# Legend at ArAIEval Shared Task: Persuasion Technique Detection using a
Language-Agnostic Text Representation Model

Olumide E. Ojo1,5,a, Olaronke O. Adebanji1,b, Hiram Calvo1,c, Damian O.
Dieke3,d,
Olumuyiwa E. Ojo4,e, Seye E. Akinsanya2,f, Tolulope O. Abiola2,g, Anna
Feldman5,h
1Instituto Politécnico Nacional, Centro de Investigación en Computación, CDMX,
Mexico
2Federal University Oye-Ekiti, Nigeria; 3Caritas University, Nigeria; 4Lead
City University, Nigeria; 5Montclair State University, USA
{aolumideoea, bolaronke.oluwayemisi, chiramcalvo, ddieketobesky, emuyeskin,
fakinsanyaseye<EMAIL_ADDRESS>
<EMAIL_ADDRESS>
###### Abstract

In this paper, we share our best performing submission to the Arabic AI Tasks
Evaluation Challenge (ArAIEval) at ArabicNLP 2023. Our focus was on Task 1,
which involves identifying persuasion techniques in excerpts from tweets and
news articles. The persuasion technique in Arabic texts was detected using a
training loop with XLM-RoBERTa, a language-agnostic text representation model.
This approach proved to be potent, leveraging fine-tuning of a multilingual
language model. In our evaluation of the test set, we achieved a micro F1
score of 0.64 for subtask A of the competition.

##  1 Introduction

In an era defined by the rapid dissemination of information through digital
channels, the task of recognizing persuasion techniques in text is now more
crucial than ever (Maram et al., 2023a; Hossain et al., 2021; Gupta et al.,
2021; Sadeghi et al., 2023; Alam et al., 2022; Abujaber et al., 2021). The
advent of the Internet and social media has created new avenues for influence
and manipulation (Dholakia et al., 2023; Ruffo et al., 2023; Botes, 2023).
Although these technological advances have undoubtedly given people
unparalleled access to information and a platform to express their thoughts,
they have also introduced new avenues for persuasion, influence, and even
propaganda. At the heart of this shift in our way of life is the fundamental
challenge of distinguishing between genuinely informative and impartial
content and content subtly crafted to promote a specific agenda or ideology. A
critical component of the fight against spreading misinformation is the
development of tools and resources in NLP that can detect persuasion technique
in news articles and posts on social media.

Arabic language is among the most spoken languages in the world (Ghazzawi,
1992). The Arabic speaking world stands out in importance due to its intricate
mix of language, culture, and geography. The diversity of linguistic
expressions in Arabic extends beyond the spoken word and permeates every
aspect of life, including digital text. Arabic connects a vast and diverse
population of native speakers and foreigners with its rich heritage and
multiple dialects. Its influence extends over a wide territory, from Arab
nations in the southern part of the Arabian Peninsula, to Asia, and to the
Maghreb in North Africa and the heart of the Arabian Peninsula (Huafeng et
al., 2019). In this digital age, the importance and extensive use of Arabic in
various forms reflects the profound impact of technology on this linguistic
community. It has provided a platform for Arabic speakers around the world to
engage in dialogue, share ideas, and express their thoughts in a global
context. The diverse Arab-speaking populations foster a rich and dynamic
environment where individuals can connect, collaborate, and debate issues of
global significance. However, the proliferation of digital media in Arabic
also presents challenges. Digital media have become a fertile ground for the
dissemination of persuasive content, including propaganda, misinformation, and
various forms of manipulation (Aleroud et al., 2023; Abd Elaziz et al., 2023).
The use of technology in preserving the integrity of the Arabic language and
ensuring responsible use of digital media is of utmost importance.

In today’s world, we are surrounded by information, especially on the Internet
and social media. Text classification can serve as a foundational step for the
detection of the persuasion technique in text on social media and the
Internet. These texts can be classified according to their emotional tone
using sentiment analysis techniques (Nikolaidis et al., 2023; Ojo et al.,
2022b, 2021, 2020, 2023, a; Piskorski et al., 2023; Hromadka et al., 2023).
Persuasion techniques can be tricky to spot because they come in many forms,
such as stories, logical arguments, or even subtle language tricks to sway our
thinking. These techniques are powerful and are not always used for good
reasons. To deal with this, researchers and experts are working on ways to
detect when someone is trying to persuade people through text. In this way, we
will be able to recognize when we are influenced and when people are spreading
false or misleading information, which can be harmful. In this paper, we
develop a methodology to automatically identify and analyze persuasion
techniques in text using the XLM-RoBERTa model. Using the power of NLP, we can
harness the capabilities of state-of-the-art models and unravel the persuasion
techniques embedded within Arabic text, contributing to both media ethics and
the combating of misinformation. The intricacies of persuasion technique
detection in Arabic are discussed in detail, along with the possibility of
applying this knowledge across different languages.

##  2 Related Work

A significant amount of research has been conducted on the detection of
persuasion techniques in text (Maram et al., 2023a; Modzelewski et al., 2023;
Hossain et al., 2021; Sadeghi et al., 2023; Abujaber et al., 2021).
Researchers have explored binary and multilabel approaches to detecting
persuasion techniques.

In their article, the authors in (Modzelewski et al., 2023) focused on
detecting genres and persuasion techniques in multiple languages using various
data augmentation techniques to enhance their models. For genre detection,
they created synthetic texts using the GPT-3 Davinci language model, while for
persuasion technique detection, they augmented the dataset using text
translation with the DeepL translator. Their fine-tuned models achieved top
ten rankings in all languages, demonstrating the effectiveness of their
approach. They also excelled in genre detection, securing top positions in
Spanish, German, and Italian. They presented a single multilingual system
using the RoBERTa model to classify online news genres and improved this
system by adding texts generated by the GPT3-Davinci model to the training
dataset.

(Maram et al., 2023b) addressed misinformation in mainstream and social media
and the challenges faced by manual detection and verification efforts by
journalists and fact checkers in the SemEval-2023 task Piskorski et al.
(2023). The task included three subtasks, six languages, and three surprise
test languages, totaling 27 different test scenarios. The authors successfully
submitted entries for all 27 test setups and the official results placed their
system among the top three for 10 of these setups. They fine-tuned transformer
models in the multiclass and multilabel classification settings, experimenting
with both monolingual and multilingual pre-trained models, as well as data
augmentation. Their multilingual model based on XLM-RoBERTa demonstrated
superior performance in all tasks, even for languages not seen during
training.

