# Recent progress in the JARVIS infrastructure for next-generation data-driven
materials design

Daniel Wines  Material Measurement Laboratory, National Institute of Standards
and Technology, Gaithersburg, Maryland 20899, USA  Ramya Gurunathan  Material
Measurement Laboratory, National Institute of Standards and Technology,
Gaithersburg, Maryland 20899, USA  Kevin F. Garrity  Material Measurement
Laboratory, National Institute of Standards and Technology, Gaithersburg,
Maryland 20899, USA  Brian DeCost  Material Measurement Laboratory, National
Institute of Standards and Technology, Gaithersburg, Maryland 20899, USA  Adam
J. Biacchi  Physical Measurement Laboratory, National Institute of Standards
and Technology, Gaithersburg, Maryland 20899, USA  Francesca Tavazza  Material
Measurement Laboratory, National Institute of Standards and Technology,
Gaithersburg, Maryland 20899, USA  Kamal Choudhary<EMAIL_ADDRESS>Material Measurement Laboratory, National Institute of Standards and
Technology, Gaithersburg, Maryland 20899, USA

###### Abstract

The Joint Automated Repository for Various Integrated Simulations (JARVIS)
infrastructure at the National Institute of Standards and Technology (NIST) is
a large-scale collection of curated datasets and tools with more than 80000
materials and millions of properties. JARVIS uses a combination of electronic
structure, artificial intelligence (AI), advanced computation and experimental
methods to accelerate materials design. Here we report some of the new
features that were recently included in the infrastructure such as: 1)
doubling the number of materials in the database since its first release, 2)
including more accurate electronic structure methods such as Quantum Monte
Carlo, 3) including graph neural network-based materials design, 4)
development of unified force-field, 5) development of a universal tight-
binding model, 6) addition of computer-vision tools for advanced microscopy
applications, 7) development of a natural language processing tool for text-
generation and analysis, 8) debuting a large-scale benchmarking endeavor, 9)
including quantum computing algorithms for solids, 10) integrating several
experimental datasets and 11) staging several community engagement and
outreach events. New classes of materials, properties, and workflows added to
the database include superconductors, two-dimensional (2D) magnets, magnetic
topological materials, metal-organic frameworks, defects, and interface
systems. The rich and reliable datasets, tools, documentation, and tutorials
make JARVIS a unique platform for modern materials design. JARVIS ensures
openness of data and tools to enhance reproducibility and transparency and to
promote a healthy and collaborative scientific environment.

††preprint: AIP/123-QED

##  I Introduction

Figure 1: Major areas of ongoing research as part of the JARVIS
infrastructure. Figure 2: An overview of the history of JARVIS-related
projects since its creation in 2017 until present.

The Joint Automated Repository for Various Integrated Simulations
(JARVIS)Choudhary  _et al._ (2020a) is an integrated infrastructure to
accelerate materials discovery and design. The JARVIS infrastructure can be
separated into electronic structure methods (density functional theory (DFT)
Hohenberg and Kohn (1964), tight binding Ashcroft and Mermin (1976), dynamical
mean field theory (DMFT) Vollhardt, Byczuk, and Kollar (2012), many-body
perturbation theory (GW) Onida, Reining, and Rubio (2002), and Quantum Monte
Carlo (QMC) Foulkes  _et al._ (2001)) Martin (2020), classical force-fields
(FF) Allen and Tildesley (2017), machine learning (ML) techniques Hastie  _et
al._ (2009), quantum computation algorithms Nielsen and Chuang (2001) and
experiments Leng (2009). JARVIS is motivated by the Materials Genome
Initiative (MGI) Warren (2018) principles of developing open-access databases
and tools to reduce the cost and development time of materials discovery,
optimization, and deployment. A depiction of the major areas of ongoing
research as part of the JARVIS infrastructure is depicted in Fig. 1 and the
publicly available JARVIS tools are listed in Table 1.

In the first three years since its creation in 2017 (see Fig. 2), JARVIS-DFT
grew to include standard material properties Choudhary  _et al._ (2020a) such
as formation energies, band gaps, elastic constants, piezoelectric constants,
dielectric constants, and magnetic moments, as well as more exotic properties
such as exfoliation energies for van der Waals (vdW) bonded materials
Choudhary  _et al._ (2017), spin-orbit coupling (SOC) spillage Choudhary,
Garrity, and Tavazza (2019); Choudhary  _et al._ (2020b, 2021a), improved
meta-GGA band gaps Choudhary  _et al._ (2018a), frequency-dependent dielectric
functions Choudhary  _et al._ (2018a), solar cell efficiency Choudhary  _et
al._ (2019), thermoelectric properties Choudhary, Garrity, and Tavazza (2020),
and Wannier tight-binding Hamiltonians Garrity and Choudhary (2021a, b).
Protocols such as automatic k-point convergence Choudhary and Tavazza (2019)
were developed to improve data reliability. Complementary to JARVIS-DFT,
JARVIS force field (JARVIS-FF) Choudhary  _et al._ (2018b) provides an
automatic framework to use classical force fields to calculate basic
properties such as the bulk modulus, defect formation energies, and phonons
that may be crucial for specific molecular-dynamics simulations. JARVIS-ML
introduced Classical Force-field Inspired Descriptors (CFID) Choudhary,
DeCost, and Tavazza (2018) in 2018 as a universal framework to represent a
material’s chemistry-structure-charge related data. Using CFID and JARVIS-DFT
data, several high-accuracy classification and regression ML models have been
developed, with applications to materials-screening and energy-landscape
mapping. Trained property models include formation energies, exfoliation
energies, band gaps, magnetic moments, refractive indexes, dielectric
constants, thermoelectric performance, and maximum piezoelectric and infrared
modes Choudhary  _et al._ (2020a).

Table 1:  A summary of the publicly available JARVIS tools. Model Name | Link | Ref.
---|---|---
JARVIS Tools | https://github.com/usnistgov/jarvis | Choudhary  _et al._ (2020a)
TB3PY | https://github.com/usnistgov/tb3py |  Garrity and Choudhary (2021a), Garrity and Choudhary (2021b)
ALIGNN | https://github.com/usnistgov/alignn | Choudhary and DeCost (2021)
AtomVision | https://github.com/usnistgov/atomvision | Choudhary  _et al._ (2023a)
ChemNLP | https://github.com/usnistgov/chemnlp | Choudhary and Kelley (2022a)
AtomQC | https://github.com/usnistgov/atomqc | Choudhary (2021)
JARVIS Notebooks | https://github.com/JARVIS-Materials-Design/jarvis-tools-notebooks | Jar
JARVIS Leaderboard | https://github.com/usnistgov/jarvis_leaderboard | usnistgov (2023)

In this review article, we will give an overview of the several major updates
that have been made to the JARVIS infrastructure (see Fig. 2). Recent updates
to JARVIS-DFT, which now contains over 80000 materials, include identifying
the anomalous quantum confinement effect in materials Choudhary and Tavazza
(2021), screening bulk magnetic topological materials Choudhary  _et al._
(2021a), and screening bulk and two-dimensional (2D) superconducting materials
Choudhary and Garrity (2022); Wines  _et al._ (2023a). With regards to other
electronic structure methods, tight binding models Garrity and Choudhary
(2021a, b) and QMC methods Foulkes  _et al._ (2001); Wines, Choudhary, and
Tavazza (2023); Wines  _et al._ (2023b) have recently been added to the JARVIS
infrastructure. JARVIS-ML has been expanded to include the Atomistic Line
Graph Neural Network (ALIGNN) Choudhary and DeCost (2021) model that has been
utilized for fast and accurate property and spectra prediction of formation
energies, band gaps, electron and phonon density-of-states Kaundinya,
Choudhary, and Kalidindi (2022); Gurunathan, Choudhary, and Tavazza (2023),
properties of metal-organic frameworks for carbon capture Choudhary  _et al._
(2022a), and properties of superconductors Choudhary and Garrity (2022). The
ALIGNN model has also been recently used to develop universal force fields for
the periodic table (ALIGNN-FF) Choudhary  _et al._ (2023b). The AtomVision
Choudhary  _et al._ (2023a) model has been added to JARVIS-ML, with the
intention of generating and analyzing scanning tunneling microscope (STM) and
high angle annular dark field (HAADF) scanning transmission electron
microscope (STEM) images to accelerate the interpretation of experimental
images. A natural language processing-based library for materials chemistry
text data (ChemNLP) Choudhary and Kelley (2022a) and tools to perform quantum
computation algorithms Choudhary (2021) such as variational quantum eigen
solver (VQE) Peruzzo  _et al._ (2014) and variational quantum deflation (VQD)
Higgott, Wang, and Brierley (2019) have also been added to the JARVIS
infrastructure. Finally, several experimental measurements have been performed
to validate our computational predictions. In addition to the major recent
updates of JARVIS, we will detail large-scale data efforts, educational
notebooks, leaderboard, and external outreach.

