Materials Learning Algorithms (MALA): Scalable machine learning for electronic structure calculations in large-scale atomistic simulations

Cangi, Attila; Fiedler, Lenz; Brzoza, Bartosz; Shah, Karan; Callow, Timothy J.; Kotik, Daniel; Schmerler, Steve; Barry, Matthew Campbell; Goff, James Michael; Rohskopf, Andrew Dale; Vogel, Dayton Jonathan; Modine, Normand A.; Thompson, Aidan P.; Rajamanickam, Sivasankaran

doi:10.1016/j.cpc.2025.109654

Materials Learning Algorithms (MALA): Scalable machine learning for electronic structure calculations in large-scale atomistic simulations

Journal Article · Fri May 09 00:00:00 EDT 2025 · Computer Physics Communications

DOI:https://doi.org/10.1016/j.cpc.2025.109654· OSTI ID:2583701

^[1]; Fiedler, Lenz ^[1]; Brzoza, Bartosz ^[1]; Shah, Karan ^[1]; Callow, Timothy J. ^[1]; Kotik, Daniel ^[1]; Schmerler, Steve ^[2]; ^[3]; Goff, James Michael ^[3]; Rohskopf, Andrew Dale ^[3]; Vogel, Dayton Jonathan ^[3]; Modine, Normand A. ^[3]; ^[3]; ^[3]

Helmholtz-Zentrum Dresden-Rossendorf (HZDR) (Germany); Center for Advanced Systems Understanding, Görlitz (Germany)
Helmholtz-Zentrum Dresden-Rossendorf (HZDR) (Germany)
Sandia National Laboratories (SNL-NM), Albuquerque, NM (United States)

We present the Materials Learning Algorithms (MALA) package, a scalable machine learning framework designed to accelerate density functional theory (DFT) calculations suitable for large-scale atomistic simulations. Using local descriptors of the atomic environment, MALA models efficiently predict key electronic observables, including local density of states, electronic density, density of states, and total energy. The package integrates data sampling, model training and scalable inference into a unified library, while ensuring compatibility with standard DFT and molecular dynamics codes. We demonstrate MALA's capabilities with examples including boron clusters, aluminum across its solid-liquid phase boundary, and predicting the electronic structure of a stacking fault in a large beryllium slab. Scaling analyses reveal MALA's computational efficiency and identify bottlenecks for future optimization. With its ability to model electronic structures at scales far beyond standard DFT, MALA is well suited for modeling complex material systems, making it a versatile tool for advanced materials research.

View Accepted Manuscript (DOE)

Research Organization:: Sandia National Laboratories (SNL-NM), Albuquerque, NM (United States)

Sponsoring Organization:: USDOE National Nuclear Security Administration (NNSA)

Grant/Contract Number:: NA0003525

OSTI ID:: 2583701

Alternate ID(s):: OSTI ID: 2585662

Report Number(s):: SAND--2025-06723J

Journal Information:: Computer Physics Communications, Journal Name: Computer Physics Communications Vol. 314; ISSN 0010-4655

Publisher:: ElsevierCopyright Statement

Country of Publication:: United States

Language:: English

References (93)