The most effective solution in the detection of persuasion techniques for
Subtask 3 of SemEval 2023 Task 3 by (Hromadka et al., 2023) delivered
promising performance, with micro-F1 scores ranging from 36 to 55% for
languages seen during training and 26 to 45% for languages unseen. Given the
multilingual nature of the data and the presence of 23 labels (resulting in
limited labeled data for some language-label combinations), the authors chose
to fine-tune pre-trained transformer-based language models. Through extensive
experimentation, they identified the optimal configuration, featuring a large
multilingual model (XLM-RoBERTa) trained on all input data, with carefully
calibrated confidence thresholds for known and surprise languages separately.
Their final system demonstrated superior performance, ranking first in six of
nine languages, including two surprise languages, and achieving highly
competitive results in the remaining three languages.

The experiments of (Nikolaidis et al., 2023) focused on the detection of
persuasion techniques in online news articles in Polish and Russian. These
experiments used a taxonomy comprising 23 distinct persuasion techniques.
Persuasion techniques were evaluated in several ways, including the
granularity of the classification (coarse with six labels or fine with 23
labels) and the level of location of the labels (subword, sentence,
paragraph). The study compared the performance of state-of-the-art
transformer-based models trained both monolingually and multilingually. The
findings indicate that multilingual models generally outperform monolingual
models in various evaluation scenarios. However, due to the complexity of the
task, there remains substantial room for improvement in the field of
persuasion technique detection within online news articles.

Inspired by (Maram et al., 2023b; Hromadka et al., 2023), our research focus
is to determine whether a multi-genre snippet (tweets and news paragraphs of
news articles) contains a persuasion technique or not. This is a binary
classification task, and we are categorizing Arabic text either as containing
a persuasion technique or as lacking persuasion technique. Our approach
involves fine-tuning a large pre-trained language model based on transformers.
We conducted experiments with different language models and concluded with
XLM-RoBERTa due to its superior performance. Furthermore, we fine-tuned our
system by tweaking hyperparameters and conducting multiple iterations. This
process involved calculating cross-entropy loss, performing backpropagation,
and updating the model’s weights.

##  3 Persuation Technique Detection

###  3.1 Dataset Analysis

Datasets provided by the organizers consist of a diverse collection of Arabic
text samples, each associated with a label. These texts have been carefully
selected to represent where persuasion techniques are present or not. The
dataset were labeled as ’true’ or ’false’, where the true class represents
texts where persuasion techniques are used to influence the reader’s opinion,
and the false class consists of texts that do not use persuasion techniques.
The method involves binary classification to determine the presence of a
persuasion technique within the document.

The dataset comprises 2,427 samples in the training set and 503 in the test
set. Within the training data, there is an imbalance in the label
distribution, with 1,918 samples labeled as "true" and 509 labeled as "false".
An example of text that represents the persuasion technique in the dataset is
shown in Figure 1.

Figure 1: Persuation technique in the Arabic text

###  3.2 Application of XLM-RoBERTa

Leveraging the Hugging Face Transformers library, we prepared and formatted
the data so that it could be seamlessly incorporated into our model. In line
with the methodology outlined in Section 4, we designed a custom model
architecture and then proceeded to encode and load the data for further
processing. During training, we optimized the model’s classification head to
minimize cross-entropy loss, and predictions are made on unseen text, followed
by post-processing. This approach demonstrates the adaptability and
effectiveness of XLM-RoBERTa in diverse linguistic contexts, offering
practical solutions to automate the detection of persuasion techniques across
languages.

##  4 System Setup and Experiments

###  4.1 Training Strategy

Our training strategy involves fine-tuning the XLM-RoBERTa model using the
provided dataset. To optimize the performance of the model, we incorporate
several key components and hyperparameters, which are summarized in Table 1.

Hyperparameter | Value
---|---
Learning rate | $5\times 10^{-5}$
Batch size | 16
Epochs | 6
Optimizer | ADAM
Early stopping | Cross-entropy loss
Learning rate scheduler | StepLR (factor=0.85, step size=2)
Table 1: Model Hyperparameters

###  4.2 Model Fine-Tuning

During model fine-tuning, we added a classification layer at the end of the
pre-trained XLM-RoBERTa model. This additional layer allows the model to
perform the specific classification task required. To prevent overfitting, a
dropout layer was incorporated.

###  4.3 Class Weights

To address the class imbalance in the dataset, we adjusted the learning
process using class weights. This ensures that the model effectively learns
from all classes and is not biased by data imbalance.

###  4.4 Evaluation Metric

The model’s performance was evaluated using the micro-score F1, the default
metric for this subtask. This metric provides a comprehensive measure of the
model’s classification performance.

###  4.5 Training Process

The training process involved conducting a total of 6 epochs, where each epoch
represents a complete pass through the entire training dataset. To avoid
overfitting, early stopping was employed on the basis of cross-entropy loss.

###  4.6 Learning Rate Scheduler

A learning rate scheduler was implemented to dynamically adjust the learning
rate during training. Specifically, we used a StepLR scheduler with a
reduction factor of 0.85 applied every 2 epochs. This scheduling strategy
contributes to training stability and controlled convergence.

###  4.7 Optimization Process

To initiate the optimization process, we reset the gradients (setting them to
zero). Subsequently, we conducted backpropagation to calculate gradients for
all model parameters and, lastly, update the model’s parameters using the
computed gradients.

Our approach leverages these components and hyperparameters to fine-tune the
model effectively, ensuring robust and controlled training.

##  5 Results

The evolution of pre-trained language models has ushered in significant
advancements across different NLP tasks. In this section, we present the
results of our experiments on persuasion technique detection in Arabic text.
Our findings revealed the versatility of XLM-RoBERTa in effectively handling
multilingual data. We evaluated the model using the micro-F1 score and an
overview of the results achieved by our model on the dataset is shown in Table
2.

Model | F1-Score
---|---
Baseline model | 0.4771
XLM-RoBERTa | 0.6402
Table 2: Performance Comparison of Models for Persuasion Technique Detection
in Arabic Text

From Table 1, our findings reveal the effectiveness of XLM-RoBERTa in
identifying persuasion techniques within the Arabic text. The model’s pre-
trained knowledge, combined with its cross-lingual capabilities, makes it a
promising tool for similar tasks in other languages as well. As Arabic is a
morphologically rich language with various dialects, the success of XLM-
RoBERTa in this task is a testament to its robustness and versatility.