##  II Electronic Structure

###  II.1 Density Functional Theory

####  II.1.1 Magnetic Topological Materials Screening

Figure 3: Flow chart for screening high-spillage materials and analysis. (a)
Flowchart for screening, (b) spillage distribution analysis for all the
materials under investigation, (c) pie chart showing high-spillage insulators
and metals, (d) magnetic moment distribution for high-spillage materials, (e)
Perdew-Burke-Ernzerhof (PBE) Perdew, Burke, and Ernzerhof (1996) vs. Strongly
Constrained and Appropriately Normed (SCAN) semilocal Sun, Ruzsinszky, and
Perdew (2015) band gaps.

Magnetic topological insulators and semimetals have a variety of exotic
properties that make them appropriate for applications in spintronics and
quantum computation, but very few high-quality candidate materials have been
discovered. Recently, we utilized the spin-orbit spillage (SOS) screening
criteria, which is a method to measure spin-orbit-induced band inversion (a
signature of topological materials) by comparing the wave functions with and
without spin-orbit coupling (SOC) Liu and Vanderbilt (2014); Choudhary,
Garrity, and Tavazza (2019); Choudhary  _et al._ (2020b). This study is an
extension of our previous work, which utilized the same SOS screening for bulk
nonmagnetic materials as well as 2D materials with and without magnetism
Choudhary, Garrity, and Tavazza (2019); Choudhary  _et al._ (2020b).

Table 2: A summary of materials, including chemical formula (Form.), spacegroup number (Spg), JARVIS-DFT ID (JID) and their maximum spillage values.  Form. | Spg | JID | Spillage
---|---|---|---
Mn2Sb |  $P6_{3}$/$mmc$ | 15693 | 0.5
NaMnTe2 | $P\bar{3}m1$ | 16806 | 1.04
Rb3Ga | $Fm\bar{3}m$ | 38248 | 0.47
CoSI | $F\bar{4}3m$ | 78508 | 0.69
Mn3Sn |  $P6_{3}$/$mmc$ | 18209 | 0.79
Sc3In |  $P6_{3}$/$mmc$ | 17478 | 1.01
Sr3Cr | $Pm\bar{3}m$ | 37600 | 1.01
Mn3Ge | $Fm\bar{3}m$ | 78840 | 3.01
NaRuO2 | $R\bar{3}m$ | 8122 | 0.5
CoNb3S6 | $P6_{3}22$ | 21459 | 1.03
Y3Sn |  $P6_{3}$/$mmc$ | 37701 | 0.29
CaMn2Bi2 | $P\bar{3}m1$ | 18532 | 1.17

We used systematic high-throughput DFT calculations to identify magnetic
topological materials from the over 40000 bulk materials in the JARVIS-DFT
database Choudhary  _et al._ (2021a). First, we screen materials with net
magnetic moment > 0.5 $\mu_{\textrm{B}}$ and SOS > 0.25, resulting in 25
insulating and 564 metallic candidates. We then perform Wannier tight-binding
Hamiltonian (WTBH)-based techniques to calculate Wannier charge centers, Chern
numbers, anomalous Hall conductivities (AHC), surface band structures, and
Fermi surfaces to determine interesting topological characteristics of the
screened compounds. After narrowing down the search, we experimentally
synthesized and characterized a few candidate materials such as CoNb3S6 and
Mn3Ge.

The full workflow is given in Fig. 3a), while a full analysis of the data
trends for the materials is given in Fig. 3b) - e). A summary of candidate
materials with high values of SOS is given in Table 2. Further analysis of the
electronic band structure (with and without SOC) and k-dependent spin-orbit
spillage was conducted. Strong focus was placed on Y3Sn (JVASP-37701), which
is as a candidate semimetal, and further analysis of the Fermi surface (001)
surface band structure, nodal points-lines, and AHC was performed. In
addition, strong focus was placed on NaRuO2 (JVASP-8122), which is a candidate
Chern insulator, and further analysis of the Wannier charge center and AHC
were performed. Further details of computational screening, methodologies, and
specific calculated results can be found in Ref. Choudhary  _et al._ , 2021a.

####  II.1.2 Anomalous Quantum Confinement Effect

Figure 4: Bulk vs. monolayer band gaps using OptB88vdW (OPT), HSE06 and PBE0,
demonstrating the AQCE.

Materials with vdW bonding are known to exhibit quantum confinement effects,
in which the electronic band gap of the 3D realization of a material is lower
than that of its 2D counterpart. However, the possibility of an anomalous
quantum confinement effect (AQCE) exists, where the band gap trend is
reversed. Using DFT, we have computed $\approx$1000 OptB88vdW Klimeš, Bowler,
and Michaelides (2009) (semilocal functional), $\approx$50 HSE06 Heyd,
Scuseria, and Ernzerhof (2003) and $\approx$50 PBE0 Adamo and Barone (1999)
(hybrid functionals) electronic band gaps for bulk and their corresponding
monolayers, using structures from the JARVIS-DFT database. OptB88vdW
identifies 65 AQCE materials, but the hybrid functionals only confirm such
findings in 14 cases. Their list and correspondent energy gaps are given in
Ref. Choudhary and Tavazza, 2021. For some systems, the band gaps differences
are small, on the order of 0.5 eV or less, while for others they are on the
order of 1 eV to 2 eV. A summary of these calculated results are depicted in
Fig. 4. The majority of the AQCE materials are either hydroxides, oxide
hydroxide compounds (AlOH2, Mg(OH)2, Mg2H2O3, Ni(OH)2, SrH2O3), Sb-halogen-
chalcogenide compounds (SbSBr, SbSeI) or alkali-chalcogenides (RbLiS and
RbLiSe).

Interestingly, among the 14 AQCE materials, we find examples of 0D and 1D
compounds as well, not just 2D. We used Perdew-Burke-Ernzerhof (PBE)-based SOC
calculations to determine the effect of SOC on the band gap predictions and to
calculate SOS (similar procedure to Section II.1.1), which acts as a signature
of the topologically non-trivial nature of the materials. We found that none
of the 14 materials display topological properties and their electronic band
gaps don’t change significantly when SOC is applied. To understand the origin
of the AQCE, we investigated changes in bond distances and electronic
structure. We found that major changes occur for H-H bonds for (OH) containing
materials, an effect that could be at least partially responsible for the
AQCE. Electronic structure analysis, based on band-structure and projected
density of states, shows AQCE is often characterized by lowering of the
conduction band in the monolayer and corresponding changes in the pz
electronic orbital contribution, with z being the non-periodic direction in
the 2D case. More details on this work can be found in Ref. Choudhary and
Tavazza, 2021.

####  II.1.3 Bulk and 2D BCS Superconductors

Table 3: JARVIS screening workflow for some of the potential candidate superconductors: ($T_{c}$), chemical formula (Form.), spacegroup number (Spg), JARVIS ID (JID), Inorganic Crystal Structure Database ID (ICSD) Belsky  _et al._ (2002) wherever available, JARVIS-DFT based formation energy ($E_{form}$ (eV/atom)) and energy above convex hull ($E_{hull}$ (eV)). Form. | Spg | JID | ICSD | $E_{form}$ | $E_{hull}$ |  $T_{C}$(K)
---|---|---|---|---|---|---
MoN | 187 | 16897 | 187185 | -0.47 | 0.09 | 33.4
CaB2 | 191 | 36379 | 237011 | -0.25 | 0.09 | 31.0
ZrN | 194 | 13861 | 161885 | -1.76 | 0.18 | 30.0
VC | 225 | 19657 | 619079 | -0.48 | 0.06 | 28.1
V2CN | 123 | 105356 | - | -0.82 | 0.11 | 26.2
Mn | 225 | 25344 | 41509 | 0.08 | 0.08 | 23.0
NbFeB | 187 | 4546 | - | -0.15 | 0.39 | 22.1
NbVC2 | 5 | 102190 | - | -0.46 | 0.08 | 21.9
ScN | 225 | 15086 | 290470 | -2.15 | 0.0 | 20.8
LaN2 | 2 | 118592 |  | -1.05 | 0.0 | 20.4
VRu | 221 | 19694 | 106010 | -0.22 | 0.01 | 20.3
TiReN3 | 161 | 36745 | - | -0.68 | 0.10 | 20.0
B2CN | 51 | 91700 | 183794 | -0.53 | 0.19 | 19.4
KB6 | 221 | 20067 | 98987 | -0.09 | 0.0 | 19.0
ZrMoC2 | 166 | 99893 | - | -0.49 | 0.08 | 17.9
TaB2 | 191 | 20082 | 30420 | -0.60 | 0.0 | 17.2
NbS | 194 | 18923 | 44992 | -0.98 | 0.05 | 17.0
TaVC2 | 166 | 101106 | - | -0.54 | 0.05 | 16.3
TaC | 187 | 36405 |  | -0.24 | 0.40 | 16.1
MgBH | 11 | 120827 | - | -0.03 | 0.11 | 15.5
CoN | 216 | 14724 | 236792 | -0.02 | 0.0 | 15.0
NbRu3C | 221 | 8528 | 77216 | -0.02 | 0.19 | 15.0

Since the discovery of superconductivity in 1911 by Onnes Kamerlingh Onnes
(1911), the identification of novel superconducting materials with high
transition temperatures ($T_{C}$) has been an active area of research in
condensed matter physics Poole, Farach, and Creswick (2013); Rogalla and Kes
(2011). A more systematic data-driven search can assist in expediting the
discovery of potentially high-$T_{C}$ superconductors. There are two key
ingredients required to computationally identify Bardeen–Cooper–Schrieffer
(BCS) conventional superconductors Cooper and Feldman (2010); Giustino (2017)
with high-$T_{C}$: 1) a robust computational workflow for electron-phonon
coupling calculations (EPC), and 2) a database of curated materials with prior
knowledge that can help pre-screen candidate materials. Using density
functional theory perturbation theory (DFT-PT), the electron-phonon coupling
can be calculated and used to predict $T_{C}$ with reasonable accuracy for a
variety of materials Giustino (2017); Kawamura, Hizume, and Ozaki (2020).

