi, W.W. Huebsch, and A.P. Rothmayer.  _Fundamentals of Fluid Mechanics_.  Wiley, 2013.  ISBN 9781118116135.  URL https://books.google.com/books?id=R17cthBdckYC.
  * Hornung et al. [1995] Hans G Hornung, Christian Willert, and Stewart Turner.  The flow field downstream of a hydraulic jump.  _Journal of Fluid Mechanics_ , 287:299–316, 1995.
  * Baumgarten and Fritts [2014] Gerd Baumgarten and David C Fritts.  Quantifying kelvin-helmholtz instability dynamics observed in noctilucent clouds: 1. methods and observations.  _Journal of Geophysical Research: Atmospheres_ , 119(15):9324–9337, 2014.
  * Davis and Chyu [1966] RT Davis and WJ Chyu.  Laminar flow past a sphere at high mach number.  _Journal of Fluid Mechanics_ , 24(3):481–495, 1966.
  * Howe [1979] MS Howe.  Attenuation of sound in a low mach number nozzle flow.  _Journal of Fluid Mechanics_ , 91(2):209–229, 1979.
  * Luo et al. [2020] Tengfei Luo, Jianchun Wang, Chenyue Xie, Minping Wan, and Shiyi Chen.  Effects of compressibility and atwood number on the single-mode rayleigh-taylor instability.  _Physics of fluids_ , 32(1), 2020.
  * Ker [1988] Robert M Ker.  Simulation of rayleigh-taylor flows using vortex blobs.  _Journal of Computational Physics_ , 76(1):48–84, 1988.
  * Andrews and Dalziel [2010] Malcolm J Andrews and Stuart B Dalziel.  Small atwood number rayleigh–taylor experiments.  _Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences_ , 368(1916):1663–1679, 2010.
  * Abbott et al. [1945] Ira H Abbott, Albert E Von Doenhoff, and Louis Stivers Jr.  Summary of airfoil data.  Technical report, 1945.
  * Burzynski et al. [2020] David A Burzynski, Ilia V Roisman, and Stephan E Bansmer.  On the splashing of high-speed drops impacting a dry surface.  _Journal of Fluid Mechanics_ , 892:A2, 2020.
  * Liu et al. [2023a] Haotian Liu, Chunyuan Li, Yuheng Li, and Yong Jae Lee.  Improved baselines with visual instruction tuning.  _arXiv preprint arXiv:2310.03744_ , 2023a.
  * Lin et al. [2023] Bin Lin, Bin Zhu, Yang Ye, Munan Ning, Peng Jin, and Li Yuan.  Video-llava: Learning united visual representation by alignment before projection.  _arXiv preprint arXiv:2311.10122_ , 2023.
  * Li et al. [2023] C Li, C Wong, S Zhang, et al.  Llava-med: training a large language-and-vision assistant for biomedicine in one day. arxiv.  _arXiv preprint arXiv:2306.00890_ , 2023.
  * Liu et al. [2023b] Shilong Liu, Hao Cheng, Haotian Liu, Hao Zhang, Feng Li, Tianhe Ren, Xueyan Zou, Jianwei Yang, Hang Su, Jun Zhu, et al.  Llava-plus: Learning to use tools for creating multimodal agents.  _arXiv preprint arXiv:2311.05437_ , 2023b.
  * Gao et al. [2023] Jiahui Gao, Renjie Pi, Jipeng Zhang, Jiacheng Ye, Wanjun Zhong, Yufei Wang, Lanqing Hong, Jianhua Han, Hang Xu, Zhenguo Li, et al.  G-llava: Solving geometric problem with multi-modal large language model.  _arXiv preprint arXiv:2312.11370_ , 2023.
  * Ren et al. [2024] Jie Ren, Han Xu, Pengfei He, Yingqian Cui, Shenglai Zeng, Jiankun Zhang, Hongzhi Wen, Jiayuan Ding, Hui Liu, Yi Chang, et al.  Copyright protection in generative ai: A technical perspective.  _arXiv preprint arXiv:2402.02333_ , 2024.
  * Zhu et al. [2023] Deyao Zhu, Jun Chen, Kilichbek Haydarov, Xiaoqian Shen, Wenxuan Zhang, and Mohamed Elhoseiny.  Chatgpt asks, blip-2 answers: Automatic questioning towards enriched visual descriptions.  _arXiv preprint arXiv:2303.06594_ , 2023.