Die Berechnung optischer und elektrostatischer Gitterpotentiale Ewald, P. P. Annalen der Physik, Vol. 369, Issue 3 https://doi.org/10.1002/andp.19213690304	journal	January 1921
Zur Quantentheorie der Molekeln Born, M.; Oppenheimer, R. Annalen der Physik, Vol. 389, Issue 20 https://doi.org/10.1002/andp.19273892002	journal	January 1927
Boron‐Induced Electronic‐Structure Reformation of CoP Nanoparticles Drives Enhanced pH‐Universal Hydrogen Evolution Cao, Erping; Chen, Zhimin; Wu, Hao Angewandte Chemie International Edition, Vol. 59, Issue 10 https://doi.org/10.1002/anie.201915254	journal	January 2020
Accelerating VASP electronic structure calculations using graphic processing units Hacene, Mohamed; Anciaux-Sedrakian, Ani; Rozanska, Xavier Journal of Computational Chemistry, Vol. 33, Issue 32 https://doi.org/10.1002/jcc.23096	journal	August 2012
Nonlinear gradient denoising: Finding accurate extrema from inaccurate functional derivatives Snyder, John C.; Rupp, Matthias; Müller, Klaus-Robert International Journal of Quantum Chemistry, Vol. 115, Issue 16 https://doi.org/10.1002/qua.24937	journal	May 2015
Fast Parallel Algorithms for Short-Range Molecular Dynamics Plimpton, Steve Journal of Computational Physics, Vol. 117, Issue 1 https://doi.org/10.1006/jcph.1995.1039	journal	March 1995
An Introduction to Orbital-Free Density Functional Theory Lignères, Vincent L.; Carter, Emily A. Handbook of Materials Modeling https://doi.org/10.1007/978-1-4020-3286-8_9	book	January 2005
Progress on New Approaches to Old Ideas: Orbital-Free Density Functionals Karasiev, Valentin V.; Chakraborty, Debajit; Trickey, S. B. Many-Electron Approaches in Physics, Chemistry and Mathematics https://doi.org/10.1007/978-3-319-06379-9_6	book	January 2014
Beyond Manual Tuning of Hyperparameters Hutter, Frank; Lücke, Jörg; Schmidt-Thieme, Lars KI - Künstliche Intelligenz, Vol. 29, Issue 4, p. 329-337 https://doi.org/10.1007/s13218-015-0381-0	journal	July 2015
Efficiency of ab-initio total energy calculations for metals and semiconductors using a plane-wave basis set Kresse, G.; Furthmüller, J. Computational Materials Science, Vol. 6, Issue 1, p. 15-50 https://doi.org/10.1016/0927-0256(96)00008-0	journal	July 1996
Direct search methods: then and now Lewis, Robert Michael; Torczon, Virginia; Trosset, Michael W. Journal of Computational and Applied Mathematics, Vol. 124, Issue 1-2 https://doi.org/10.1016/S0377-0427(00)00423-4	journal	December 2000
AiiDA: automated interactive infrastructure and database for computational science Pizzi, Giovanni; Cepellotti, Andrea; Sabatini, Riccardo Computational Materials Science, Vol. 111 https://doi.org/10.1016/j.commatsci.2015.09.013	journal	January 2016
Learning models for electron densities with Bayesian regression Schmidt, Eric; Fowler, Andrew T.; Elliott, James A. Computational Materials Science, Vol. 149 https://doi.org/10.1016/j.commatsci.2018.03.029	journal	June 2018
Workflows in AiiDA: Engineering a high-throughput, event-based engine for robust and modular computational workflows Uhrin, Martin; Huber, Sebastiaan P.; Yu, Jusong Computational Materials Science, Vol. 187 https://doi.org/10.1016/j.commatsci.2020.110086	journal	February 2021
Machine learning electron density in sulfur crosslinked carbon nanotubes Alred, John M.; Bets, Ksenia V.; Xie, Yu Composites Science and Technology, Vol. 166 https://doi.org/10.1016/j.compscitech.2018.03.035	journal	September 2018