Recently, we developed such a computational approach to discover BCS
superconductors, combining several methods at various levels of computational
expense and accuracy Choudhary and Garrity (2022). We start with a BCS-
inspired pre-screening based for materials with high Debye temperature
($\theta_{D}$) and high electron density of states (DOS) at Fermi-level
($N(0)$), using the existing JARVIS-DFT database Choudhary  _et al._ (2020a).
We then develop and apply a DFT-PT workflow to compute $T_{C}$ using electron-
phonon coupling and the McMillan-Allen-Dynes formula McMillan (1968), with
initially low k-point and q-point convergence settings. We benchmark the DFT
workflow on known superconductors and apply it to materials from our pre-
screening step. For the best candidates, we perform additional convergence
tests to validate our predictions. In addition, we use the dataset to develop
deep-learning models using the atomistic line-graph graph neural network
(ALIGNN) Choudhary and DeCost (2021) (more details in Section III.1). A full
schematic of this workflow is given in Fig. 5.

Figure 5: Schematic showing the steps involved in identifying high-$T_{C}$
superconductors. a) statistical distribution of Debye temperature (K) and b)
statistical distribution of electronic density of states (DOS) (states per eV
per number of electrons) at the Fermi level from the JARVIS-DFT database, c)
probability that compounds containing a given element have $\theta_{D}>$300 K.
The flow chart shows the application of BCS-inspired screening, density
functional theory calculations and deep-learning training.

We specifically pre-screened 1736 materials with high Debye temperature and
electronic density of states. We then performed EPC calculations for 1058
materials. Using the McMillan-Allen-Dynes formula, we identified 105
dynamically stable materials with transition temperatures, $T_{C}$ above 5 K.
As shown in Table 3, some of our highest $T_{C}$ candidate superconductors
include MoN, VC, Mn, MnN, LaN2, KB6, and TaC. MoN in a rock-salt structure has
been previously been reported with a $T_{C}$ as high as 30 K Inumaru  _et al._
(2008); Wang  _et al._ (2015); however, here we propose a hexagonal form which
has not been observed experimentally. Similarly, ZrN in rock-salt form is
known to have $T_{C}$ of 10 K; however, here we propose a hexagonal form of
ZrN to have a $T_{C}$ around 30 K. Lanthanum nitride Vaitheeswaran, Kanchana,
and Rajagopalan (2002) in a 1:1 ratio has been found to have superconducting
properties. Lanthanum nitride in 1:2 ratio is not characterized for the
superconducting properties to the best of our knowledge. Further details of
the worfklow and more specific calculated results and analysis for bulk BCS
superconductors can be found in Ref. Choudhary and Garrity, 2022.

We extended this workflow to 2D, since superconductivity in 2D systems has
attracted a great deal of attention Campi, Kumari, and Marzari (2021); Bekaert
_et al._ (2017); Singh  _et al._ (2022) for potential applications in
nanoscale devices such as superconducting transistors, quantum interferometers
and superconducting qubits De Franceschi  _et al._ (2010); Huefner  _et al._
(2009); Delahaye  _et al._ (2003); Romans  _et al._ (2010); Liu and Hersam
(2019). There have been very few 2D materials that have been discovered to
have a high $T_{C}$ (experimentally and theoretically). The starting point
involved pre-screening the 1079 monolayer materials in the JARVIS-DFT
database. Due to the fact that the elastic tensor (and therefore the Debye
temperature) is more computationally expensive to compute for 2D materials
than bulk materials, it is only available for a selected number of 2D
materials in the database. For this reason, we had to modify the BCS screening
workflow. Instead of screening the DOS at the Fermi level and the Debye
temperature (as we did for bulk materials), we screened materials based on the
DOS at the Fermi level, the total magnetic moment, and the electronic band gap
(calculated with the OptB88vdW functional). This screening process is based on
the a priori notion that a potential 2D superconductor will have a high
density of states at the Fermi level (metallic) and zero magnetic moment per
unit cell. In addition to selecting 2D materials in JARVIS that meet the
criteria of E${}_{\textrm{gap}}$ $<$ 0.05 eV (band gap), M $<$ 0.05
$\mu_{\textrm{B}}$ (magnetic moment), and DOS at E${}_{\textrm{Fermi}}$ $>$ 1
states per eV per number of electrons (density of states at the Fermi level),
we identified 24 additional 2D materials, based on an extensive literature
search of 2D and 3D superconductors. A full schematic of this workflow and an
overview of the results is given in Fig. 6.

Figure 6: a) A full schematic of the the high-throughput workflow used to
identify high $T_{c}$ 2D superconductors and b) - c) the relation between
electron-phonon coupling (EPC) parameters ($\lambda$ and $\omega_{log}$) for
all 2D materials.

We find that several candidate 2D superconductors that have a high $T_{C}$ are
based on nitrides, borides and carbides. In addition, several oxide and
niobium-based compounds and transition metal dichalcogenides such as NbS2/Se2
in both their T (octahedral phase (1T)-centered honeycombs) and H (the
trigonal prismatic phase (2H)-hexagonal honeycombs) phases exhibit strong
superconducting properties. We observe the highest transition temperature for
monolayer Mg2B4N2, which has a calculated $T_{c}$ of 21.8 K. To our knowledge,
this material has previously been undiscovered in bulk and 2D form. In
addition, we found another previously unknown layered polymorph of Mg2B4N2
(which we deem $\alpha$-Mg2B4N2) with a high $T_{c}$ of 7.4 K. This
hypothetical polymorph has a higher formation energy than the other Mg2B4N2
structure (0.06 eV/atom vs. -0.24 eV/atom). Consistent with recent EPC
calculations Campi, Kumari, and Marzari (2021), we find W2N3 to have a notably
high $T_{c}$ of 18.7 K. We also investigated several 2D analogs of non-layered
boron, carbon and nitrogen-based materials bulk materials (such as 2D MgB2,
B2N, NbC, ScC) and several 2D oxide-based materials (NbO2, ZrBrO, TiClO),
which possess strong superconducting properties. Further details can be found
in Ref. Wines  _et al._ , 2023a.

###  II.2 Tight Binding

There are two types of tight-binding projects available in JARVIS: 1) Wannier
tight-binding Hamiltonians (WTBH) Garrity and Choudhary (2021a), 2) a
parametrized universal tight-binding model fit to first principles
calculations (ThreeBodyTB.jl) Garrity and Choudhary (2021b). The WTBH database
provides a computationally efficient way to interpolate and understand the
electronic properties of a set of 1771 preselected materials, based on a DFT
calculation for each of those materials. The quality of the WTBH are evaluated
by comparing the Wannier band structures to directly calculated DFT band
structures including SOC. The WTBH database is used for predicting the AHC,
surface band structures, and various topological indexes.

In contrast to the WTBH database, the goal of the ThreeBodyTB.jl parametrized
tight-binding model is to produce a tight-binding Hamiltonian and total energy
without doing a computationally expensive DFT calculation first. Because
tight-binding uses a minimal basis set of atomic orbitals, the calculations
are up to three orders of magnitude faster than comparable plane-wave DFT
calculations, enabling computationally efficient materials prediction. Despite
their simplicity, tight-binding approaches incorporate single-particle quantum
mechanics as well as electrostatics as a self-consistency stepElstner  _et
al._ (1998); Frauenheim  _et al._ (2000); Koskinen and Mäkinen (2009). This
built-in physics can enable improved predictions outside the set of training
data, relative to classical force-fields or pure machine-learning approaches.

Unlike typical parametrized tight-binding models that consider only
interactions between pairs of atoms when generating the tight-binding
HamiltonianKoskinen and Mäkinen (2009); Hourahine  _et al._ (2020), our model
includes three-body contributions that modify the two-body contributions as
well. These extra terms allow for improved transerability as compared to
simpler models, at the cost of needing to fit more parameters.