##  6 Conclusion

The application of XLM-RoBERTa, a language-agnostic text representation model,
for the detection of the persuasion technique in Arabic text illustrates the
growing potential of cross-lingual models in specialized NLP tasks. Arabic,
with its rich morphology and diverse dialects, presents unique challenges for
text analysis. Our proposed model has the ability to capture the underlying
structure and semantics of persuasion technique in text, regardless of
language. The results obtained in our analysis demonstrate that XLM-RoBERTa
can adapt effectively and perform well on such intricate tasks, even in
languages that are structurally different from the ones they were originally
trained on. This not only underscores the versatility of XLM-RoBERTa but also
sets a promising direction for further research in detecting persuasion
techniques across various languages. In future work, we plan to accommodate
more languages in the dataset, and fine-tune other multilingual models for
this task.

## Ethics Statement

We acknowledge the influence that scientific research can have on society and
recognize our responsibility to ensure its positive impact. Our research is
carried out with the aim of addressing real-world challenges, promoting well-
being, and improving quality of life. We actively seek feedback and input from
those affected by our research. In the event that our research may have
unintended negative impacts, we are committed to addressing and rectifying
those issues promptly.

## Acknowledgments

This work was done with partial support from the Mexican Government through
the grant A1-S-47854 of CONACYT, Mexico, grants 20232138, 20230140, 20232080
and 20231567 of the Secretaría de Investigación y Posgrado of the Instituto
Politécnico Nacional, Mexico. The authors thank CONACYT for the computing
resources brought to them through the Plataforma de Aprendizaje Profundo para
Tecnologías del Lenguaje of the Laboratorio de Supercómputo of the INAOE,
Mexico and acknowledge the support of Microsoft through the Microsoft Latin
America PhD Award.

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# Machine learning accelerated discovery of corrosion-resistant high-entropy
alloys

Cheng Zeng${}^{\text{*},{\ddagger}}$ The Roux Institute, Northeastern
University, Portland, Maine, 04101, United States.
‡ The Experiential AI Institute, Northeastern University, Boston,
Massachusetts, 02115, United States
* Corresponding authors: Email<EMAIL_ADDRESS>and<EMAIL_ADDRESS>Tel: +1 401-396-6668 and +1 781-605-8671
Andrew Neils  The Roux Institute, Northeastern University, Portland, Maine,
04101, United States.
‡ The Experiential AI Institute, Northeastern University, Boston,
Massachusetts, 02115, United States
* Corresponding authors: Email<EMAIL_ADDRESS>and<EMAIL_ADDRESS>Tel: +1 401-396-6668 and +1 781-605-8671
Jack Lesko  The Roux Institute, Northeastern University, Portland, Maine,
04101, United States.
‡ The Experiential AI Institute, Northeastern University, Boston,
Massachusetts, 02115, United States
* Corresponding authors: Email<EMAIL_ADDRESS>and<EMAIL_ADDRESS>Tel: +1 401-396-6668 and +1 781-605-8671
Nathan Post${}^{\text{*}}$ The Roux Institute, Northeastern University,
Portland, Maine, 04101, United States.
‡ The Experiential AI Institute, Northeastern University, Boston,
Massachusetts, 02115, United States
* Corresponding authors: Email<EMAIL_ADDRESS>and<EMAIL_ADDRESS>Tel: +1 401-396-6668 and +1 781-605-8671

###### Abstract

Corrosion has a wide impact on society, causing catastrophic damage to
structurally engineered components. An emerging class of corrosion-resistant
materials are high-entropy alloys. However, high-entropy alloys live in high-
dimensional composition and configuration space, making materials designs via
experimental trial-and-error or brute-force ab initio calculations almost
impossible. Here we develop a physics-informed machine-learning framework to
identify corrosion-resistant high-entropy alloys. Three metrics are used to
evaluate the corrosion resistance, including single-phase formability, surface
energy and the compactness of oxide films formed on an alloy surface evaluated
by Pilling-Bedworth ratios. We used random forest models to predict the
single-phase formability, trained on an experimental dataset. Machine learning
inter-atomic potentials were employed to calculate surface energies and
Pilling-Bedworth ratios, which are trained on first-principles data fast
sampled using embedded atom models. A combination of random forest models and
high-fidelity machine learning potentials represents the first of its kind to
relate chemical compositions to corrosion resistance of high-entropy alloys,
paving the way for automatic design of materials with superior corrosion
protection. This framework was demonstrated on AlCrFeCoNi high-entropy alloys
and we identified composition regions with high corrosion resistance from a
wide range of compositions. Machine learning predicted lattice constants and
surface energies are consistent with values by first-principles calculations.
The predicted single-phase formability and corrosion-resistant compositions of
AlCrFeCoNi agree well with experiments. This framework provides a
computationally efficient approach to navigate high-dimensional composition
space of high-entropy alloys. It is general in its application and applicable
to other complex materials, enabling high-throughput screening of material
candidates and potentially accelerating the iteration of integrated
computational materials engineering.

Keywords: High-entropy alloy, Corrosion protection, Machine learning
potential, Random forest classification

Graphical abstract:

##  1 Introduction

High-entropy alloys are generally defined as alloys comprising no less than
four elements and the percentage of each principal element is between 5 at.%
and 35 at.%. The high-entropy concept was coined by Cantor [1] and Yeh [2] for
equiatomic alloys with no less than five elements in 2004 almost the same
time. The definition has been slightly extended to non-equimolar alloys with
no less than four principal elements. This new class of materials has
attracted increasing attention, found to display superior materials
performance for mechanical properties [3, 4, 5, 6, 7], radiation resistance
[8, 9] and corrosion resistance [10, 11, 12]. The high entropy of mixing
usually leads to the formation of a disordered single phase for high-entropy
alloys, such as face-centered cubic (FCC), body-centered cubic (BCC) and
hexagonal closely-packed structures (HCP) [13, 14]. The homogeneous single
phase improves passivity. In addition, high-entropy alloys can consist of
elements with high passivation potency such as nickel, chromium, aluminum and
titanium, leading to high pitting corrosion resistance.

