Skip to main content

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

  • Perspective
  • Published:

Accelerating the design of compositionally complex materials via physics-informed artificial intelligence

Abstract

The chemical space for designing materials is practically infinite. This makes disruptive progress by traditional physics-based modeling alone challenging. Yet, training data for identifying composition–structure–property relations by artificial intelligence are sparse. We discuss opportunities to discover new chemically complex materials by hybrid methods where physics laws are combined with artificial intelligence.

This is a preview of subscription content, access via your institution

Access options

Buy this article

Prices may be subject to local taxes which are calculated during checkout

Fig. 1: Chemical complexity influences microstructure complexity.
Fig. 2: Combinations of AI and physics-based models for the simulation of compositionally complex materials.
Fig. 3: Active learning in materials science.
Fig. 4: Different applications of data-driven and physics-informed AI for the modeling of compositionally complex materials.

Similar content being viewed by others

References

  1. Raabe, D., Tasan, C. C. & Olivetti, E. A. Strategies for improving the sustainability of structural metals. Nature 575, 64–74 (2019).

    Article  Google Scholar 

  2. Olivetti, E. A. & Cullen, J. M. Toward a sustainable materials system. Science 360, 1396–1398 (2018).

    Article  Google Scholar 

  3. Reed, R. C. The Superalloys (Cambridge Univ. Press, 2009); https://doi.org/10.1017/cbo9780511541285

  4. Suzuki, A., Inui, H. & Pollock, T. M. L12-strengthened cobalt-base superalloys. Annu. Rev. Mater. Res. 45, 345–368 (2015).

    Article  Google Scholar 

  5. Sato, J. et al. Cobalt-base high-temperature alloys. Science 312, 90–91 (2006).

    Article  Google Scholar 

  6. Nicolas, M. & Deschamps, A. Characterisation and modelling of precipitate evolution in an Al–Zn–Mg alloy during non-isothermal heat treatments. Acta Mater. 51, 6077–6094 (2003).

    Article  Google Scholar 

  7. Dorin, T., Deschamps, A., Geuser, F., De & Sigli, C. Quantification and modelling of the microstructure/strength relationship by tailoring the morphological parameters of the T1 phase in an Al–Cu–Li alloy. Acta Mater. 75, 134–146 (2014).

    Article  Google Scholar 

  8. Zhao, H. et al. Hydrogen trapping and embrittlement in high-strength Al-alloys. Nature 602, 437–441 (2022).

    Article  Google Scholar 

  9. Gutfleisch, O. Controlling the properties of high energy density permanent magnetic materials by different processing routes. J. Phys. D 33, R157–R172 (2000).

    Article  Google Scholar 

  10. Han, L. et al. A mechanically strong and ductile soft magnet with extremely low coercivity. Nature 608, 310–316 (2022).

  11. Yeh, J. W. et al. Nanostructured high-entropy alloys with multiple principal elements: novel alloy design concepts and outcomes. Adv. Eng. Mater. 6, 299–303 (2004).

    Article  Google Scholar 

  12. Yeh, J. W. in High-Entropy Alloys: Fundamentals and Applications (eds Gao, M. et al.) https://doi.org/10.1007/978-3-319-27013-5_1 (Springer, 2016).

  13. Cantor, B., Chang, I. T. H., Knight, P. & Vincent, A. J. B. Microstructural development in equiatomic multicomponent alloys. Mater. Sci. Eng. A 375–377, 213–218 (2004).

    Article  Google Scholar 

  14. Cantor, B. Multicomponent and high entropy alloys. Entropy 16, 4749–4768 (2014).

    Article  Google Scholar 

  15. Zhou, X. et al. The hidden structure dependence of the chemical life of dislocations. Sci. Adv. 7, 1–10 (2021).

    Article  Google Scholar 

  16. Singh, R., Sharma, A., Singh, P., Balasubramanian, G. & Johnson, D. D. Accelerating computational modeling and design of high-entropy alloys. Nat. Comput. Sci. 1, 54–61 (2021).

  17. Kalidindi, S. R. Hierarchical Materials Informatics (Butterworth-Heineman, 2016).

  18. Aykol, M. et al. Network analysis of synthesizable materials discovery. Nat. Commun. 10, 2018 (2019).

    Article  Google Scholar 

  19. Li, J. et al. Accelerated discovery of high-strength aluminum alloys by machine learning. Commun. Mater. 1, 73 (2020).