VASP on a GPU: Application to exact-exchange calculations of the stability of elemental boron Hutchinson, M.; Widom, M. Computer Physics Communications, Vol. 183, Issue 7 https://doi.org/10.1016/j.cpc.2012.02.017	journal	July 2012
The PseudoDojo: Training and grading a 85 element optimized norm-conserving pseudopotential table van Setten, M. J.; Giantomassi, M.; Bousquet, E. Computer Physics Communications, Vol. 226 https://doi.org/10.1016/j.cpc.2018.01.012	journal	May 2018
LAMMPS - a flexible simulation tool for particle-based materials modeling at the atomic, meso, and continuum scales Thompson, Aidan P.; Aktulga, H. Metin; Berger, Richard Computer Physics Communications, Vol. 271 https://doi.org/10.1016/j.cpc.2021.108171	journal	February 2022
Spectral neighbor analysis method for automated generation of quantum-accurate interatomic potentials Thompson, A. P.; Swiler, L. P.; Trott, C. R. Journal of Computational Physics, Vol. 285 https://doi.org/10.1016/j.jcp.2014.12.018	journal	March 2015
Atomic cluster expansion: Completeness, efficiency and stability Dusson, Geneviève; Bachmayr, Markus; Csányi, Gábor Journal of Computational Physics, Vol. 454 https://doi.org/10.1016/j.jcp.2022.110946	journal	April 2022
Permutation-adapted complete and independent basis for atomic cluster expansion descriptors Goff, J. M.; Sievers, C.; Wood, M. A. Journal of Computational Physics, Vol. 510 https://doi.org/10.1016/j.jcp.2024.113073	journal	August 2024
Boron modulating electronic structure of FeN4C to initiate high-efficiency oxygen reduction reaction and high-performance zinc-air battery Zhao, Xue; Li, Xue; Bi, Zenghui Journal of Energy Chemistry, Vol. 66, p. 514-524 https://doi.org/10.1016/j.jechem.2021.08.067	journal	March 2022
Kokkos: Enabling manycore performance portability through polymorphic memory access patterns Carter Edwards, H.; Trott, Christian R.; Sunderland, Daniel Journal of Parallel and Distributed Computing, Vol. 74, Issue 12 https://doi.org/10.1016/j.jpdc.2014.07.003	journal	December 2014
Physics-Inspired Structural Representations for Molecules and Materials Musil, Felix; Grisafi, Andrea; Bartók, Albert P. Chemical Reviews, Vol. 121, Issue 16 https://doi.org/10.1021/acs.chemrev.1c00021	journal	July 2021
Learning Electron Densities in the Condensed Phase Lewis, Alan M.; Grisafi, Andrea; Ceriotti, Michele Journal of Chemical Theory and Computation, Vol. 17, Issue 11 https://doi.org/10.1021/acs.jctc.1c00576	journal	October 2021
Explicit Multielement Extension of the Spectral Neighbor Analysis Potential for Chemically Complex Systems Cusentino, M. A.; Wood, M. A.; Thompson, A. P. The Journal of Physical Chemistry A, Vol. 124, Issue 26 https://doi.org/10.1021/acs.jpca.0c02450	journal	May 2020
Transferable Machine-Learning Model of the Electron Density Grisafi, Andrea; Fabrizio, Alberto; Meyer, Benjamin ACS Central Science, Vol. 5, Issue 1 https://doi.org/10.1021/acscentsci.8b00551	journal	December 2018
Linear Scaling Self-Consistent Field Calculations with Millions of Atoms in the Condensed Phase VandeVondele, Joost; Borštnik, Urban; Hutter, Jürg Journal of Chemical Theory and Computation, Vol. 8, Issue 10 https://doi.org/10.1021/ct200897x	journal	March 2012
Understanding Modern Molecular Dynamics: Techniques and Applications Tuckerman, Mark E.; Martyna, Glenn J. The Journal of Physical Chemistry B, Vol. 104, Issue 2 https://doi.org/10.1021/jp992433y	journal	January 2000