Conventional corrosion-resistant alloys are mostly found by serendipity.
Advances in physical theories, computational hardware and algorithms allow for
rapid screening of candidate materials, paving the way for integrated
computational materials engineering which aims to demystify the linkage
between process, structure, property and performance. However, computational
screening of corrosion-resistant alloys is challenging in that many factors
can influence corrosion performance, including environmental conditions,
chemical compositions and microstructures. Moreover, fundamental understanding
of corrosion and various corrosion types adds more complexity to the material
design. Recent works have been focused on building reliable databases for
corrosion informatics, identifying reliable descriptors for corrosion
performance and understanding the corrosion kinetics with multi-physics
simulations [15, 16, 17]. Nyby et al. compiled a database for four types of
alloys with an emphasis on six metrics used to describe their localized
pitting corrosion [16]. Diao et al. collected a dataset for low-alloy steel
and built machine learning models to predict their corrosion rate [18]. Roy et
al. used machine learning algorithms to select the top three descriptors for
prediction of the corrosion rates, including pH of the medium, halide
concentration and composition of elements with the minimum reduction potential
[19]. Taylor et al. identified a number of corrosion descriptors, such as
cohesive energies, oxide formation energies and surface enrichment of passive
elements, and related those descriptors to corrosion resistance with respect
to surface passivation, dissolution and microstructure control [15]. Ke and
Taylor reviewed the role of density functional theory (DFT) in modeling
corrosion, and they pointed out corrosion metrics accessible by DFT, including
oxygen and chloride adsorption energy, dissolution potential and surface
energy [20]. Other computational methods based on peridynamics and phase-field
modeling are often used to study the evolution of pitting corrosion [17, 21].

Unfortunately, the complexity of corrosion process makes it almost impossible
to relate chemical compositions and microstructures of alloys directly to the
corrosion performance. The vast composition and microstructure space of high-
entropy alloys create complexity for the materials design problem. A
workaround is multi-objective optimization based on empirical rules, which
allows for screening material candidates with relative superior corrosion
resistance. While some data-driven approaches and first-principles
calculations exist to identify corrosion descriptors, those data-driven
methods in nature lack physical insights and first-principles calculations are
costly computationally. A physically meaningful and efficient approach to
relating compositions with corrosion performance is still lacking.

The objective of this work is to bridge the technical gap for locating high-
entropy alloys with potential high corrosion resistance in the high-
dimensional composition space, in particular for pitting corrosion. We focused
on pitting corrosion because the rate of localized pitting corrosion can be
faster than uniform corrosion by orders of magnitude, hence pitting corrosion
is more critical in applications where it exists [16]. Pitting corrosion
normally occurs under non-equilibrium conditions and the pitting event may be
subject to inherent randomness, making it almost impossible to be predicted
exactly [22, 23]. A complete picture of pitting corrosion requires multi-scale
and multi-physics simulations together with stochastic modeling to understand
the formation of passive film, passive film breakdown and pit growth stability
[24], which to the best of our knowledge are not available. Pitting corrosion
resistance is empirically associated with the ability of alloys to form a
passive film, protectiveness of the passive film and pitting growth rate when
the passive film breaks down. Although it is challenging to predict the exact
pitting process, it is well-acknowledged that a more compact passive film and
a slower pit growth rate make the structures less susceptible to pitting
corrosion [24]. In this work, we chose three corrosion metrics considered to
be influential to pitting corrosion, including single phase formability,
Pilling-Bedworth ratio of passive elements, surface energy. All three metrics
used here are either rationalized in theory or validated in experiments.
Finding single-phase solid solutions is a classic strategy for the design of
corrosion-resistant alloys since single-phase alloys tend to form more
homogeneous and compact passive films [12]. Pilling-Bedworth ratio is a well-
acknowledged metric for evaluation of the compactness of oxide films formed on
an alloy surface as it accounts for the volume change when a passive film
forms on a metal surface [25, 26]. Surface energies were first used by Song et
al to describe the experimental relationship between surface orientation and
corrosion resistance, and it was found that a more closely packed surface with
a lower surface energy tend to exhibit superior corrosion resistance [27]. In
addition, surface energies have often been used in atomistic simulations to
gain insights into corrosion performance of alloys [15, 20]. Moreover, one may
also need to consider the key role of chloride ions in pitting corrosion. A
more comprehensive optimization of corrosion-resistant high-entropy alloys may
directly model the chloride effects via simulating the adsorption of chloride
on a metal surface or on a passive film surface, which can affect the
breakdown of passive films or the fast growth of the initiated pit [28, 15,
20]. More sophisticated models study the fast diffusion of chloride ions
through the defects in the passive films and the accumulation of those ions at
the interface between metal and oxides [29, 30]. Despite not modeling the
chloride effect explicitly in this work, it is arguable that single-phase
structures are more corrosion resistant in a salt solution with chloride ions
because single phase structures tend to form a homogeneous passive film which
will provide fewer fast diffusion channels compared to a heterogeneous passive
film. Besides, lower surface energies are more likely to show a weaker binding
between metal and chloride ions at the metal/oxide interface when a pit is
initialized [15]. A physics-informed machine learning (ML) framework was then
introduced to quantify the three corrosion metrics for a wide range of
compositions of high-entropy alloys. Details of theories and how to calculate
the three corrosion metrics will be elaborated in the subsequent section. We
tested this framework for AlCrFeCoNi high-entropy alloys by studying the three
corrosion metrics as a function of compositions of high-entropy alloys, based
on which compositions with high corrosion resistance will be identified and
compared to experiments. AlCrFeCoNi high-entropy alloys were considered
because they belong to an emerging class of materials with superior mechanical
properties and corrosion resistance [31, 10].

##  2 Theories and Methods

The aim of this work is to develop machine learning methods to quantify three
corrosion metrics for high-entropy alloys. There are two types of machine
learning models involved in the prediction of the three metrics. One is a
random forest model trained on an experimental dataset where the inputs are
the chemical formulas and the output is a boolean to show whether a single-
phase structure is formed or not. The other machine learning model is a
machine learning potential trained on first-principles data where the inputs
are atomic structures and the outputs are potential energy and forces of the
structures obtained by first-principles calculations. The single-phase
formability is calculated by the random forest model, whereas Pilling-Bedworth
ratios and surface energies are computed by the machine learning potential.
The overall workflow of how to train these two types of machine learning
models is illustrated in Figure 1. In this section, we discuss the concept and
training of a state-of-the-art machine learning potential as well as how to
quantify each of the corrosion metrics by the trained machine learning models.