    Article  Google Scholar 

  20. Gubernatis, J. E. & Lookman, T. Machine learning in materials design and discovery: examples from the present and suggestions for the future. Phys. Rev. Mater. 2, 120301 (2018).

    Article  Google Scholar 

  21. Wen, C. et al. Machine learning assisted design of high entropy alloys with desired property. Acta Mater. 170, 109–117 (2019).

    Article  Google Scholar 

  22. Chang, Y. A. et al. Phase diagram calculation: past, present and future. Prog. Mater. Sci. https://doi.org/10.1016/S0079-6425(03)00025-2 (2004).

  23. Schmid-Fetzer, R. Phase diagrams: the beginning of wisdom. J. Phase Equilibria Diffus. 35, 735–760 (2014).

    Article  Google Scholar 

  24. Kumari, P., Gupta, A. K., Mishra, R. K., Ahmad, M. S. & Shahi, R. R. A comprehensive review: recent progress on magnetic high entropy alloys and oxides. J. Magn. Magn. Mater. 554, 169142 (2022).

    Article  Google Scholar 

  25. Han, L. et al. Ultrastrong and ductile soft magnetic high-entropy alloys via coherent ordered nanoprecipitates. Adv. Mater. 33, 2102139 (2021).

    Article  Google Scholar 

  26. George, E. P., Raabe, D. & Ritchie, R. O. High-entropy alloys. Nat. Rev. Mater. 4, 515–534 (2019).

    Article  Google Scholar 

  27. Oses, C., Toher, C. & Curtarolo, S. High-entropy ceramics. Nat. Rev. Mater. 5, 295–309 (2020).

    Article  Google Scholar 

  28. Murty, B. S., Yeh, J. W. & Ranganathan, S. High Entropy Alloys 57–76 (Butterworth-Heinemann, 2014); https://doi.org/10.1016/b978-0-12-800251-3.00004-3

  29. Gorsse, S., Couzinié, J. P. & Miracle, D. B. From high-entropy alloys to complex concentrated alloys. C. R. Phys. 19, 721–736 (2018).

    Article  Google Scholar 

  30. Pei, Z., Yin, J., Hawk, J. A., Alman, D. E. & Gao, M. C. Machine-learning informed prediction of high-entropy solid solution formation: beyond the Hume–Rothery rules. npj Comput. Mater. 6, 50 (2020).

  31. Zhao, H. et al. Interplay of chemistry and faceting at grain boundaries in a model Al alloy. Phys. Rev. Lett. 124, 106102 (2020).

    Article  Google Scholar 

  32. Zhao, X., Chen, H., Wilson, N., Liu, Q. & Nie, J. F. Direct observation and impact of co-segregated atoms in magnesium having multiple alloying elements. Nat. Commun. 10, 3243 (2019).

    Article  Google Scholar 

  33. Raabe, D. et al. Grain boundary segregation engineering in metallic alloys: a pathway to the design of interfaces. Curr. Opin. Solid State Mater. Sci. 18, 253–261 (2014).

    Article  Google Scholar 

  34. Rao, Z. et al. Invar effects in FeNiCo medium entropy alloys: from an Invar treasure map to alloy design. Intermetallics 111, 106520 (2019).

    Article  Google Scholar 

  35. Wu, X. et al. Role of magnetic ordering for the design of quinary TWIP-TRIP high entropy alloys. Phys. Rev. Mater. 4, 33601 (2020).

    Article  Google Scholar 

  36. Counts, W. A., Friak, M., Raabe, D. & Neugebauer, J. Using ab initio calculations in designing bcc Mg–Li alloys for ultra-lightweight applications. Acta Mater. 57, 69–76 (2009).

    Article  Google Scholar 

  37. Grabowski, B., Ismer, L., Hickel, T. & Neugebauer, J. Ab initio up to the melting point: anharmonicity and vacancies in aluminum. Phys. Rev. B 79, 134106 (2009).

    Article  Google Scholar 

  38. Senkov, O. N., Miller, J. D., Miracle, D. B. & Woodward, C. Accelerated exploration of multi-principal element alloys for structural applications. Calphad 50, 32–48 (2015).

    Article  Google Scholar 

  39. Gorsse, S. & Senkov, O. N. About the reliability of CALPHAD predictions in multicomponent systems. Entropy 20, 899 (2018).