Learning representations by back-propagating errors Rumelhart, David E.; Hinton, Geoffrey E.; Williams, Ronald J. Nature, Vol. 323, Issue 6088 https://doi.org/10.1038/323533a0	journal	October 1986
Bypassing the Kohn-Sham equations with machine learning Brockherde, Felix; Vogt, Leslie; Li, Li Nature Communications, Vol. 8, Issue 1 https://doi.org/10.1038/s41467-017-00839-3	journal	October 2017
Machine learning electronic structure methods based on the one-electron reduced density matrix Shao, Xuecheng; Paetow, Lukas; Tuckerman, Mark E. Nature Communications, Vol. 14, Issue 1 https://doi.org/10.1038/s41467-023-41953-9	journal	October 2023
Solving the electronic structure problem with machine learning Chandrasekaran, Anand; Kamal, Deepak; Batra, Rohit npj Computational Materials, Vol. 5, Issue 1 https://doi.org/10.1038/s41524-019-0162-7	journal	February 2019
Performant implementation of the atomic cluster expansion (PACE) and application to copper and silicon Lysogorskiy, Yury; Oord, Cas van der; Bochkarev, Anton npj Computational Materials, Vol. 7, Issue 1 https://doi.org/10.1038/s41524-021-00559-9	journal	June 2021
Predicting electronic structures at any length scale with machine learning Fiedler, Lenz; Modine, Normand A.; Schmerler, Steve npj Computational Materials, Vol. 9, Issue 1 https://doi.org/10.1038/s41524-023-01070-z	journal	June 2023
Intrinsically flexible all-carbon-nanotube electronics enabled by a hybrid organic–inorganic gate dielectric Huang, Qiuyue; Wang, Jialiang; Li, Chenglin npj Flexible Electronics, Vol. 6, Issue 1 https://doi.org/10.1038/s41528-022-00190-8	journal	July 2022
Synergistic polarization engineering of dielectric towards low-voltage high-mobility solution-processed ultraflexible organic transistors Zhang, Mingxin; Wang, Xue; Sun, Jing npj Flexible Electronics, Vol. 8, Issue 1 https://doi.org/10.1038/s41528-024-00316-0	journal	May 2024
Theory-guided design of catalytic materials using scaling relationships and reactivity descriptors Zhao, Zhi-Jian; Liu, Sihang; Zha, Shenjun Nature Reviews Materials, Vol. 4, Issue 12 https://doi.org/10.1038/s41578-019-0152-x	journal	November 2019
Array programming with NumPy Harris, Charles R.; Millman, K. Jarrod; van der Walt, Stéfan J. Nature, Vol. 585, Issue 7825 https://doi.org/10.1038/s41586-020-2649-2	journal	September 2020
Control of proton transport and hydrogenation in double-gated graphene Tong, J.; Fu, Y.; Domaretskiy, D. Nature, Vol. 630, Issue 8017, p. 619-624 https://doi.org/10.1038/s41586-024-07435-8	journal	June 2024
SciPy 1.0: fundamental algorithms for scientific computing in Python Virtanen, Pauli; Gommers, Ralf; Oliphant, Travis E. Nature Methods https://doi.org/10.1038/s41592-019-0686-2	journal	February 2020
AiiDA 1.0, a scalable computational infrastructure for automated reproducible workflows and data provenance Huber, Sebastiaan P.; Zoupanos, Spyros; Uhrin, Martin Scientific Data, Vol. 7, Issue 1 https://doi.org/10.1038/s41597-020-00638-4	journal	September 2020
Exploring proton-coupled electron transfer at multiple scales Hammes-Schiffer, Sharon Nature Computational Science, Vol. 3, Issue 4 https://doi.org/10.1038/s43588-023-00422-5	journal	April 2023
Structure and dynamics in drug discovery Wei, Haixin; McCammon, J. Andrew npj Drug Discovery, Vol. 1, Issue 1 https://doi.org/10.1038/s44386-024-00001-2	journal	November 2024
Accurate and efficient linear scaling DFT calculations with universal applicability Mohr, Stephan; Ratcliff, Laura E.; Genovese, Luigi Physical Chemistry Chemical Physics, Vol. 17, Issue 47 https://doi.org/10.1039/C5CP00437C	journal	January 2015