###  2.1 Machine learning potentials

Potential energy surfaces (PESs) represent one-to-one mappings between atomic
positions ($\\{R\\}$) and potential energy ($E$) of a material system. PESs
provide a plethora of information for material systems. For example, local
minima on PESs represent stable states and the minimum energy trajectory
connecting two local minima indicates a fundamental reaction pathway. The most
often used methods to build reliable PESs are DFT calculations. However,
standard DFT calculations are limited to hundreds of atoms due to the
formidable $\mathcal{O}(M^{2-3})$ scaling with system sizes (M), such as
numbers of basis sets, atoms or electrons [32]. It is thus computationally
prohibitive to sample all points on ab initio PESs. One should note that DFT,
first-principles and ab initio calculations are used interchangeably as they
have the same meaning in this work. In the past decade, fitting ab initio PESs
with machine learning (ML) algorithms have gained increasing momentum, and the
ML-fitted PESs are termed machine learning potentials (MLP). Most MLPs relies
on the nearsightedness principles [33], also known as all chemistry is local,
implying that the total potential energy of a system with $N$ atoms can be
largely decomposed into a linear sum of all atomic contributions and each
atomic contribution comes from the atom $i$ interacting with neighboring atoms
in a cutoff region, written as Eq. 1.

$E=E(\\{R\\})=\sum_{i=1}^{N}E_{i}=\sum_{i=1}^{N}E_{i}^{\mathrm{(local)}}$ (1)

Thanks to and only because of the nearsightedness principle, MLPs can be
trained with small-size first-principles data while allowing for reliable
predictions on much larger systems [34]. It should be noted that the
nearsightedness of first-principles calculations and machine learning
algorithms should be well aligned to strike a good balance between
computational efficiency and prediction accuracy [35]. A variety of ML
algorithms have proven effective in fitting ab initio PESs, such as neural
networks [34, 36], Gaussian process [37] and kernel ridge regression [38].
MLPs find applications in many fields, ranging from small molecules, to
nanoparticle alloy catalysts and extended systems [39, 40, 41]. In this work,
we employed a class of machine learning potentials termed moment tensor
potentials (MTPs) for the high-entropy alloys which were found to be superior
to other types of MLPs when tested on single-element systems by various
simulation tasks [42]. Readers should refer to the work of Shapeev for
implementation details of MTPs [43, 44]. MTPs were trained with systematically
generated and first-principles calculated training data for high-entropy
alloys AlCrFeCoNi, as outlined in the bottom row of Figure 1. We primed the
algorithm with FCC bulk and surface structures. For each of the initial
structures, atomic positions and lattice geometry are both optimized to find
the stable structure, the process of which is termed structure optimization,
also known as relaxation. The structure optimization used the embedded atom
method (EAM) developed by Farkas and Caro [45]. Starting with relaxed
structures and using EAM, we also sampled a diverse pool of atomic
configurations via molecular dynamics and Monte-Carlo simulations. The
molecular dynamics simulations were used to perturb atomic positions, whereas
the Monte-Carlo simulations were adopted to simulate exchange of two different
atoms. Electronic structure calculations were performed with an open Python
package Grid-based Projected Augmented Waves (GPAW) [46] to refine the energy
and forces for a part of the EAM-sampled configurations. Additionally, we
carried out first-principles calculations for simple bulk and surface
structures with numbers of elements ranging from one to five. Simple bulk
structures included special quasi-random structures generated using the tool
in the alloy theoretic automated toolkit (ATAT) for simple bulk structures
with more than two elements to best approximate a random solid solution [47,
48]. In total, 1569 first-principles structures were curated. We performed a
5-fold cross-validation on the generated structures. We then trained a MTP
upon the full dataset, and we used the MTP to carry out simulations needed to
calculate PBRs for the oxidation of Cr and surface energies of FCC(111)
facets. Atomic structures were created and manipulated with the Atomic
Simulation Environment (ASE) [49] and LAMMPS [50]. Computational settings of
MTPs and GPAW calculations and details of the training data can be found in
the SI. MTP enabled simulations to calculate relevant corrosion metrics are
also elaborated in the SI. Scripts and notebooks for atomistic modeling and
curation of training data will be supplied as a supporting dataset.

Figure 1: Workflow of machine learning accelerated discovery of corrosion-
resistant high-entropy alloys.

###  2.2 Single phase formability

It is crucial to form a homogeneous single phase for enhanced corrosion
protection because it enhances passivity and prevents the fast galvanic
corrosion. A physically rigorous approach to model single phase formation is
thermodynamic modeling carried out with CALPHAD. The reliability of CALPHAD
calculations is determined by the quality of experimental data as well as
relevant first-principles calculations [51]. Instead of thermodynamic
modeling, we used random forest models trained on an experimental dataset to
predict the probability of forming single phases for an arbitrary alloy
composition. The workflow for single phase formability is shown in the top row
of Figure 1. The experimental dataset was summarized by Yan et al. [52]. The
raw data in total has 1807 entries and it takes input as the chemical
compositions and output as the indicator for single phase formability. Single-
phase alloys are labeled as ’1’, whereas multiple-phase alloys are labeled as
’0’. It should be noted that phase formations are also dependent on the
manufacturing processes and thermal history. It is assumed that most alloys
found in this experimental dataset were processed with similar techniques and
environmental conditions, and the remaining exceptions represent outliers and
noise in the dataset, whose impact on the robustness of ML models will be
diminished by a cross-validation strategy due to the averaging effect. Each
input composition was converted to eight physical descriptors including atomic
size difference, mixing enthalpy, mixing entropy, Pauli electronegativity
difference, molar volume, bulk modulus, melting temperature and valence
electron concentration, as considered by Yan et al [52]. Next, random forest
models were trained to relate the eight descriptors to the single phase
formability. The trained random forest models are thus able to predict if
alloys will form single phase or multiple phases for a given composition. For
the purpose of model validation, we held out 20% of the entire dataset for
testing, which were used to examine the prediction accuracy of the final model
on some unseen dataset, hence avoiding overfitting. Five-fold cross-validation
was used on the remaining 80% dataset to tune the hyperparameters and to train
the random forest classifier. The entire dataset was shuffled before splitting
with a given random state to a test set and a data set for cross-validation,
and ten random states were used to estimate uncertainties due to data
splitting. One should however note that the model trained in this work may
differ from that by Yan et al as the constructed eight descriptors may be
different, and Yan et al only used five descriptors rather than all the eight
descriptors used in this work. We attempted to reproduce Yan’s results by
matching available model settings, and we found a prediction accuracy of 88%
on the test set, less accurate than that using all eight features. The code to
reproduce our computational experiment is included in a public github
repository. Details of each descriptor, exploratory data analysis (Figure
S1-S3), and hyperparameters of random forest models are included in the
supporting information (SI).

###  2.3 Pilling-Bedworth ratio

Pilling-Bedworth ratio (PBR) was used to describe the compactness and growth
stress of an oxidation process. It describes the volume change due to
oxidation on an alloy surface, which follows Eq. (2) with respect to the
oxidation of a metallic element B.