    Article  Google Scholar 

  40. Zhang, C. & Gao, M. C. in High-Entropy Alloys: Fundamentals and Applications (eds Gao, M. et al.) 399–444 (Springer, 2016); https://doi.org/10.1007/978-3-319-27013-5_12

  41. Miracle, D. B. & Senkov, O. N. A critical review of high entropy alloys and related concepts. Acta Mater. 122, 448–511 (2017).

    Article  Google Scholar 

  42. Zhang, F. et al. An understanding of high entropy alloys from phase diagram calculations. Calphad 45, 1–10 (2014).

    Article  Google Scholar 

  43. Ma, D. et al. Phase stability of non-equiatomic CoCrFeMnNi high entropy alloys. Acta Mater. 98, 288–296 (2015).

    Article  Google Scholar 

  44. Grabowski, B. et al. Ab initio vibrational free energies including anharmonicity for multicomponent alloys. npj Comput. Mater. 5, 80 (2019).

  45. Kostiuchenko, T., Körmann, F., Neugebauer, J. & Shapeev, A. Impact of lattice relaxations on phase transitions in a high-entropy alloy studied by machine-learning potentials. npj Comput. Mater. 5, 55 (2019).

  46. Husic, B. E. et al. Coarse graining molecular dynamics with graph neural networks. J. Chem. Phys. 153, 194101 (2020).

    Article  Google Scholar 

  47. Zhou, Z. et al. Machine learning guided appraisal and exploration of phase design for high entropy alloys. npj Comput. Mater. 5, 128Z (2019).

    Article  Google Scholar 

  48. Butler, K. T., Davies, D. W., Cartwright, H., Isayev, O. & Walsh, A. Machine learning for molecular and materials science. Nature 559, 547–555 (2018).

    Article  Google Scholar 

  49. Noé, F., Tkatchenko, A., Müller, K. R. & Clementi, C. Machine learning for molecular simulation. Annu. Rev. Phys. Chem. 71, 361–390 (2020).

    Article  Google Scholar 

  50. Gubaev, K. et al. Finite-temperature interplay of structural stability, chemical complexity, and elastic properties of bcc multicomponent alloys from ab initio trained machine-learning potentials. Phys. Rev. Mater. 5, 073801 (2021).

    Article  Google Scholar 

  51. Li, Z., Kermode, J. R. & De Vita, A. Molecular dynamics with on-the-fly machine learning of quantum-mechanical forces. Phys. Rev. Lett. 114, 096405 (2015).

    Article  Google Scholar 

  52. Dhaliwal, G., Nair, P. B. & Singh, C. V. Machine learned interatomic potentials using random features. npj Comput. Mater. 8, 7 (2022).

  53. Wang, J. et al. Machine learning of coarse-grained molecular dynamics force fields. ACS Cent. Sci. 5, 755–767 (2019).

    Article  Google Scholar 

  54. Westermayr, J., Gastegger, M., Schütt, K. T. & Maurer, R. J. Perspective on integrating machine learning into computational chemistry and materials science. J. Chem. Phys. 154, 230903 (2021).

    Article  Google Scholar 

  55. Chen, L.-Q. Q. Phase-field models for microstructure evolution. Annu. Rev. Mater. Sci. 32, 113–140 (2002).

    Article  Google Scholar 

  56. Hu, S. Y. & Chen, L. Q. A phase-field model for evolving microstructures with strong elastic inhomogeneity. Acta Mater. 49, 1879–1890 (2001).

    Article  Google Scholar 

  57. Diehl, M. et al. Solving material mechanics and multiphysics problems of metals with complex microstructures using DAMASK—the Düsseldorf Advanced Material Simulation Kit. Adv. Eng. Mater. 22, 1901044 (2020).

    Article  Google Scholar 

  58. Montes de Oca Zapiain, D., Stewart, J. A. & Dingreville, R. Accelerating phase-field-based microstructure evolution predictions via surrogate models trained by machine learning methods. npj Comput. Mater. 7, 3 (2021).

    Article  Google Scholar 

  59. Teichert, G. H. & Garikipati, K. Machine learning materials physics: Surrogate optimization and multi-fidelity algorithms predict precipitate morphology in an alternative to phase field dynamics. Comput. Methods Appl. Mech. Eng. 344, 666–693 (2019).

    Article  MathSciNet  MATH  Google Scholar 

  60. Peivaste, I. et al. Machine-learning-based surrogate modeling of microstructure evolution using phase-field. Comput. Mater. Sci. 214, 111750 (2022).