Our fitting procedure is summarized in Fig. 7. For a given elemental or binary
system, we first generate a set of standard crystal structures, perform DFT
calculations, and fit an initial parameter set to reproduce the band
structures and total energies. Then, we employ an active learning strategy to
test and improve the model by using the current model to relax randomly
generated crystal structures Pickard and Needs (2011) and test our tight-
binding results versus new DFT calculations. If the results are poor, we add
these new structures to our fitting database and repeat the process until
results improve.

Figure 7: Overview of the three-body tight binding (TB) model fitting
workflow.

Our current parameter set can predict total energies, volumes, and band gaps
with comparable accuracy to machine learning approaches, as well as produce
band structures. Importantly the results generalize to surfaces and vacancy
calculations that are completely outside the fitting dataset, as shown in Fig.
8. For testing results and details see Ref. Garrity and Choudhary, 2021b. The
julia code with a python interface are available, and underlying DFT database
with over one million materials is available in JARVIS-QETB.

Figure 8: Comparison of DFT and three-body tight-binding calculations for
unrelaxed a) point vacancy formation energy (eV) and b) $(111)$ surface
energies ($J$ $mm^{-2}$) of elemental solids. Tight-binding results are out-
of-sample.

###  II.3 Quantum Monte Carlo

A recent effort of the JARVIS infrastructure has been to incorporate many-body
methods that go beyond the standard accuracy of DFT for selected materials
that have a complicated or correlated electronic structure. Diffusion Monte
Carlo (DMC) Foulkes  _et al._ (2001) is a many-body correlated electronic
structure method that has been applied successfully to the calculation of
electronic and magnetic properties of a variety of periodic systems. It
involves solving the imaginary-time Schrödinger equation for the near-exact
ground state wavefunction using projector techniques (more details can be
found in Ref. Foulkes  _et al._ , 2001). Although it is a more computationally
expensive method, DMC has a weaker dependence on the starting density
functional and Hubbard U parameters Dudarev  _et al._ (1998), scales similarly
to DFT with respect to the number of electrons in the simulation ($\sim
N^{3-4})$ Foulkes  _et al._ (2001), and can achieve results that are more
accurate than DFT Foulkes  _et al._ (2001).

####  II.3.1 Systematic Benchmark of 2D CrX3

Figure 9: a) The full high throughput workflow proposed in to obtain the
accurate magnetic properties of a 2D system using a combination of DFT+U and
QMC and b) top and side view of the atomic structure of monolayer CrX3 (X = I,
Br, Cl, F).

We designed a workflow that applied a combination of DFT+U and DMC techniques
to compute accurate magnetic properties for 2D CrX3 materials (X = I, Br, Cl,
F) Wines, Choudhary, and Tavazza (2023). We chose these materials (depicted in
Fig. 9b) as a case study since they have been experimentally synthesized Huang
_et al._ (2017); Zhang  _et al._ (2019); Cai  _et al._ (2019), have a nonzero
critical temperature Huang  _et al._ (2017); Torelli  _et al._ (2020), and
have been studied with DFT extensively Torelli  _et al._ (2020). Our first-
principles data can be mapped to a 2D model spin Hamiltonian to extract useful
observable quantities such as $T_{c}$ Torelli and Olsen (2018); Lado and
Fernández-Rossier (2017). In our case, this Hamiltonian was a function of
Heisenberg isotropic exchange ($J$), easy axis single ion anisotropy ($D$) and
anisotropic exchange ($\gamma$). To obtain $J$, $\gamma$ and $D$, we performed
spin-orbit (noncollinear) DFT+U calculations by rotating the easy axis by 90∘
and calculating the energy difference between the rotated and non-rotated
configurations for ferromagnetic (FM) and antiferromagnetic (AFM) separately.
We automated these four calculations using the JARVIS workflow, where four
distinct total energy values were obtained for each structure. We benchmarked
this for 2D CrI3 (JVASP-76195), CrBr3 (JVASP-6088), CrCl3 (JVASP-76498) and
CrF3 (JVASP-153105) using multiple DFT functionals and values of U. The
influence of the geometric structure on the magnetic properties was also
assessed (see Ref. Wines, Choudhary, and Tavazza, 2023 for more details).

These results can be systematically improved with QMC in two ways: i)
variationally determining the optimal U value using DMC and ii) calculating a
statistical bound for the $J$ parameter by separately performing DMC
simulations for the FM and AFM orientations. These QMC energies are spin-
polarized (collinear), in contrast to the previous spin-orbit (noncollinear)
DFT calculations. Spin-orbit implementation is currently limited in DMC,
forcing us to neglect the spin-orbit-dependent $\gamma$ contribution when
calculating $J$ with QMC. This has little impact on the final result for $J$,
since $J>>\gamma$. As a result, we designed a high-throughput workflow that
allows us to variationally determine the optimal value of U using DMC,
calculate a statistical bound on $J$ by performing collinear DMC calculations
for the FM and AFM phases, and use that optimal determined U to perform DFT+U
simulations and extract the anisotropy parameters ($D$, $\gamma$), with the
end goal of using these parameters to accurately estimate the 2D critical
temperatureTorelli and Olsen (2018). A full schematic of this workflow is
depicted in Fig. 9a). As a result of our DFT+U/QMC workflow, we estimated a
maximum value of 43.56 K for the Tc of CrI3 and of 20.78 K for the Tc of
CrBr3. We also extracted the spin-density and magnetic moments from our DMC
results and provided a detailed comparison with DFT+U. For more details see
Ref. Wines, Choudhary, and Tavazza, 2023.

Figure 10: A summary of the deviation of the geometric properties (lattice
constant ($a$) and V-Se distance ($d^{\textrm{V}-\textrm{Se}}$)) and relative
to the DMC calculated geometric properties for a) T-VSe2 and b) H-VSe2 and c)
the the deviation of T - H energy relative to the DMC calculated T - H energy
(E${}^{\textrm{T}-\textrm{H}}$) for a variety of DFT functionals (U = 2 eV),
where the DMC error bar (standard error about the mean) is represented by the
red bars. The insets depicts the top and side view of the atomic structure.

####  II.3.2 Structure and Phase Stability of 2D 1T- and 2H-VSe2

Previously, controversial claims of near-room temperature ferromagnetism
(ranging from 291 K to 470 K Bonilla  _et al._ (2018); Yu  _et al._ (2019);
Wang  _et al._ (2021); Fuh  _et al._ (2016)) in 2D VSe2 have existed
throughout the experimental and theoretical literature. These discrepancies in
calculated and measured magnetic properties (including varying magnetic
moments, preferred magnetic ground state and Curie temperature Bonilla  _et
al._ (2018); Yu  _et al._ (2019); Wang  _et al._ (2021); Fuh  _et al._ (2016);
Duvjir  _et al._ (2018)) between the T (octahedral phase (1T)-centered
honeycombs) phase and the H (the trigonal prismatic phase (2H)-hexagonal
honeycombs) phase of 2D VSe2 (depicted in the insets of Fig. 10) are most
likely due to the structural parameters being coupled to the magnetic
properties. This is due to both phases having a close lattice constant and
similar total energies, making it difficult to determine which phase is being
experimentally observed Li  _et al._ (2020); Pushkarev  _et al._ (2019); Yu
_et al._ (2019); Bonilla  _et al._ (2018). To resolve these types of
discrepancies in correlated materials, many-body methods such as DMC can be
utilized. We used a combination of DFT, DMC and a recently developed surrogate
Hessian line-search structural optimization technique Tiihonen, Kent, and
Krogel (2022) to resolve the structural parameters and relative phase
stability of monolayer T-VSe2 and H-VSe2.

A summary of the DFT benchmarking results (for multiple DFT functionals and
with U correction) for lattice constant ($a$), V-Se distance
($d^{\textrm{V}-\textrm{Se}}$), and relative energy between the phases
(E${}^{\textrm{T}-\textrm{H}}$) is presented in Fig. 10. As seen in the
figure, a large disagreement between methods is prevalent, indicating the need
for a more accurate, many-body theory. With DMC accuracy, we determined the
lattice constant and V-Se distance to be 3.414(12) Å and 2.505(7) Å
respectively for T-VSe2 and 3.335(8) Å and 2.503(5) Å respectively for H-VSe2.
We found the relative energy to be 0.06(2) eV per formula unit at the DMC
level, which indicates that in freestanding form, H-VSe2 is more energetically
favorable than T-VSe2. We went on to estimate the phase diagram between T and
H phase (with DMC accuracy) from the potential energy surface and determined
that a phase transition can be induced by applying strain. In addition, we
benchmarked the magnetic properties such as the spin density and magnetic
moments and we find substantial differences between DMC and DFT+U. This work
demonstrates the success of DMC coupled with the surrogate Hessian line-search
structural optimization technique when applied to a correlated 2D system. The
high quality reference data help clarify the previously inconclusive
theoretical and experimental results regarding T- and H-VSe2, aiding in the
computational metrology goals of JARVIS and NIST. More detailed information
can be found in Ref. Wines  _et al._ , 2023b.