Extensive deep neural networks for transferring small scale learning to large scale systems Mills, Kyle; Ryczko, Kevin; Luchak, Iryna Chemical Science, Vol. 10, Issue 15 https://doi.org/10.1039/C8SC04578J	journal	January 2019
Electron density learning of non-covalent systems Fabrizio, Alberto; Grisafi, Andrea; Meyer, Benjamin Chemical Science, Vol. 10, Issue 41 https://doi.org/10.1039/C9SC02696G	journal	January 2019
Heterogeneous catalysis: Enigmas, illusions, challenges, realities, and emergent strategies of design Thomas, John Meurig The Journal of Chemical Physics, Vol. 128, Issue 18 https://doi.org/10.1063/1.2832309	journal	May 2008
Particle mesh Ewald: An N ⋅log( N ) method for Ewald sums in large systems Darden, Tom; York, Darrin; Pedersen, Lee The Journal of Chemical Physics, Vol. 98, Issue 12 https://doi.org/10.1063/1.464397	journal	June 1993
Perspective on density functional theory Burke, Kieron The Journal of Chemical Physics, Vol. 136, Issue 15 https://doi.org/10.1063/1.4704546	journal	April 2012
Commentary: The Materials Project: A materials genome approach to accelerating materials innovation Jain, Anubhav; Ong, Shyue Ping; Hautier, Geoffroy APL Materials, Vol. 1, Issue 1 https://doi.org/10.1063/1.4812323	journal	July 2013
Extending the accuracy of the SNAP interatomic potential form Wood, Mitchell A.; Thompson, Aidan P. The Journal of Chemical Physics, Vol. 148, Issue 24 https://doi.org/10.1063/1.5017641	journal	June 2018
Large scale and linear scaling DFT with the CONQUEST code Nakata, Ayako; Baker, Jack S.; Mujahed, Shereif Y. The Journal of Chemical Physics, Vol. 152, Issue 16 https://doi.org/10.1063/5.0005074	journal	April 2020
Q uantum ESPRESSO toward the exascale Giannozzi, Paolo; Baseggio, Oscar; Bonfà, Pietro The Journal of Chemical Physics, Vol. 152, Issue 15 https://doi.org/10.1063/5.0005082	journal	April 2020
Calculation of pair and triplet correlation functions for a Lennard-Jones fluid at ρ≤1.41 and T≤25 Gottschalk, Matthias AIP Advances, Vol. 11, Issue 4 https://doi.org/10.1063/5.0048450	journal	April 2021
Nearsightedness of electronic matter Prodan, E.; Kohn, W. Proceedings of the National Academy of Sciences, Vol. 102, Issue 33 https://doi.org/10.1073/pnas.0505436102	journal	August 2005
QUANTUM ESPRESSO: a modular and open-source software project for quantum simulations of materials Giannozzi, Paolo; Baroni, Stefano; Bonini, Nicola Journal of Physics: Condensed Matter, Vol. 21, Issue 39, Article No. 395502 https://doi.org/10.1088/0953-8984/21/39/395502	journal	September 2009
Calculations for millions of atoms with density functional theory: linear scaling shows its potential Bowler, D. R.; Miyazaki, T. Journal of Physics: Condensed Matter, Vol. 22, Issue 7 https://doi.org/10.1088/0953-8984/22/7/074207	journal	February 2010
An embedded atom method potential of beryllium Agrawal, Anupriya; Mishra, Rohan; Ward, Logan Modelling and Simulation in Materials Science and Engineering, Vol. 21, Issue 8 https://doi.org/10.1088/0965-0393/21/8/085001	journal	October 2013
Advanced capabilities for materials modelling with Quantum ESPRESSO Giannozzi, P.; Andreussi, O.; Brumme, T. Journal of Physics: Condensed Matter, Vol. 29, Issue 46 https://doi.org/10.1088/1361-648X/aa8f79	journal	October 2017
Inhomogeneous Electron Gas Hohenberg, P.; Kohn, W. Physical Review, Vol. 136, Issue 3B, p. B864-B871 https://doi.org/10.1103/PhysRev.136.B864	journal	November 1964