    Article  Google Scholar 

  61. Roters, F. et al. DAMASK—the Düsseldorf Advanced Material Simulation Kit for modeling multi-physics crystal plasticity, thermal, and damage phenomena from the single crystal up to the component scale. Comput. Mater. Sci. 158, 420–478 (2019).

    Article  Google Scholar 

  62. Roters, F. et al. Overview of constitutive laws, kinematics, homogenization and multiscale methods in crystal plasticity finite-element modeling: theory, experiments, applications. Acta Mater. 58, 1152–1211 (2010).

    Article  Google Scholar 

  63. Mika, D. P. & Dawson, P. R. Effects of grain interaction on deformation in polycrystals. Mater. Sci. Eng. A 257, 62–76 (1998).

    Article  Google Scholar 

  64. Beaudoin, A. J., Dawson, P. R., Mathur, K. K., Kocks, U. F. & Korzekwa, D. A. Application of polycrystal plasticity to sheet forming. Comput. Methods Appl. Mech. Eng. 117, 49–70 (1994).

    Article  MATH  Google Scholar 

  65. Kalidindi, S. R., Duvvuru, H. K. & Knezevic, M. Spectral calibration of crystal plasticity models. Acta Mater. 54, 1795–1804 (2006).

    Article  Google Scholar 

  66. Helm, D., Butz, A., Raabe, D. & Gumbsch, P. Microstructure-based description of the deformation of metals: theory and application. JOM 63, 26–33 (2011).

    Article  Google Scholar 

  67. Liu, C. et al. An integrated crystal plasticity-phase field model for spatially resolved twin nucleation, propagation, and growth in hexagonal materials. Int. J. Plast. 106, 203–227 (2018).

    Article  Google Scholar 

  68. Shanthraj, P., Svendsen, B., Sharma, L., Roters, F. & Raabe, D. Elasto-viscoplastic phase field modelling of anisotropic cleavage fracture. J. Mech. Phys. Solids 99, 19–34 (2017).

    Article  MathSciNet  MATH  Google Scholar 

  69. Khorrami, M. S. et al. An artificial neural network for surrogate modeling of stress fields in viscoplastic polycrystalline materials. Preprint at https://arxiv.org/abs/2208.13490 (2022).

  70. Fernández, M., Rezaei, S., Rezaei Mianroodi, J., Fritzen, F. & Reese, S. Application of artificial neural networks for the prediction of interface mechanics: a study on grain boundary constitutive behavior. Adv. Model. Simul. Eng. Sci. 7, 1 (2020).

    Article  Google Scholar 

  71. Mianroodi, J. R., H. Siboni, N. & Raabe, D. Teaching solid mechanics to artificial intelligence—a fast solver for heterogeneous materials. npj Comput. Mater. 7, 99 (2021).

    Article  Google Scholar 

  72. Ibragimova, O., Brahme, A., Muhammad, W., Lévesque, J. & Inal, K. A new ANN based crystal plasticity model for fcc materials and its application to non-monotonic strain paths. Int. J. Plast. 144, 103059 (2021).

    Article  Google Scholar 

  73. Mangal, A. & Holm, E. A. Applied machine learning to predict stress hotspots I: Face centered cubic materials. Int. J. Plast. 111, 122–134 (2018).

    Article  Google Scholar 

  74. Schneeweiss, O. et al. Magnetic properties of the CrMnFeCoNi high-entropy alloy. Phys. Rev. B 96, 014437 (2017).

    Article  Google Scholar 

  75. Oh, H. S. et al. Lattice distortions in the FeCoNiCrMn high entropy alloy studied by theory and experiment. Entropy 18, 321 (2016).

    Article  Google Scholar 

  76. Ma, D., Grabowski, B., Körmann, F., Neugebauer, J. & Raabe, D. Ab initio thermodynamics of the CoCrFeMnNi high entropy alloy: importance of entropy contributions beyond the configurational one. Acta Mater. 100, 90–97 (2015).

    Article  Google Scholar 

  77. Löffler, A. et al. Quaternary Al–Cu–Mg–Si Q phase: sample preparation, heat capacity measurement and first-principles calculations. J. Phase Equilibria Diffus. 37, 119–126 (2016).

    Google Scholar 

  78. Kaufmann, K. et al. Discovery of high-entropy ceramics via machine learning. npj Comput. Mater. 6, 42 (2020).

    Article  Google Scholar 

  79. Sarker, P. et al. High-entropy high-hardness metal carbides discovered by entropy descriptors. Nat. Commun. 9, 4980 (2018).