##  III AI/ML

###  III.1 ALIGNN

Non-Euclidean graphs are increasingly being used to represent crystal
structures in deep-learning models. In comparison to composition-only based
descriptors, the graph representation preserves the bond connectivity of
atoms. Graph neural networks (GNN) are deep-learning frameworks which perform
inference on graph data structures, and several high-performing GNN models
have been proposed for the prediction of material properties, including but
not limited to: SchNetSchütt  _et al._ (2018), Crystal Graph Convolutional
Neural Networks (CGCNN)Xie and Grossman (2018), improved Crystal Graph
Convolutional Neural Networks (iCGCNN)Park and Wolverton (2020), MatErials
Graph Network (MEGNet)Chen  _et al._ (2019), and OrbNetQiao  _et al._ (2020).
In these frameworks, the graph nodes represent atoms and encode for elemental
features, while the edges represent bonds and encode for bond distances.
Therefore, only pairwise interactions are explicitly encoded in the materials
representation. Through the use of multiple graph convolutional layers in the
neural network, nodes (atoms) are updated based on neighboring states,
allowing for an implicit handling of many-body interactionsChoudhary and
DeCost (2021).

However, several material properties, for example those related to wave-like
electronic and phononic states, are influenced by local geometric distortions
captured by changes in bond angles. In order to explicitly encode bond angles
and three-body configurations of atoms, we introduced the Atomistic Line Graph
Neural Network (ALIGNN) Choudhary and DeCost (2021) into the suite of JARVIS
tools. Following the original work on line graph neural networks by Chen et
al.Chen, Li, and Bruna (2019), the ALIGNN framework sequentially updates two
graph representations: 1) the crystal graph with nodes representing atoms and
edges representing bonds, and 2) the line graph built from the crystal graph
with nodes representing bonds and edges representing bond pairs sharing a
common atom or triplets of atoms. Note that the edges of the crystal graph and
nodes of the line graph share the same latent representation. Figure 11
depicts how the compositional and structural features of a material are
encoded in both graph representations. The atomistic feature set ($\nu_{i}$
for the $i$th atom) describing a crystal graph node includes the following
elemental descriptors: electronegativity, covalent radius, group number,
block, valence electron count, atomic volume, first ionization energy, and
electron affinityChoudhary and DeCost (2021). The bond features
($\epsilon_{ij}$ for pairs of atoms $i$ and $j$) are the bond distances,
represented using a radial basis function (RBF) expansion. Finally, the
triplet features ($t_{ijk}$ for set of atoms $i$, $j$ and $k$) are an RBF
expansion of the bond angle cosines.

The ALIGNN model was first applied to predict 52 solid-states and molecular
properties, including formation energy, elastic constants, electronic
bandstructure attributes, dielectric constants, and thermoelectric
coefficientsChoudhary and DeCost (2021). In almost every task, the ALIGNN
model outperformed classical force-field inspired descriptors (CFID)Choudhary,
DeCost, and Tavazza (2018) and the original CGCNN modelXie and Grossman (2018)
by yielding a lower mean absolute error (MAE) for predictions using comparable
or improved training speed. In a comparison to 18 other machine learning
algorithms, the ALIGNN model also yields the lowest prediction MAE error for
several tasks including band gap and formation energy prediction, as
documented on the matbench websiteDunn  _et al._ (2020). Since then, the
ALIGNN model has also been used to guide new materials searches in the realm
of metal-organic frameworks for carbon captureChoudhary  _et al._ (2022a) and
high-$T_{c}$ conventional superconductorsChoudhary and Garrity (2022).

Figure 11: Schematic of a crystal and line graph encoding of the Mg_2Si
crystal structure (a). In the crystal graph (b), nodes represent atom sites
and include an atomic feature set consisting of attributes like the
electronegativity ($\chi$), ionization energy ($E$), and volume per atom
($V_{0i}$). The edges in crystal graph represent bonds. Therefore, the edge
features represent bond distances $r_{ij}$ which are encoded in the model
using a radial basis function (RBF). The line graph (c) is constructed from
the previous crystal graph, such that the nodes now represent the bonds of the
crystal. The edges, therefore, represent pairs of bonds with a common atom or
“triplets" featurized by the bond angles, which once again are encoded using a
radial basis function. Note that, for simplicity of the undirected graph
representations, these graphs are constructed by setting the maximum nearest
neighbor value to 1.

Since the initial presentation of the ALIGNN model in 2021Choudhary and DeCost
(2021), additional models built from ALIGNN have been introduced. ALIGNN-d is
an extension of the ALIGNN representation to explicitly include four-body
dihedral angles, which was successfully used to predict the peak location and
intensity in the optical spectra of Cu(II)-aqua complexesHsu  _et al._ (2022).
The de-ALIGNN model introduced by Gong et al.Gong  _et al._ (2022)
concatenates global descriptors of the material, such as average bond length
or lattice parameters, to the learned features in the ALIGNN representation.
Over 13 property prediction tasks, only two phonon-related tasks, phonon
internal energy and heat capacity, showed large (>10 %) prediction improvement
in the de-ALIGNN model versus the original ALIGNN model. In Section III.1.1,
however, we show that phonon properties can be quickly and accurately
predicted using ALIGNN through a direct prediction of the phonon density-of-
statesGurunathan, Choudhary, and Tavazza (2023).

In the following subsections, we will discuss specialized uses of ALIGNN to
predict defect properties, spectral properties, and forces.

####  III.1.1 ALIGNN-Spectra

Figure 12: Performance of the ALIGNN phonon density-of-states (DOS) model.
Panel (a) shows the distribution of ALIGNN-predicted phonon density of states
(DOS) with respect to mean absolute error (MAE), indicating that 78 % of
samples show an MAE of less than 0.086. The example spectra below show the
ALIGNN prediction (colored) against the DFT spectrum (black) to highlight the
types of prediction errors that occur at each MAE level. In panels (b) and
(c), we show that the room temperature heat capacity ($C_{\mathrm{V}}$) and
vibrational entropy ($S_{\mathrm{vib}}$) derived from the ALIGNN phonon DOS
closely corresponds to the target DFT-derived values.

Thus far, the performance of ALIGNN has mainly been discussed in terms of
scalar material property predictions, but the model has also been applied to
predict spectral or frequency-dependent properties. The latter task requires
multi-output predictions, which is relatively less well-developed for machine
learning algorithms. Kaundiya et al. first extended the ALIGNN model to enable
multiple output features for the prediction of the electronic density-of-
states (DOS)Kaundinya, Choudhary, and Kalidindi (2022). Two ALIGNN models
trained using different representations of the DOS were compared: 1) a
discretized electronic DOS with 300 evenly spaced frequency bins (D-ALIGNN),
and 2) a low-dimensional representation of the electronic DOS generated using
an autoenconder network with a latent dimensionality of 8, 12, 16, or 20
features (AE-ALIGNN). The D-ALIGNN model slightly outperformed the AE-ALIGNN
model, but both yielded good prediction accuracy with over 80 % of test
samples showing an MAE of less than 0.2 states per eV per electron.

The phonon DOS is the subject of a later work, which further emphasizes DOS-
derived properties obtained using a weighted integration of the phonon
DOSGurunathan, Choudhary, and Tavazza (2023). These thermal and thermodynamic
properties include the heat capacity ($C_{\mathrm{V}}$), vibrational entropy
($S_{\mathrm{vib}}$), and the phonon-isotope scattering rate
($\tau^{-1}_{\mathrm{i}}$). The phonon DOS ALIGNN model was trained on a
database of 14,000 DFT-computed phonon spectra calculated using the finite-
difference methodChoudhary  _et al._ (2020a). As shown in the histogram and
example spectra of Figure 12a, the spectra in the test set are concentrated at
low prediction error levels and the ALIGNN model does a good job of capturing
the location of peaks and general distribution of phonon modes, although the
shape of the peaks is often altered. The ALIGNN phonon DOS predictions yield
highly accurate estimates of the DOS-derived properties with correlation
coefficients between ALIGNN and DFT values greater than 0.97 for all
properties of interest. A general conclusion shown in this work is that a DOS-
mediated approach outperforms a direct deep-learning approach for phononic
properties. In other words, calculating properties like $C_{\mathrm{V}}$ and
$S_{\mathrm{vib}}$ from the ALIGNN-predicted phonon DOS yields higher accuracy
than training an ALIGNN model to predict $C_{\mathrm{V}}$ or
$S_{\mathrm{vib}}$ directly. More details can be found in Ref. Gurunathan,
Choudhary, and Tavazza, 2023.