  * Johnson et al. [2023] OV Johnson, O Mohammed Alyasiri, D Akhtom, and OE Johnson.  Image analysis through the lens of chatgpt-4.  _Journal of Applied Artificial Intelligence_ , 4(2), 2023.
  * Steer et al. [2021] James N Steer, O Kimmoun, and F Dias.  Breaking-wave induced pressure and acceleration on a clifftop boulder.  _Journal of Fluid Mechanics_ , 929:R1, 2021.
  * Brandner et al. [2022] Paul A Brandner, James A Venning, and Bryce W Pearce.  Nucleation effects on cavitation about a sphere.  _Journal of Fluid Mechanics_ , 946, 2022.
  * Zhang et al. [2023] Hang Zhang, Xin Li, and Lidong Bing.  Video-llama: An instruction-tuned audio-visual language model for video understanding.  _arXiv preprint arXiv:2306.02858_ , 2023.
  * Meskó and Topol [2023] Bertalan Meskó and Eric J Topol.  The imperative for regulatory oversight of large language models (or generative ai) in healthcare.  _NPJ digital medicine_ , 6(1):120, 2023.
  * Megahed et al. [2024] Fadel M Megahed, Ying-Ju Chen, Joshua A Ferris, Sven Knoth, and L Allison Jones-Farmer.  How generative ai models such as chatgpt can be (mis) used in spc practice, education, and research? an exploratory study.  _Quality Engineering_ , 36(2):287–315, 2024.
  * Theis et al. [2015] Lucas Theis, Aäron van den Oord, and Matthias Bethge.  A note on the evaluation of generative models.  _arXiv preprint arXiv:1511.01844_ , 2015.
  * Yang and Lerch [2020] Li-Chia Yang and Alexander Lerch.  On the evaluation of generative models in music.  _Neural Computing and Applications_ , 32(9):4773–4784, 2020.
  * Xue et al. [2020] Tianju Xue, Thomas J Wallin, Yigit Menguc, Sigrid Adriaenssens, and Maurizio Chiaramonte.  Machine learning generative models for automatic design of multi-material 3d printed composite solids.  _Extreme Mechanics Letters_ , 41:100992, 2020.
  * Regenwetter et al. [2022] Lyle Regenwetter, Amin Heyrani Nobari, and Faez Ahmed.  Deep generative models in engineering design: A review.  _Journal of Mechanical Design_ , 144(7):071704, 2022.
  * Kashefi and Mukerji [2022] Ali Kashefi and Tapan Mukerji.  Physics-informed pointnet: A deep learning solver for steady-state incompressible flows and thermal fields on multiple sets of irregular geometries.  _Journal of Computational Physics_ , 468:111510, 2022.
  * Kashefi et al. [2023] Ali Kashefi, Leonidas J Guibas, and Tapan Mukerji.  Physics-informed pointnet: On how many irregular geometries can it solve an inverse problem simultaneously? application to linear elasticity.  _Journal of Machine Learning for Modeling and Computing_ , 4(4), 2023.
  * Pal et al. [2024] Soumen Pal, Manojit Bhattacharya, Sang-Soo Lee, and Chiranjib Chakraborty.  A domain-specific next-generation large language model (llm) or chatgpt is required for biomedical engineering and research.  _Annals of Biomedical Engineering_ , 52(3):451–454, 2024.
  * Ni and Buehler [2024] Bo Ni and Markus J Buehler.  Mechagents: Large language model multi-agent collaborations can solve mechanics problems, generate new data, and integrate knowledge.  _Extreme Mechanics Letters_ , page 102131, 2024.
  * Polverini and Gregorcic [2024] Giulia Polverini and Bor Gregorcic.  How understanding large language models can inform the use of chatgpt in physics education.  _European Journal of Physics_ , 45(2):025701, 2024.
  * Luu and Buehler [2024] Rachel K Luu and Markus J Buehler.  Bioinspiredllm: Conversational large language model for the mechanics of biological and bio-inspired materials.  _Advanced Science_ , 11(10):2306724, 2024.
  * Li et al. [2024b] Bai Li, Xinyuan Li, Yaodong Cui, Xuepeng Bian, Siyu Teng, Siji Ma, Lili Fan, Yonglin Tian, Fei-Yue Wang, et al.  Integrating large language models and metaverse in autonomous racing: An education-oriented perspective.  _IEEE Transactions on Intelligent Vehicles_ , 2024b.