    Article  Google Scholar 

  80. Kaufmann, K. et al. Crystal symmetry determination in electron diffraction using machine learning. Science 367, 564–568 (2020).

    Article  Google Scholar 

  81. Kaufmann, L. & Bernstein, H. Computer Calculation of Phase Diagrams (Academic Press, 1970).

  82. Spencer, P. J. A brief history of CALPHAD. Calphad 32, 1–8 (2008).

    Article  Google Scholar 

  83. Sandlöbes, S. et al. The relation between ductility and stacking fault energies in Mg and Mg–Y alloys. Acta Mater. 60, 3011–3021 (2012).

    Article  Google Scholar 

  84. Lei, Z. et al. Enhanced strength and ductility in a high-entropy alloy via ordered oxygen complexes. Nature 563, 546–550 (2018).

    Article  Google Scholar 

  85. Güvenç, O., Roters, F., Hickel, T. & Bambach, M. ICME for crashworthiness of TWIP steels: from ab initio to the crash performance. JOM 67, 120–128 (2015).

    Article  Google Scholar 

  86. De Cooman, B. C., Estrin, Y. & Kim, S. K. Twinning-induced plasticity (TWIP) steels. Acta Mater. 142, 283–362 (2018).

    Article  Google Scholar 

  87. Wei, S., He, F. & Tasan, C. C. Metastability in high-entropy alloys: a review. J. Mater. Res. 33, 2924–2937 (2018).

    Article  Google Scholar 

  88. Raabe, D., Li, Z. & Ponge, D. Metastability alloy design. MRS Bull. 44, 266–272 (2019).

    Article  Google Scholar 

  89. Curtin, W. A., Olmsted, D. L. & Hector, L. G. A predictive mechanism for dynamic strain ageing in aluminium–magnesium alloys. Nat. Mater. 5, 875–880 (2006).

    Article  Google Scholar 

  90. George, E. P., Curtin, W. A. & Tasan, C. C. High entropy alloys: a focused review of mechanical properties and deformation mechanisms. Acta Mater. https://doi.org/10.1016/j.actamat.2019.12.015 (2019).

  91. Varvenne, C., Leyson, G. P. M., Ghazisaeidi, M. & Curtin, W. A. Solute strengthening in random alloys. Acta Mater. 124, 660–683 (2017).

    Article  Google Scholar 

  92. Li, Z., Pradeep, K. G., Deng, Y., Raabe, D. & Tasan, C. C. Metastable high-entropy dual-phase alloys overcome the strength-ductility trade-off. Nature 534, 227–230 (2016).

    Article  Google Scholar 

  93. Li, Z., Tasan, C. C., Pradeep, K. G. & Raabe, D. A TRIP-assisted dual-phase high-entropy alloy: grain size and phase fraction effects on deformation behavior. Acta Mater. 131, 323–335 (2017).

    Article  Google Scholar 

  94. Pei, Z. et al. Rapid theory-guided prototyping of ductile Mg alloys: from binary to multi-component materials. New J. Phys. 17, 93009 (2015).

    Article  Google Scholar 

  95. Nikolov, S. et al. Revealing the design principles of high-performance biological composites using ab initio and multiscale simulations: The example of lobster cuticle. Adv. Mater. 22, 519–526 (2010).

  96. Pei, Z. et al. From generalized stacking fault energies to dislocation properties: five-energy-point approach and solid solution effects in magnesium. Phys. Rev. B 92, 64107 (2015).

    Article  Google Scholar 

  97. Li, Q. et al. Quantification of flexoelectricity in PbTiO3/SrTiO3 superlattice polar vortices using machine learning and phase-field modeling. Nat. Commun. 8, 1468 (2017).

    Article  Google Scholar 

  98. Mianroodi, J. R., Siboni, N. H. & Raabe, D. Computational discovery of energy-efficient heat treatment for microstructure design using deep reinforcement learning. Preprint at https://arxiv.org/abs/2209.11259 (2022).

  99. Yuan, M., Paradiso, S., Meredig, B. & Niezgoda, S. R. Machine learning-based reduce order crystal plasticity modeling for ICME applications. Integr. Mater. Manuf. Innov. 7, 214–230 (2018).