####  III.1.2 ALIGNN-FF

In the previous sections, we described the application of the ALIGNN model for
scalar and vector data, which are graph level outputs. Node level outputs such
as forces, charges, and magnetic moments are the motivation for which the
ALIGNN-atomwise model was developed. Specifically, for atomwise properties
such as forces, they should be derivatives of energy and should be equivariant
Batzner  _et al._ (2022) as the material system is rotated. For this
objective, we developed the atomistic line graph neural network-based FF
(ALIGNN-FF) Choudhary  _et al._ (2023b) to model both structurally and
chemically diverse solids with any combination of 89 elements from the
periodic table. To train the ALIGNN-FF model, we used the JARVIS-DFT dataset,
containing around 80000 materials and 4 million energy-force entries (out of
which 307113 are taken).

Figure 13: Energy-volume/expansion-contraction curves for a few example
systems: a) silicon, b) SiO2, c) Ni3Al, d) MoS2 to distinguish polymorphs. We
optimize the structures and then apply volumetric strains between ranges of
-0.05 to 0.05 with an interval of 0.01.

Classical force fields (FFs) based on ML methods show great potential for
large scale simulations of solids. In the past, MLFFs have been primarily been
designed and fitted for specific systems and are not usually transferable to
chemistries beyond the specific training set. However, we demonstrate ALIGNN-
FF applicability beyond specific system-types, as it is built to predict
atomistic properties for solids made of any combination of 89 periodic table
elements. It was validated on predictions of properties such as lattice
constants, and energy-volume curve. As an example, Fig. 13 shows ALIGNN-FF
ability to distinguish the polymorphs of various compounds (Si, SiO2, Ni3Al,
and vdW-bonded MoS2).

ALIGNN-FF can also be used for fast optimization of atomic structures and
structure prediction using evolution algorithms such as genetic algorithms.
When compared to DFT and embedded-atom method (EAM) force fields, ALIGN-FF
produced very similar equation of state curves. Moreover, ALIGNN-FF was used
to optimize crystal structures in the crystallography open database (COD) as
well as in the JARVIS database. For additional testing, ALIGNN-FF was used
along with a genetic algorithm to predict the convex hull of a Ni-Al alloy
system. Promisingly, the resulting convex hull reproduced the expected low
energy structures without generating any unphysical low energy structures for
Ni-Al phase diagram. As timing analysis shows that ALIGNN-FF is over 100 times
faster than DFT methods, it can be used as pre-structure-optimizer before
carrying out DFT calculations. More details on ALIGNN-FF can be found in Ref.
Choudhary  _et al._ , 2023b.

####  III.1.3 ALIGNN-Superconducting

Figure 14: Atomistic line graph neural network based deep-learning (DL)
regression model performance on 5 % test set for a) Debye temperature and b)
DOS. Classical force-field descriptor (CFID) (c,d,e) and DL (f,g,h) based
regression model performance on 5 % test set for DFT calculated transition
temperature ($T_{C}$), EPC parameter $\omega_{log}$, and EPC parameter
$\lambda$. In (f), we show performance with direct $T_{C}$ prediction (red
color), $T_{C}$ prediction with direct prediction of $\omega_{log}$ and
$\lambda$ and then using McMillan-Allen-Dynes formula McMillan (1968) (green
color) and $T_{C}$ prediction with Eliashberg function (black color).

We developed deep-learning models to accelerate both our initial BCS-inspired
screening and our calculation of the EPC parameters (see Section II.1.3).
While the BCS pre-screening step is less expensive than a full EPC
calculation, it still requires the DOS at the Fermi level and $\theta_{D}$,
which can be computationally expensive. Therefore, we developed regression
models to predict these properties directly from an arbitrary crystal
structure, using the large datasets available in the JARVIS-DFT database. Our
results of these models on 5 % held-out test sets are shown in Fig. 14. The
baseline model MAE consists simply of the mean of the training data applied to
the 5 % test data. We observe that the MAE for the Debye temperature is 49 K
and for the DOS is 1.5 staes per eV per number of electrons. The baseline
model MAE for the Debye temperature and DOS are 145.5 K and 3.62 staes per eV
per number of electrons, respectively. In addition, we developed machine-
learning models to directly predict EPC properties using our database of 626
EPC parameters of dynamically stable materials explicitly computed with DFT-
PT. Two methods were used: CFID and ALIGNN. Specifically, we trained models
for the McMillan-Allen-Dynes transition temperature ($T_{C}$) and the EPC
parameters ($\omega_{log}$ and $\lambda$). We note that usually ML models
require larger datasets, but we display preliminary useful results with our
current smaller dataset, which will continue to grow.

CFID based performances are shown in Fig. 14c), Fig. 14d) and Fig. 14e) for
$T_{C}$, $\omega_{log}$ and $\lambda$. Similarly, ALIGNN based performances
are shown in Fig. 14f, Fig. 14g and Fig. 14h. We observe that the MAE using
the CFID approach for $T_{C}$, $\omega_{log}$ and $\lambda$ are 1.84 K, 53.48
K and 0.19. Additionally, the MAEs for the ALIGNN approach are 1.84 K, 37.43 K
and 0.14 respectively. ALIGNN outperforms CFID in predicting $\omega_{log}$,
but the performances for the other quantities are similar. Moreover, we notice
that it is significantly easier to learn $\omega_{log}$ than $T_{C}$ and
$\lambda$. We observe that the model for $\lambda$ is only slightly better
than the baseline model. Using ALIGNN for $\omega_{log}$ and $\lambda$, we
predict TC with a MAE of 1.77 K.

We attempt an alternate method to directly predict the Eliashberg function
using the ALIGNN model. We choose an energy range of 0 to 100 meV with 1 meV
bin size and predict the Eliashberg functions. We find that the ALIGNN model
does a good job of capturing most of the peaks. We calculate the $T_{C}$ using
the ALIGNN-based Eliashberg function predictions, and find the MAE to be 1.39
K, which improves on our direct prediction method above by 24 %. This implies
that learning more fundamental and information-rich quantities such as
Eliashberg functions can be useful for ML approaches with limited data, as
compared to direct predictions of integrated quantities. More details can be
found in Ref. Choudhary and Garrity, 2022.

###  III.2 AtomVision

Figure 15: Schematic of select capabilities in the AtomVision package. (a) An
example 2D crystal structure is sampled from the JARVIS-2D DFT
databaseChoudhary  _et al._ (2020a) and a Rutherford scattering contrast model
is applied to produce a synthetic HAADF-STEM image (b). Next, image analysis
tasks implemented in the package are demonstrated, including: (c) localizing
atom positions, (d) generating a non-Euclidean graph over the image, and (e)
reconstructing the image from a low-dimensional representation using an
autoencoder.

The AtomVision library is designed to be a general toolkit for both generating
and analyzing image databasesChoudhary  _et al._ (2023a). Currently, the
library implements contrast models that can be used to simulate scanning
tunneling microscope (STM) and high angle annular dark field (HAADF) scanning
transmission electron microscope (STEM) images given the crystal structure,
and easily generate databases of simulated atomistic images. The STM images
are computed using the Tersoff-Hamann formalism, which models the STM tip as
an s-wave spherical stateTersoff and Hamann (1983). The HAADF STEM images are
simulated using a convolution approximation often applied to thin film
samples. This method convolves a point-spread function centered around the
probe with a transmission function that considers the atomic number of the
imaged specimenCombs  _et al._ (2019). The atomic number ($Z$) dependence of
the intensity of the imaged atom is roughly proportional to $Z^{2}$, as
predicted by Rutherford scatteringYamashita  _et al._ (2018). Relevant images
can also be curated from the literature through integration with the ChemNLP
natural language processing packageChoudhary and Kelley (2022a) (more
information in Section III.3). In contrast to other image datasets, which
focus on a specific chemistry, the AtomVision package prioritizes chemical and
structural diversity.

Numerous analysis tools are also provided, primarily based on machine learning
methods. Although the datasets published with the package are focused on STM
and STEM images, the analysis scripts can be used to easily train deep
learning methods on any user-provided image data by simply providing directory
paths for the training and test set of images.

First, the t-distributed stochastic neighbor embedding (t-SNE)van der Maaten
and Hinton (2008) is implemented, which performs a dimensionality reduction in
the high-dimensional image data, allowing the spread of samples (images) to be
visualized in a two or three-dimensional plot. The Euclidean distance between
data points in a t-SNE plot relates to their similarity; however, the
distances can only be interpreted qualitatively. Images that cluster together
in the plot will tend to be more similar in their featurization, be it pixel
intensity, red, green, blue triplets, or graph representations of images,
which will be described in the next paragraph.

One critical image analysis task that is implemented in AtomVision, known as
segmentation, consists of classifying pixels based on whether they compose the
background or an object of interest. We utilize the U-Net pretrained
modelRonneberger, Fischer, and Brox (2015) to distinguish atoms from
background in the atomistic images. After this pixelwise classification, we
can identify atom positions as well as characteristics of their intensity peak
(e.g. peak width, maximum intensity) using a blob detection method implemented
in the scikit-learn packagePedregosa  _et al._ (2011a). With the atom
positions identified, it is then possible to construct a non-Euclidean graph
representation of the atomistic image. The atom peaks in the image become the
nodes, which are featurized using the blob characteristics described above,
and edges (representing bond vectors) are formed between atoms using the k-d
tree nearest neighbor search algorithm. An additional line graph can then be
constructed, as in the ALIGNN model, where bond vectors are the graph nodes
and bond angles are the graph edges.