$PBR_{\textrm{B}}=\frac{\mathrm{Volume~{}of~{}a~{}mole~{}of~{}B_{x}O_{y}}}{\mathrm{Volume~{}of~{}x~{}moles~{}of~{}B~{}in~{}metal}}$
(2)

It is well accepted that when $PBR<1$, the formed oxide offers no protection
to the alloy surface. If $1\leq PBR\leq 2$, the oxide forms a passive layer
and prevents structural alloys from direct corrosion although some compression
stresses develop inside the oxide. When $PBR\gg 2$, the compression stresses
become significant, causing the breakdown of the oxides. This simple analysis
well explains that corrosion-resistant alloys typically contain Al, Zr, Ni,
Ti, Fe or Cr whose PBR values are larger than 1 and not much larger than 2
[53, 12, 54].

When it comes to the oxidation of alloys, one or more elements may oxidize and
form passive layers. Hence we need to identify elements that are
thermodynamically preferential for oxidation. We can then calculate the PBR of
the identified passive element by analyzing the volume change due to its
oxidation. Xu and Gao introduced methods to compute PBR for the oxidation of
alloys [25]. There are two possible cases for PBR values of alloys, depending
on the relative diffusion rate of the passive element in alloys versus that in
oxides. Generally the diffusion rate of passive elements within alloys are
much faster relative to the rate within oxides so that alloy compositions near
the surface can maintain a stoichiometry close to the original composition.
For example, the diffusion coefficient of Cr in CrCrFeMnNi high-entropy alloys
at 900 ∘C is about $10^{-12}$ cm2/s while self-diffusion of Cr in Cr2O3 has a
coefficient on the order of $10^{-21}$ to $10^{-17}$ cm2/s [55, 56]. We
recommend that readers consult the work of Xu and Gao [25] for calculation
details of PBR for oxidation of alloys. For our benchmark material system
AlCrFeCoNi, we examined the passivation of the Cr element. We chose to study
Cr oxides because experiments by Shi et al indicates that it is the more
compact Cr oxides that offer the major protection against pitting corrosion
than the more porous Al oxides/hydroxides when it comes to the passivation of
AlCrFeCoNi [57] although thermodynamic data favors the formation of Al oxides
over Cr oxides, as tabulated in Table S1 of SI. Therefore, we consider the
oxidation of Cr, which forms Cr2O3 with a mole weight of 102 g/mol and a
density of 5.22 g/cm3. The volume of Cr in the alloy was calculated using a
FCC crystal whose lattice parameters were obtained by machine learning
potentials.

###  2.4 Surface energy

Surface energies are calculated by the trained moment tensor potential. The
electrochemical dissolution rate $I_{A}$ of a metal ‘A’ with an exposed
crystal plane (h,k,l) at a temperature $T$ follows the relation:

$I_{A,(h,k,l)}\propto\exp\left(\frac{\alpha\gamma_{(h,k,l)}}{RT}\right)$ (3)

where R is the gas constant, $\gamma_{(h,k,l)}$ is the surface energy and
$\alpha$ is a transition coefficient to relate surface energy to dissolution
activation energy. Ramachandran and Nosonovsky found that a lower surface
energy leads to a more hydrophobic surface, and hydrophobic surfaces tend to
show higher corrosion resistance [58]. In this work, we used surface energy as
a metric to describe the trend of average dissolution of atoms on the
crystallographic plane FCC(111) of AlCrFeCoNi alloys with different
compositions. An FCC(111) facet wast used because of its high stability over
other types of facets. It is arguable that a higher surface energy is
associated with a higher average dissolution rate, resulting in faster pitting
growth, although a more rigorous treatment may need to take into account
sequential atom-by-atom dissolution on a metallic surface constrained by
broken passive films formed on top of it, which we elected not to consider for
the sake of simplicity. Surface energy of a facet reads as:

$\gamma=\frac{E_{\mathrm{slab}}-E_{\mathrm{bulk}}}{2A}$ (4)

where $E_{\mathrm{slab}}$ and $E_{\mathrm{bulk}}$ are respective potential
energies of the FCC(111) facet and bulk cell, and A is the exposed area of the
facet. The bulk cells used to calculate surface energies are of L12
structures, and the surface structures are the putative most stable structures
found by Markov chain Monte-Carlo (MCMC) simulations. All terms in Eq. 4 were
found by atomistic modeling using machine learning potentials. The details of
MCMC simulations are provided in the SI.

###  2.5 Mapping corrosion metrics with respect to Al and Cr compositions in
AlCrFeCoNi

We tested the above methods on predicting the three corrosion metrics for
AlCrFeCoNi high-entropy alloys. We varied the compositions of Al and Cr while
equalizing remaining Fe, Co and Ni compositions. For a given composition, its
single-phase formability was calculated by a random forest classifier and its
Pilling-Bedworth ratio and surface energy were quantified by the MTPs.
Therefore, we mapped the three corrosion metrics as a function of AlCrFeCoNi
compositions, based on which we can identify composition regions with desired
values for all corrosion metrics, which are potentially associated with
superior relative corrosion resistance. We changed Al compositions in the
range of 0–25 at.%, and Cr compositions in the range of 10–30 at.% (see Figure
3). The lower bound for the Cr composition was set as 10% because Cr is the
passive element, and a percolation model for passivation of alloys suggests
that the smallest amount of elements to enable passivation is around 10% [59].
In other words, an alloy only forms a continuous and protective passive film
with the passive element being of no less than 10 at.%. For single-phase
formability, an interval of 1% was used for both Al and Cr composition mesh
grids as the inference by the trained random forest classifier for each
composition took less than 1 second. For PBRCr, an interval of 5% was used to
find the lattice parameters of L12 bulk cells using MTPs. The lattice
parameters of MTP-relaxed structures were then fitted by a linear regression
as a function of Al and Cr compositions. The fitted function was used to
calculate lattice parameters for arbitrary Al and Cr compositions. The volume
of Cr will be used to calculate PBRCr. In terms of surface energies, a
composition interval of 5% was used to generate structures needed.

##  3 Results and discussion

###  3.1 ML prediction accuracy and transferability

ML models are often criticized for their poor transferability to data that are
not existent in the training data set. While issues with ML transferability
can be mitigated via a transfer learning approach where models are fine tuned
to assimilate new data [60], limitations in transferability often originate
from inaccessibility to a wide range of data and the way that the data are
represented and encoded in the machine learning models. As a result, it is of
great importance to evaluate ML model performance before we deploy the models.