    Article  Google Scholar 

  100. Sangid, M. D. Coupling in situ experiments and modeling—opportunities for data fusion, machine learning, and discovery of emergent behavior. Curr. Opin. Solid State Mater. Sci. 24, 100797 (2020).

    Article  Google Scholar 

  101. Saidi, P. et al. Deep learning and crystal plasticity: a preconditioning approach for accurate orientation evolution prediction. Comput. Methods Appl. Mech. Eng. 389, 114392 (2022).

    Article  MathSciNet  MATH  Google Scholar 

  102. Salmenjoki, H., Alava, M. J. & Laurson, L. Machine learning plastic deformation of crystals. Nat. Commun. 9, 5307 (2018).

    Article  Google Scholar 

  103. Holm, E. A. et al. Overview: computer vision and machine learning for microstructural characterization and analysis. Metall. Mater. Trans. A 51, 5985–5999 (2020).

    Article  Google Scholar 

  104. Bock, F. E. et al. A review of the application of machine learning and data mining approaches in continuum materials mechanics. Front. Mater. 6, 110 (2019).

  105. Devi, M. A. et al. An informatic approach to predict the mechanical properties of aluminum alloys using machine learning techniques. In Proc. International Conference on Smart Electronics and Communication. 536–541 (2020); https://doi.org/10.1109/ICOSEC49089.2020.9215277

  106. Conduit, B. D., Jones, N. G., Stone, H. J. & Conduit, G. J. Design of a nickel-base superalloy using a neural network. Mater. Des. 131, 358–365 (2017).

    Article  Google Scholar 

  107. Barnett, M. R. et al. A scrap-tolerant alloying concept based on high entropy alloys. Acta Mater. 200, 735–744 (2020).

    Article  Google Scholar 

  108. Bartók, A. P. et al. Machine learning unifies the modeling of materials and molecules. Sci. Adv. 3, e1701816 (2017).

    Article  Google Scholar 

  109. Ganesh, M., Hawkins, S. C., Kordzakhia, N. & Unicomb, S. An efficient Bayesian neural network surrogate algorithm for shape detection. ANZIAM J. 62, C112–C127 (2022).

    Article  Google Scholar 

  110. Vahid, A. et al. New Bayesian-optimization-based design of high-strength 7xxx-series alloys from recycled aluminum. JOM https://doi.org/10.1007/s11837-018-2984-z (2018).

  111. Aggarwal, C. C. et al. Multi-objective Bayesian materials discovery. Comput. Mater. Sci. 3, 227–235 (2017).

    Google Scholar 

  112. Swain, M. C. & Cole, J. M. ChemDataExtractor: a toolkit for automated extraction of chemical information from the scientific literature. J. Chem. Inf. Model. 56, 1894–1904 (2016).

    Article  Google Scholar 

  113. Kim, E. et al. Materials synthesis insights from scientific literature via text extraction and machine learning. Chem. Mater. 29, 9436–9444 (2017).

    Article  Google Scholar 

  114. Mahbub, R. et al. Text mining for processing conditions of solid-state battery electrolyte. Electrochem. Commun. 121, 106860 (2020).

  115. Olivetti, E. A. et al. Data-driven materials research enabled by natural language processing and information extraction. Appl. Phys. Rev. 7, 041317 (2020).

  116. Pei, Z., Yin, J., Liaw, P. K. & Raabe, D. Toward the design of ultrahigh-entropy alloys via mining six million texts. Nat. Commun. 14, 54 (2023).

  117. Zhang, T. & Sun, S. Thermodynamics-informed neural network (TINN) for phase equilibrium calculations considering capillary pressure. Energies 14, 7724 (2021).

    Article  Google Scholar 

  118. Mnih, V. et al. Human-level control through deep reinforcement learning. Nature 518, 529–533 (2015).

    Article  Google Scholar 

  119. Muhammad, W., Brahme, A. P., Ibragimova, O., Kang, J. & Inal, K. A machine learning framework to predict local strain distribution and the evolution of plastic anisotropy & fracture in additively manufactured alloys. Int. J. Plast. 136, 1–38 (2021).

    Article  Google Scholar 

  120. Hernandez, Q., Badias, A., Chinesta, F. & Cueto, E. Thermodynamics-informed graph neural networks. IEEE Trans. Artif. Intell. 4581, 1–1 (2022).