Thermal Properties of the Inhomogeneous Electron Gas Mermin, N. David Physical Review, Vol. 137, Issue 5A https://doi.org/10.1103/PhysRev.137.A1441	journal	March 1965
Self-Consistent Equations Including Exchange and Correlation Effects Kohn, W.; Sham, L. J. Physical Review, Vol. 140, Issue 4A, p. A1133-A1138 https://doi.org/10.1103/PhysRev.140.A1133	journal	November 1965
Canonical dynamics: Equilibrium phase-space distributions Hoover, William G. Physical Review A, Vol. 31, Issue 3 https://doi.org/10.1103/PhysRevA.31.1695	journal	March 1985
Learning the electronic density of states in condensed matter Ben Mahmoud, Chiheb; Anelli, Andrea; Csányi, Gábor Physical Review B, Vol. 102, Issue 23 https://doi.org/10.1103/PhysRevB.102.235130	journal	December 2020
Accelerating finite-temperature Kohn-Sham density functional theory with deep neural networks Ellis, J. A.; Fiedler, L.; Popoola, G. A. Physical Review B, Vol. 104, Issue 3 https://doi.org/10.1103/PhysRevB.104.035120	journal	July 2021
Benchmarking exchange-correlation functionals in the spin-polarized inhomogeneous electron gas under warm dense conditions Moldabekov, Zhandos; Dornheim, Tobias; Vorberger, Jan Physical Review B, Vol. 105, Issue 3 https://doi.org/10.1103/PhysRevB.105.035134	journal	January 2022
Machine learning the electronic structure of matter across temperatures Fiedler, Lenz; Modine, Normand A.; Miller, Kyle D. Physical Review B, Vol. 108, Issue 12 https://doi.org/10.1103/PhysRevB.108.125146	journal	September 2023
Special points for Brillouin-zone integrations Monkhorst, Hendrik J.; Pack, James D. Physical Review B, Vol. 13, Issue 12, p. 5188-5192 https://doi.org/10.1103/PhysRevB.13.5188	journal	June 1976
Embedded-atom method: Derivation and application to impurities, surfaces, and other defects in metals Daw, Murray S.; Baskes, M. I. Physical Review B, Vol. 29, Issue 12 https://doi.org/10.1103/PhysRevB.29.6443	journal	June 1984
Ab initiomolecular dynamics for liquid metals Kresse, G.; Hafner, J. Physical Review B, Vol. 47, Issue 1, p. 558-561 https://doi.org/10.1103/PhysRevB.47.558	journal	January 1993
Self-consistent first-principles technique with linear scaling Hernández, E.; Gillan, M. J. Physical Review B, Vol. 51, Issue 15 https://doi.org/10.1103/PhysRevB.51.10157	journal	April 1995
Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set Kresse, G.; Furthmüller, J. Physical Review B, Vol. 54, Issue 16, p. 11169-11186 https://doi.org/10.1103/PhysRevB.54.11169	journal	October 1996
From ultrasoft pseudopotentials to the projector augmented-wave method Kresse, G.; Joubert, D. Physical Review B, Vol. 59, Issue 3, p. 1758-1775 https://doi.org/10.1103/PhysRevB.59.1758	journal	January 1999
Atomic cluster expansion for accurate and transferable interatomic potentials Drautz, Ralf Physical Review B, Vol. 99, Issue 1 https://doi.org/10.1103/PhysRevB.99.014104	journal	January 2019
Data-driven material models for atomistic simulation Wood, M. A.; Cusentino, M. A.; Wirth, B. D. Physical Review B, Vol. 99, Issue 18 https://doi.org/10.1103/PhysRevB.99.184305	journal	May 2019
Exact Conditions in Finite-Temperature Density-Functional Theory Pittalis, S.; Proetto, C. R.; Floris, A. Physical Review Letters, Vol. 107, Issue 16 https://doi.org/10.1103/PhysRevLett.107.163001	journal	October 2011
Finding Density Functionals with Machine Learning Snyder, John C.; Rupp, Matthias; Hansen, Katja Physical Review Letters, Vol. 108, Issue 25 https://doi.org/10.1103/PhysRevLett.108.253002	journal	June 2012