####  3.1.1 Random forest classifier

The experimental dataset used to train the random forest classifier includes
in total 1807 entries. The 1807 data points were split to 80% and 20% for
cross-validation and test, respectively. Hence 361 data points were used for
testing, and ten different random states for the data splitting were used to
obtain the standard deviation of model prediction accuracy on the test set.
The random forest classifier gave a prediction accuracy of 89% on the test set
with a standard deviation of 1%. The best model with the highest accuracy on
the test set was chosen for subsequent inferences. We also studied the feature
importance using shapley values based on game theories [61]. Mixing entropy,
atomic size difference and melting temperature were identified as the top
three most important features, largely consistent with the work of Yan et al
[52]. More feature importance results can be found in Figure S4 of SI.

####  3.1.2 Moment tensor potentials

For the 5-fold cross-validation over the full 1569 structures, we observed 6.2
$\pm$ 1.6 meV/atom and 0.086 $\pm$ 0.016 eV/Å for respective energy and force
average absolute differences (numbers following ‘$\pm$’ represent the standard
deviations across different folds). The MTP trained on the full dataset gave
$\sim$5 meV/atom for the average absolute difference of energy and 0.058 eV/Å
for the average absolute difference of atomic forces. To further validate the
MTPs, we compared predicted lattice constants of single-element FCC crystals
to values by DFT. We also compared the predicted surface energies of single-
element FCC(111) facets with DFT. The comparison is summarized in Table. 1.
One can see that MTP-predicted lattice constants are close to DFT
calculations, with relative deviations around 1%. In terms of FCC(111) surface
energies, although large deviations exist for elements Ni, Co and Al, the
relative order of surface energy magnitude by MTP is in accordance with that
by DFT.

Table 1: Lattice constants and FCC(111) surface energies for single-element structures: DFT versus MTP. | Lattice constant [Å] |  Surface energy [J/m2]
---|---|---
Element | MTP | DFT | MTP | DFT
Al | 4.08 | 4.04 | 0.77 | 0.86
Cr | 3.62 | 3.62 | 2.61 | 2.65
Fe | 3.44 | 3.46 | 2.49 | 2.45
Co | 3.49 | 3.46 | 1.87 | 2.12
Ni | 3.51 | 3.52 | 1.93 | 2.14

We also compared the phase stability among various single-crystal structures,
including FCC random alloys (FCC_A1), FCC L12 ordered structures and BCC B2
structures. This comparison was used to test the ability of MTPs to predict
the most stable phase of Alx(CrFeNiCo)100-x as a function Al compositions.
Experimental observation and EAM-based calculations suggest that a low Al
composition favors FCC-type phases while B2 phases are thermodynamically more
stable at higher Al compositions [7, 45]. We calculated the cohesive energies
of L12 and B2 for Al compositions up to 40%, with all Al in one sublattice and
the remaining four elements randomly distributed. The FCC_A1 structures were
generated by randomly placing the atoms in a FCC lattice. Figure 2 shows that
at low Al contents (0–10%), L12 and FCC_A1 are both more stable than B2
phases. When Al compositions increase (10–20%), the ordered L12 becomes the
most stable phase. In comparison, larger Al compositions ($>20\%$) favor the
formation of ordered B2 phases, in good agreement with well-parameterized
empirical potentials and experiments [45, 7]. The dashed line represents the
most stable phases at each Al composition. One should note that the first-
principles data used to train MTPs only consist of FCC structures. Despite not
seeing any BCC structures, the MTPs accurately predicted the trends of phase
stability that are consistent with experiments and first-principles data,
indicating decent transferability of the MTPs.

Figure 2: Cohesive energies of the FCC_A1, L12, and the ordered B2 phases for
Alx(CrFeCoNi)100-x as a function of Al compositions. The most stable phases at
all Al compositions are connected with dashed lines to guide the eyes.

###  3.2 Variation of three corrosion metrics as a function of Al and Cr
compositions in AlCrFeCoNi

We studied the three corrosion metrics as a function of Al and Cr compositions
for AlCrFeCoNi high-entropy alloys. This specific high-entropy system was
examined because of its superior corrosion performance and the availability of
extensive experimental corrosion data, which can be compared to the ML
predictions [10, 62, 63].

Figure 3: Single phase formability (a), Pilling-Bedworth ratios for oxidation
of Cr (b) and FCC(111) surface energies (c) as a function of Al and Cr
compositions in AlxCry(FeCoNi)100-x-y. The training data involving AlCrFeCoNi
high-entropy alloys are included as scatter points in (a). Red squares and
green circles in (a) represent single phase and multiple phase data,
respectively. The grey dashed line in (a) is roughly the decision boundary by
Wu et al [64]. The regions where multi phases and single phase are almost
overlapped are marked with black boxes in (a).

Single phase formability, Pilling-Bedworth ratios and surface energies are
shown in respective Figure 3 (a), (b) and (c) as a function of Al and Cr
compositions in AlCrFeCoNi. The random forest classifier used to predict
single phase formability gave a prediction accuracy of 91% on the training
data consisting of AlCrFeCoNi, although there exists some noise as both
multiple-phase and single-phase AlCrFeCoNi structures are found in small
composition regions marked with black boxes. In Figure 3(a), one can locate a
decision boundary at around 10% Al composition to separate single-phase and
multiple-phase alloys. The decision boundary is mostly determined by Al
compositions and slightly associated with Cr compositions. An increase of Cr
compositions marginally shifts the boundary to a lower Al composition. This
decision boundary agrees well with the experimental results by Wu et al [64],
which are indicated by the grey line in Figure 3(a). Nevertheless, one can
note that predictions of single-phase formation at high Al composition regions
are confounded by the noisy training data, implying high prediction
uncertainties in this region. In terms of tendency to form corrosion-resistant
passive films, it is also crucial to form specific single-phase structures. It
was experimentally found that FCC AlCrFeCoNi crystals tend to be more
resistant to pitting corrosion than BCC counterparts [10, 63]. In the same Al
and Cr composition ranges, we compared the phase stability of L12 FCC
structures versus B2 BCC structures using cohesive energies calculated by the
trained MTP, following a similar procedure describe in the Section 3.1. The
single phase stability in Figure 4 suggests that L12 FCC structures are more
favorable at low Al and Cr compositions whereas B2 BCC structures are more
stable at high Al and Cr compositions. While Figure 4 shows the trend of
single-phase stability, for a given composition one should always first
consider the possibility of forming single phase structures. In other words,
we can use the results in Figure 4 only if a single-phase structure tends to
form.

Figure 4: Single crystal phase stability (L12 versus B2) as a function of Al
and Cr compositions.