    Article  MATH  Google Scholar 

  121. Ding, J. et al. Machine learning for molecular thermodynamics. Chin. J. Chem. Eng. 31, 227–239 (2021).

    Article  MathSciNet  Google Scholar 

  122. Jagtap, A. D., Kawaguchi, K. & Karniadakis, G. E. Adaptive activation functions accelerate convergence in deep and physics-informed neural networks. J. Comput. Phys. 404, 109136 (2020).

    Article  MathSciNet  MATH  Google Scholar 

  123. Jagtap, A. D., Kawaguchi, K. & Karniadakis, G. E. Locally adaptive activation functions with slope recovery for deep and physics-informed neural networks. Proc. R. Soc. A 476, 20200334 (2020).

    Article  MathSciNet  MATH  Google Scholar 

  124. Rodriguez-Torrado, R. et al. Physics-informed attention-based neural network for hyperbolic partial differential equations: application to the Buckley–Leverett problem. Sci. Rep. 12, 7557 (2022).

    Article  Google Scholar 

  125. Zhang, Z. & Gu, G. X. Physics-informed deep learning for digital materials. Theor. Appl. Mech. Lett. 11, 100220 (2021).

  126. Wagih, M. & Schuh, C. A. Learning grain-boundary segregation: from first principles to polycrystals. Phys. Rev. Lett. 129, 046102 (2022).

    Article  Google Scholar 

  127. Wagih, M., Larsen, P. M. & Schuh, C. A. Learning grain boundary segregation energy spectra in polycrystals. Nat. Commun. 11, 6376 (2020).

    Article  Google Scholar 

  128. Galvão, T. L. P., Novell-Leruth, G., Kuznetsova, A., Tedim, J. & Gomes, J. R. B. Elucidating structure–property relationships in aluminum alloy corrosion inhibitors by machine learning. J. Phys. Chem. C 124, 5624–5635 (2020).

    Article  Google Scholar 

  129. Mangos, J. & Birbilis, N. Computational alloy design and discovery using machine learning. Preprint at https://arxiv.org/abs/2105.14806 (2021).

  130. Sasidhar, K. N. et al. Deep learning framework for uncovering compositional and environmental contributions to pitting resistance in passivating alloys. npj Mater. Degrad. 6, 71 (2022).

  131. Gaustad, G., Olivetti, E. & Kirchain, R. Toward sustainable material usage: evaluating the importance of market motivated agency in modeling material flows. Environ. Sci. Technol. 45, 4110–4117 (2011).

    Article  Google Scholar 

  132. Kirchain, R. E., Gregory, J. R. & Olivetti, E. A. Environmental life-cycle assessment. Nat. Mater. 16, 693–697 (2017).

    Article  Google Scholar 

  133. Gaustad, G., Olivetti, E. & Kirchain, R. Design for recycling. J. Ind. Ecol. 14, 286–308 (2010).

    Article  Google Scholar 

  134. Daehn, K. E., Cabrera Serrenho, A. & Allwood, J. M. How will copper contamination constrain future global steel recycling? Environ. Sci. Technol. 51, 6599–6606 (2017).

    Article  Google Scholar 

  135. Allwood, J. M. et al. Sustainable Materials: With Both Eyes Open (UIT Cambridge, 2012).

  136. Cann, J. L. et al. Sustainability through alloy design: challenges and opportunities. Prog. Mater. Sci. 117, 100722 (2020).

    Article  Google Scholar 

  137. Lederer, Y., Toher, C., Vecchio, K. S. & Curtarolo, S. The search for high entropy alloys: a high-throughput ab-initio approach. Acta Mater. 159, 364–383 (2018).

    Article  Google Scholar 

  138. Curtarolo, S. et al. The high-throughput highway to computational materials design. Nat. Mater. 12, 191–201 (2013).

    Article  Google Scholar 

  139. Raabe, D. et al. Making sustainable aluminum by recycling scrap: the science of ‘dirty’ alloys. Prog. Mater. Sci. 128, 100947 (2022).

    Article  Google Scholar 

  140. Hiraki, T. et al. Thermodynamic criteria for the removal of impurities from end-of-life magnesium alloys by evaporation and flux treatment. Sci. Technol. Adv. Mater. https://doi.org/10.1088/1468-6996/12/3/035003 (2011).

  141. Stemper, L., Tunes, M. A., Tosone, R., Uggowitzer, P. J. & Pogatscher, S. On the potential of aluminum crossover alloys. Prog. Mater. Sci. https://doi.org/10.1016/j.pmatsci.2021.100873 (2021).