Accurate Homogeneous Electron Gas Exchange-Correlation Free Energy for Local Spin-Density Calculations Karasiev, Valentin V.; Sjostrom, Travis; Dufty, James Physical Review Letters, Vol. 112, Issue 7 https://doi.org/10.1103/PhysRevLett.112.076403	journal	February 2014
Ab initio Exchange-Correlation Free Energy of the Uniform Electron Gas at Warm Dense Matter Conditions Groth, Simon; Dornheim, Tobias; Sjostrom, Travis Physical Review Letters, Vol. 119, Issue 13 https://doi.org/10.1103/PhysRevLett.119.135001	journal	September 2017
Quantum Deep Field: Data-Driven Wave Function, Electron Density Generation, and Atomization Energy Prediction and Extrapolation with Machine Learning Tsubaki, Masashi; Mizoguchi, Teruyasu Physical Review Letters, Vol. 125, Issue 20 https://doi.org/10.1103/PhysRevLett.125.206401	journal	November 2020
Density Functional and Density Matrix Method Scaling Linearly with the Number of Atoms Kohn, W. Physical Review Letters, Vol. 76, Issue 17 https://doi.org/10.1103/PhysRevLett.76.3168	journal	April 1996
Generalized Gradient Approximation Made Simple Perdew, John P.; Burke, Kieron; Ernzerhof, Matthias Physical Review Letters, Vol. 77, Issue 18, p. 3865-3868 https://doi.org/10.1103/PhysRevLett.77.3865	journal	October 1996
Three-Particle Correlations in Simple Liquids Zahn, K.; Maret, G.; Ruß, C. Physical Review Letters, Vol. 91, Issue 11 https://doi.org/10.1103/PhysRevLett.91.115502	journal	September 2003
Accelerating equilibration in first-principles molecular dynamics with orbital-free density functional theory Fiedler, Lenz; Moldabekov, Zhandos A.; Shao, Xuecheng Physical Review Research, Vol. 4, Issue 4 https://doi.org/10.1103/PhysRevResearch.4.043033	journal	October 2022
The Kokkos EcoSystem: Comprehensive Performance Portability For High Performance Computing Trott, Christian; Berger-Vergiat, Luc; Poliakoff, David Zoeller Computing in Science & Engineering https://doi.org/10.1109/MCSE.2021.3098509	journal	January 2021
Kokkos 3: Programming Model Extensions for the Exascale Era Trott, Christian; Lebrun-Grandie, Damien; Arndt, Daniel IEEE Transactions on Parallel and Distributed Systems https://doi.org/10.1109/TPDS.2021.3097283	journal	January 2021
Recent Progress in Orbital-free Density Functional Theory Wesolowski, Tomasz A.; Wang, Yan Alexander Recent Advances in Computational Chemistry https://doi.org/10.1142/8633	book	September 2012
Scalable parallel programming with CUDA Nickolls, John; Buck, Ian; Garland, Michael Queue, Vol. 6, Issue 2 https://doi.org/10.1145/1365490.1365500	journal	March 2008
Algorithm 748: enclosing zeros of continuous functions Alefeld, G. E.; Potra, F. A.; Shi, Yixun ACM Transactions on Mathematical Software, Vol. 21, Issue 3 https://doi.org/10.1145/210089.210111	journal	September 1995
`` Direct Search'' Solution of Numerical and Statistical Problems Hooke, Robert; Jeeves, T. A. Journal of the ACM, Vol. 8, Issue 2 https://doi.org/10.1145/321062.321069	journal	April 1961
Reevaluating Amdahl's law Gustafson, John L. Communications of the ACM, Vol. 31, Issue 5 https://doi.org/10.1145/42411.42415	journal	May 1988
Neural Network Potentials: A Concise Overview of Methods Kocer, Emir; Ko, Tsz Wai; Behler, Jörg Annual Review of Physical Chemistry, Vol. 73, Issue 1 https://doi.org/10.1146/annurev-physchem-082720-034254	journal	April 2022

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