Figure 3(b) shows PBRCr for different Al and Cr compositions. Likewise, a
major dependence on Al compositions and a minor dependence on Cr compositions
are identified. Higher PBRCr can be found at higher Al and Cr compositions,
and PBRCr values over the composition space studied spans in a range between
2.00 and 2.18, close to the PBRCr of pure Cr (2.04). PBR values can be used to
estimate the average stresses in oxide passive films. The analysis by
Bernstein [65] and Huntz et al. [66] suggests that the average stresses are
given by $\epsilon=\omega[(PBR)^{1/3}-1]$ where $\omega$ is a correction
scaling factor around 0.18. Using this simple analysis, oxide stresses across
over compositions studied have a negligible difference of around 0.5%. In
contrast, the surface energies exhibit larger variations over compositions,
ranging from 1.92 to 2.24 J/m2. High surface energies are concentrated at the
regions with high Al and Cr compositions, while low surface energies are found
with Cr contents around 18% and with either low or high Al contents. Besides,
we can relate the surface energies to electrochemical dissolution rate using
Eq. 3. Using an atomic density of $1\times 10^{19}~{}\textrm{atoms/m}^{2}$ and
a transition coefficient $\alpha$ of 1/2, electrochemical dissolution rates
over the studied composition ranges vary by 50 folds. To understand surface
energy dependency on Al and Cr compositions, we studied the surface
segregation of Al and Cr for each composition, and the results are depicted in
Figure 5. The surface segregation for an element $\rm{M}$ is defined as:

$\Delta x_{\rm{M}}=c_{\rm{M}}^{\mathrm{surface}}-c_{\rm{M}}^{0}$ (5)

where $c_{M}^{\mathrm{surface}}$ is the surface composition of metal M and
$c_{M}^{0}$ is the composition given by the chemical formula. It is thus
inferred that the low surface energies in the middle and bottom-right regions
of Figure 3(c) originate from Al segregation and Cr depletion, as marked by
‘*’ in Figure 5 since a Al FCC(111) surface has a much lower surface energy
(0.77 J/m2) compared to a Cr FCC(111) surface (2.61 J/m2), as shown in Table
1. The Cr depletion on the surface lends itself difficult to the formation of
Cr2O3 passive films. In summary, highly corrosion-resistant AlCrFeCoNi alloys
can potentially be found with low Al contents and around 18% Cr contents
because the alloy with AlCrFeCoNi alloys with these compositions tend to form
single-phase alloys and to exhibit lower surface energies. The identified Al
compositions are consistent with experimental measurement [10, 57, 63].

Figure 5: Surface segregation of Al and Cr for different Al and Cr
compositions for FCC(111) surfaces of AlxCry(FeCoNi)100-x-y.

##  4 Conclusion and outlook

A machine learning framework was proposed and developed to accelerate the
discovery of corrosion-resistant high-entropy alloys. We demonstrated that the
proposed framework can provide an accurate evaluation of relative corrosion
resistance for a wide range of compositions for high-entropy alloys. The
physics-informed framework consists of two machine learning approaches. One
approach uses experimental data to train random forest classifier for
predictions of single phase formability. The other approach uses first-
principles data to develop robust machine learning potentials, allowing for
fast downstream simulations to obtain corrosion metrics such as Pilling-
Bedworth ratio and surface energy. Current computational methods to understand
corrosion performance of alloys mostly use pure statistical fitting or first-
principles calculations. Unlike statistical fitting, the random forest
classifier encodes meaningful physical knowledge into the feature engineering
process. In comparison with first-principles calculations, the machine
learning potentials can significantly mitigate the computational overhead of
massive first-principles calculations. This framework was tested on a specific
class of high-entropy alloys AlCrFeCoNi. The AlCrFeCoNi compositions were
sampled by varying the Al and Cr compositions while enforcing the remaining
Fe, Co and Ni compositions to be almost identical. The three corrosion metrics
were evaluated on those sampled compositions, based on which the desired
compositions for corrosion protection were identified. We found that low Al
compositions and around 18% Cr compositions tend to form corrosion-resistant
alloys, in satisfactory agreement with experimental observations. Although
additional corrosion descriptors, such as cohesive energy, and adsorption
energy of oxygen and chloride, may be needed to provide a more comprehensive
description of corrosion performance, the three simple corrosion metrics used
in this work have proved to be effective in narrowing down the composition
space for further selection.

Our scheme is not limited to AlCrFeCoNi high-entropy alloys and corrosion
properties. The methodology can be easily adapted for other material
applications where the relationship of chemical compositions with properties
is sought after and where ML accelerated molecular simulations are
indispensable for high-throughput screening of material candidates. For
instance, ductility of alloys can be evaluated by stacking fault energies
which can be calculated by using MLPs, and hardness can be estimated using
machine learning regression on experimental dataset [67, 68]. One should note
that most state-of-the-art machine learning potentials use element-specific
features, which limit the transferability of MLPs. In other words, MLPs
trained on certain elements cannot be applied to elements not existing in the
training data. Moreover, a large amount of training structures are required to
build reliable ML models for high-entropy systems. Developing a robust
element-agnostic featurization method, and reducing numbers of representative
images and features are promising future directions. Element-agnostic
featurization methods are just emerging in recent years and needs further
development. For example, there are methods using multipole expansions of the
electron density around atoms [69] or graph representation of materials [70].
Current image and feature selection methods use linear correlations in the
feature space [71]. More advanced methods may require understand the complex
non-linear mapping between features and outputs (e.g. energy and forces).

### Declaration of competing interest

The authors declare that they have no known competing financial interests or
personal relationships that could have appeared to influence the work reported
in this paper.

### Acknowledgments

This work was completed in part using the Discovery cluster, supported by the
Research Computing team at Northeastern University. This work is partially
supported by The Experiential AI Institute, Roux Institute, and the Alfond
Foundation at Northeastern University. We thank Dr. Liang Qi (University of
Michigan) for providing valuable technical feedback to our poster presented at
ICME2023 conference in Orlando, Florida, USA.

### Supporting information

Standard enthalpy of formation for oxides of certain metals, Computational
settings of DFT calculations, Details of moment tensor potential (MTP), Random
forest classifier for single phase formability, Fast sampling of
configurations using the embedded atom method (EAM), First-principles data for
MTP, MTP-enabled simulations for corrosion metrics, and Supporting results are
included in the supporting information.

### Data and code availability

Code and data to reproduce the findings can be found on github:
https://github.com/cengc13/ml-hea-corrosion-code-data.

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