There are then two main representations of images in the AtomVision package:
2D arrays of pixel intensities, and the graph representation. The AtomVision
package allows the user to train neural networks based on either image
representation to perform tasks such as image classification. The pixel-based
data can be used to train convolutional neural networks (CNN) based on popular
frameworks that include VGGSimonyan and Zisserman (2014), ResNetHe  _et al._
(2015), and DenseNetHuang  _et al._ (2016) amongst others that are included in
the AtomVision package. Similarly, the graph-based data can be used to train
graph neural networks like the ALIGNN method described in Section III.1. We
demonstrate both model types in an image classification task performed on the
HAADF STEM image dataset in which we train a model to classify images into the
2D Bravais lattice type of the material in the image. In this particular test,
the best performing CNN was the DenseNet with a classification accuracy of 83
%, while the ALIGNN classifier had an accuracy of 78 %.

The pixelated images in the atomistic image datasets are described by 50,176
pixel intensities, and therefore exist in a very high-dimensional feature
space. The manifold hypothesis suggests that the underlying structure of the
data can be described by relatively fewer dimensions using feature extraction
methods. The AtomVision package facilitates training and usage of an
autoencoder network, which can create a low-dimensional representation of the
image and then reconstruct the pixelated image from that latent
representation.

The final functionality currently implemented in the AtomVision package is a
super-resolution generative adversarial network (SRGAN) modelLedig  _et al._
(2017), which can upsample a low-resolution image to produce a high-resolution
image. The SRGAN uses two separate deep learning model that compete with each
other during optimization: 1) the generator produces a super-resolution image
by first performing a feature extraction step, akin to the autoencoder model,
and then interpolating within the learned latent representation; and 2) the
discriminator should classify the image as either real or generated. As a
result of the competition loop, the generator learns to “trick" the
discriminator model with increasingly realistic super-resolution images. We
apply this model to the atomistic images and demonstrate a successful
conversion of a low resolution image (64x64 pixels) to a high resolution image
(256x256 pixels), showing the same image window. Additional information about
the AtomVision package can be found in Ref. Choudhary  _et al._ , 2023a.

###  III.3 ChemNLP

Figure 16: A schematic overview of ChemNLP. The goal of ChemNLP is to provide
a software toolkit with integrated dataset and comprehensive AI/ML tools for
expanding natural language processing technique applications for tasks such as
text classification, clustering, named entity recognition, abstractive
summarization and text generation.

Much of the data on materials science is available in text format in the form
of articles that are not easily amenable to standard automated analysis. To
address this barrier, we developed ChemNLP Choudhary and Kelley (2022a), a
library that utilizes natural language processing (NLP) for chemistry and
materials science data. Currently, ChemNLP is based on the publicly available
platforms such arXiv (https://arxiv.org/), Pubchem
(https://pubchem.ncbi.nlm.nih.gov/) datasets and Huggingface
(https://huggingface.co/) Wolf  _et al._ (2020) libraries.

ChemNLP organizes the NLP data and tools for materials chemistry application
in a format suitable for model training. In addition to data curation, it
allows the integration of useful analyses such as: 1) classifying and
clustering texts based on their categories, 2) named entity recognition for
large-scale text-mining, 3) abstractive summarization for generating titles of
articles from abstracts, 4) text generation for suggesting abstracts from
titles, 5) integration with density functional theory datasets for
identification of potential candidate materials, and 6) web-interface
development for text and reference query. A schematic of the ChemNLP library
is given in Fig. 16.

ChemNLP uses several conventional machine learning algorithms as well as state
of the art transformer models for comparison and validation. Some of the
algorithms in ChemNLP include support vector machines, random forest, graph
neural networks, Google’s T5 Raffel  _et al._ (2020), OpenAI’s GPT-2 Brown
_et al._ (2020) and Meta AI’s OPT Zhang  _et al._ (2022) transformer models,
all of which are fine-tuned on materials chemistry text data. The web-app of
ChemNLP allows for the searching of various text information (such as material
properties, synthesis procedure, etc.) given the chemistry information
(stoichiometry). As an application of transformer models, ChemNLP showed that
fine-tuning general large language models (LLMs) for abstract to title and
vice-versa can result in an improvement of performance compared to original
pre-trained model.

###  III.4 Uncertainty Analysis

Uncertainty quantification in AI-based predictions of material properties is
of great importance for the success and reliability of artificial intelligence
(AI) applications in materials science. Although confidence intervals are
commonly reported for ML models, prediction intervals, i.e., the evaluation of
the uncertainty on each prediction, are not as widely available. For this
reason, efforts have been focused on uncertainty prediction for ML models
Tavazza, DeCost, and Choudhary (2021) in JARVIS. Quantile loss function,
machine learning the prediction intervals directly, and using Gaussian
processes were used to obtain individual uncertainty and were compared and
tested on 12 ML-physical properties. All data for training and testing were
taken from the JARVIS-DFT database, and the codes developed for computing the
prediction intervals are available through JARVIS-tools. The data set size
depended on the property under examination, as computing some properties is
much more involved than computing others. The largest datasets were available
for formation energy (35885 materials), energy above the convex hull (34880
materials) and band gap computed using the OptB88vdW functional (35932
materials). The smallest data set is for exfoliation energies, counting only
806 data points.

To summarize our findings, we determined that modeling of the individual
uncertainties directly is slightly favored, since it minimizes the over- and
underestimation of the predicted errors in most cases while also being the
easiest methodology to implement and fit Tavazza, DeCost, and Choudhary
(2021). We also find that this Gaussian processes give a good estimate for
prediction intervals, although a bit overestimated, but are more time
consuming to fit than the other approaches. Using the Quantile approach
requires fitting 3 different models. Machine learning the error directly has
the enormous advantage of allowing the use of any loss function. However, it
requires splitting the data set in three parts, which could be a problem if
the data set is small to begin with. More details of this work can be found in
Ref. Tavazza, DeCost, and Choudhary, 2021.

##  IV Quantum Computation

Figure 17: Flow chart showing the steps involved in predicting electron and
phonon properties of a solid on a quantum computer (JARVIS-AtomQC package).

One of the most promising near-term applications of quantum computers is
solving quantum chemistry problems Nielsen and Chuang (2001). Quantum
algorithms such as variational quantum eigen solver (VQE) Peruzzo  _et al._
(2014) and variational quantum deflation (VQD) Higgott, Wang, and Brierley
(2019) have previously been applied to molecules Peruzzo  _et al._ (2014), but
there is a need to implement these algorithms for periodic solids. As a recent
addition to JARVIS, we have added quantum computation tools as the AtomQC
package.

In our recent work Choudhary (2021), we used WTBH approaches to demonstrate
the application of VQE and VQD to accurately predict electronic and phonon
band structure properties of several elemental and multi-component materials.
Specifically, we applied the VQE–VQD algorithms for 307 spin–orbit coupling
based electronic WTBHs and 933 finite-difference based phonon WTBHs. Although
this work deals with the single-particle picture, we believe our work can pave
the way for solving interacting Hamiltonians (such as dynamical mean-field
theory (DMFT) and Green’s function with screened Coulomb potential theory
(GW)), which can be much more suitable to simulate on quantum computers than
classical computers. We provide a preliminary workflow that can be used to
integrate the VQD algorithms with the DMFT-based solving of the lattice
Green’s function. This full quantum computation workflow is given in Fig. 17.
Our publicly available WTBH model solvers can be used for testing other
quantum algorithms and models. More information on this addition to JARVIS can
be found in Ref. Choudhary, 2021.

##  V Experiments

Although, majority of the data in JARVIS is originated from computation, we
use data validation and benchmarking with experiments whenever applicable. In
some cases, we obtain experimental data from literature or from in-house
standard reference material (SRM) data at NIST. In other cases, we perform our
own experiments along with our computational efforts. This experimental data
includes XRD and neutron diffraction patterns, CO2 adsorption isotherms Nguyen
_et al._ (2018), magnetic susceptibility measurements Wines  _et al._ (2023a),
spectroscopic ellipsometry dielectric functions, Raman spectra, STM/STEM
images and transport measurements.

Figure 18: Experimental zero-field-cooled measurements of the DC magnetic
susceptibility (using a magnetic field strength of 0.01 T) as a function of
temperature, in order to determine $T_{c}$ for layered structures: a) 2H
NbSe2, b) 2H-NbS2, c) FeSe, and d) ZrSiS.

Most recently and notably, we have conducted our own experiments for magnetic
topological materials and 2D superconductors. With regards to magnetic
toplogical materials, we measured the Anomalous Hall effect of CoNb3S6 and
conducted inverse spin-Hall signal measurements for Mn3Ge, two materials
theoretically predicted to be topological materials in Ref. Choudhary  _et
al._ , 2021a (see Section II.1.1). We performed zero-field-cooled magnetometry
experiments to determine the critical temperature of selected 2D
superconductors to verify the theoretical predictions in Ref. Wines  _et al._
, 2023a (see Section II.1.3). We conducted these experiments for layered
2H-NbSe2, 2H-NbS2, FeSe, and ZrSiS. Fig. 18 depicts the measured magnetic
susceptibility (using a magnetic field strength of 0.01 T) as a function of
temperature. We observe that out of these layered materials, 2H-NbSe2 has a
$T_{c}$ of 8.3 K, 2H-NbS2 has a $T_{c}$ of 7.1 K, FeSe has a $T_{c}$ of 7.5 K,
and ZrSiS does not have a superconducting transition due to the measured
decreasing magnetic susceptibility with increasing temperature. We discuss
these measurements within the context of our DFT-computed results in Ref.
Wines  _et al._ , 2023a.

These experimental datasets are now being integrated in the JARVIS-Leaderboard
for benchmarking and validation purposes (see Section VIII). Some simulated
experimental data, such as XRD patterns, can be computed with JARVIS-Tools. As
the experimental datasets in JARVIS are not exceedingly large at the moment,
we can currently apply machine learning algorithms on computational data, and
in the future, apply the same pipeline to experimental data.

##  VI Optimade and Nomad

Data in JARVIS are being integrated within large-scale data efforts such as
NOMAD Draxl and Scheffler (2018) and OPTIMADE Andersen  _et al._ (2021) for
sustainability, and inter-operatability.

The Open Databases Integration for Materials Design (OPTIMADE) consortium has
designed a universal application programming interface (API) to make materials
databases accessible and interoperable. The OPTIMADE API has a set of well
defined key-value pairs such as chemical formula name, number of elements etc.
for each atomic structure which allows sending a universal API search for
multiple data-efforts. The implementation required a django-rest-framework
integration with specific data-models, pagination and other specification as
detailed in OPTIMADE to be compatible with other infrastructures.

Similarly, NOMAD project allows storage of raw data files and provides several
interactive GUI tools. Although, JARVIS has its own storage mechanism, having
data distributed on platforms such as NOMAD and OPTIMADE allows enhanced
transparency, which is essential for large scale data-driven materials design.

##  VII JARVIS Notebooks

A collection of interactive python notebooks are hosted in the jarvis-tools-
notebooks GitHub RepositoryJar  that can be run on a user’s local computer or
easily through a cloud-based python development environment. All package
installation steps are included in the notebooks such that they can be
executed and edited in a standalone fashion, allowing users to easily make use
of JARVIS models. These interactive notebooks are meant to supply an example
calculation that will execute quickly and reproduce a portion of the results
in a JARVIS-associated publication. The collection of notebooks include
machine learning models that allow users to train and utilize ALIGNN or
AtomVision models for material property prediction and image classification.
There are also several electronic structure and atomistic calculation
notebooks that analyze DFT, tight-binding, or MD outputs to calculate material
properties including elastic properties, spin-orbit spillage, dielectric
functions, thermoelectric and photovoltaic properties. Finally, a notebook
based on the AtomQC and qiskitQis (2021) packages for quantum computation is
provided.

##  VIII Leaderboard

The JARVIS-Leaderboard usnistgov (2023) project provides benchmark-
performances of various methods for materials science applications. This
platform allows users to set up benchmarks and make contributions in the form
of datasets, codes and meta-data submissions. These contributions are compared
with experimental data where applicable and the accuracy of each contribution
is assigned a “score" (MAE with respect to the experimental measurement). Some
of the categories are: Artificial Intelligence (AI), Electronic Structure
(ES), Quantum Computation (QC) and Experiments (EXP). In addition to
prediction results, we attempt to capture the underlying software, hardware
and instrumental frameworks to enhance reproducibility and method validation.
Currently there are over 1000 user contributions using over 100 different
methods, and these numbers are growing rapidly.

##  IX External Outreach

In addition to the databases, tools and applications that are part of the
JARVIS infrastructure, there has been substantial effort devoted to outreach
in the materials science research community. The JARVIS team has annually
hosted the Artificial Intelligence for Materials Science (AIMS) and Quantum
Matters in Materials Science (QMMS) workshops, where speakers have been
invited from academia, government and industry to discuss key achievements and
challenges in the respective fields. Topics presented at AIMS include: dataset
and tools for employing AI for materials, integrating experiments with AI
techniques, graph neural networks, comparison of AI techniques for materials,
the challenges of applying AI to materials, uncertainty quantification and
building trust in AI predictions, generative modeling, using AI to develop
classical force-fields, natural language processing and AI-guided autonomous
experimentation. Topics presented at QMMS include: discovery and
characterization of new materials; optimization of known quantum materials,
investigation of defect induced behavior and transitions; electronics,
spintronics, quantum memory applications, challenges in applying quantum
information systems technologies at industrial scale, and accurate many-body
computational methods to treat quantum materials.

The JARVIS team has also organized a series of hands-on workshops at different
academic and government institutions, known as JARVIS-Schools. JARVIS-Schools
consist of a tutorial and hands-on session to introduce open-access databases
and tools for materials-design. These sessions are accompanied by a series of
power-point presentations on the core-topics, Google-Collab/Jupyter notebook
examples and discussion. The hands-on session/discussion topics include:
electronic structure calculations (DFT, tight-binding etc.), density
functional theory for predicting properties (e.g., solid-state materials),
machine learning (for atomistic, image and text data), quantum computation and
its applications to materials, and classical force-field calculations for
large scale properties. An updated calendar of JARVIS events can be found
here: https://jarvis.nist.gov/events/.

There are various mechanisms to collect external usage data for JARVIS inside
and outside the materials science community. These sources include the number
of users registered for the JARVIS API, Google analytics results for viewers,
number of citations for papers, downloads of software tools on GitHub, number
of views and downloads from the Figshare repository, number of attendees in
the AIMS/QMMS workshops and JARVIS-Schools and number of collaborators
developed inside and outside NIST from academia, national labs and industry. A
wide usage of JARVIS resulted in JARVIS being highlighted as a standard
platform for materials design in the NIST US CHIPS Acts strategic plan
(https://www.nist.gov/chips/implementation-strategy).

##  X Data Availability and Software

The data and software mentioned in this review article are available at
https://jarvis.nist.gov/ and https://github.com/usnistgov/jarvis. JARVIS-Tools
is an open-access software package for atomistic data-driven materials design.
JARVIS-Tools can be used for a) setting up calculations, b) analysis and
informatics, c) plotting, d) database development and e) web-page development.
Software used in workflow tasks for pre-processing, executing, and post-
processing include: VASP Kresse and Furthmüller (1996a, b), Quantum Espresso
Giannozzi  _et al._ (2009, 2020), Wien2k Blaha  _et al._ (2020), BoltzTrap
Madsen and Singh (2006), Wannier90 Mostofi  _et al._ (2014), QMCPACK Kim  _et
al._ (2018); Kent  _et al._ (2020), LAMMPS Thompson  _et al._ (2022), scikit-
learn Pedregosa  _et al._ (2011a), TensorFlow Abadi  _et al._ (2015), LightGBM
Ke  _et al._ (2017), Qiskit Qis (2021), Tequila Kottmann  _et al._ (2021),
Pennylane Bergholm  _et al._ (2022); Arrazola  _et al._ (2023), Deep Graph
Library Wang  _et al._ (2020), PyTorch Paszke  _et al._ (2019). JARVIS
databases such as JARVIS-DFT, FF, ML, WannierTB, Solar, and STM can be
downloaded. Raw input and output files can be accessed from JARVIS databases
to enhance reproducibility in calculations. Different descriptors, graphs and
datasets for training machine learning models are also included in JARVIS-
Tools. Capabilities can be easily be extended to HPC systems (Torque/PBS and
SLURM). Documentation for JARVIS-Tools, including installation instructions,
can be found here: https://jarvis-tools.readthedocs.io.

##  XI Notes

Certain commercial equipment or materials are identified in this paper to
adequately specify the experimental procedures. In no case does the
identification imply recommendation or endorsement by NIST, nor does it imply
that the materials or equipment identified are necessarily the best available
for the purpose. The authors declare no competing interests. Please note that
the use of commercial software (VASP) does not imply recommendation by the
National Institute of Standards and Technology.

##  XII Acknowledgments

All authors thank the National Institute of Standards and Technology for
funding, computational, and data-management resources. K.C. thanks the
computational support from XSEDE (Extreme Science and Engineering Discovery
Environment) computational resources under allocation number TG-DMR 190095.
Contributions from K.C. were supported by the financial assistance award
70NANB19H117 from the U.S. Department of Commerce, National Institute of
Standards and Technology.

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