  142. Draxl, C. & Scheffler, M. The NOMAD laboratory: from data sharing to artificial intelligence. J. Phys. Mater. 2, 036001 (2019).

    Article  Google Scholar 

  143. Mianroodi, J. R., Rezaei, S., Siboni, N. H., Xu, B.-X. & Raabe, D. Lossless multi-scale constitutive elastic relations with artificial intelligence. npj Comput. Mater. 8, 67 (2021).

    Article  Google Scholar 

  144. Dimiduk, D. M., Holm, E. A. & Niezgoda, S. R. Perspectives on the impact of machine learning, deep learning, and artificial intelligence on materials, processes, and structures engineering. Integr. Mater. Manuf. Innov. 7, 157–172 (2018).

    Google Scholar 

  145. Sandlöbes, S. et al. A rare-earth free magnesium alloy with improved intrinsic ductility. Sci. Rep. 7, 10458 (2017).

    Article  Google Scholar 

  146. Sandlöbes, S. et al. Ductility improvement of Mg alloys by solid solution: ab initio modeling, synthesis and mechanical properties. Acta Mater. 70, 92–104 (2014).

    Article  Google Scholar 

  147. Haghighat, E., Raissi, M., Moure, A., Gomez, H. & Juanes, R. A Physics-informed deep learning framework for inversion and surrogate modeling in solid mechanics. Comput. Methods Appl. Mech. Eng. 379, 113741 (2021).

  148. Rao, Z. et al. Machine learning-enabled high-entropy alloy discovery. Science 85, 78–85 (2022).

    Article  Google Scholar 

  149. Foppa, L., Purcell, T. A. R., Levchenko, S. V., Scheffler, M. & Ghringhelli, L. M. Hierarchical symbolic regression for identifying key physical parameters correlated with bulk properties of perovskites. Phys. Rev. Lett. 129, 55301 (2022).

    Article  Google Scholar 

  150. Court, C. J. & Cole, J. M. Auto-generated aterials database of Curie and Neél temperatures via semisupervised relationship extraction. Sci. Data 5, 180111 (2018).

    Google Scholar 

  151. Katnagallu, S. et al. Advanced data mining in field ion microscopy. Mater. Charact. 146, 307–318 (2018).

    Article  Google Scholar 

  152. Wang, C., Fu, H., Jiang, L., Xue, D. & Xie, J. A property-oriented design strategy for high performance copper alloys via machine learning. npj Comput. Mater. 5, 87 (2019).

  153. Yang, Z. et al. Deep learning approaches for mining structure-property linkages in high contrast composites from simulation datasets. Comput. Mater. Sci. 151, 278–287 (2018).

    Article  Google Scholar 

  154. Yang, Z. et al. Establishing structure-property localization linkages for elastic deformation of three-dimensional high contrast composites using deep learning approaches. Acta Mater. 166, 335–345 (2019).

    Article  Google Scholar 

  155. Wilkinson, M. D. et al. Comment: The FAIR guiding principles for scientific data management and stewardship. Sci. Data 3, 160018 (2016).

    Google Scholar 

  156. Kajikawa, Y., Sugiyama, Y., Mima, H. & Matsushima, K. Causal knowledge extraction by natural language processing in material science: a case study in chemical vapor deposition. Data Sci. J. 5, 108–118 (2006).

    Google Scholar 

  157. Cuomo, S. et al. Scientific machine learning through physics–informed neural networks: Where we are and what’s next. J. Sci. Comput. 92, 88 (2022).

  158. Cui, J. et al. Combinatorial search of thermoelastic shape-memory alloys with extremely small hysteresis width. Nat. Mater. 5, 286–290 (2006).

    Article  Google Scholar 

  159. Li, Z., Ludwig, A., Savan, A., Springer, H. & Raabe, D. Combinatorial metallurgical synthesis and processing of high-entropy alloys. J. Mater. Res. 33, 3156–3169 (2018).

    Article  Google Scholar 

  160. Löffler, T. et al. Discovery of a multinary noble metal-free oxygen reduction catalyst. Adv. Energy Mater. 8, 1802269 (2018).

    Article  Google Scholar 

  161. Raabe, D. et al. Ab initio-guided design of twinning-induced plasticity steels. MRS Bull. 41, 320–325 (2016).

    Article  Google Scholar 

  162. Gebhardt, T., Music, D., Takahashi, T. & Schneider, J. M. Combinatorial thin film materials science: from alloy discovery and optimization to alloy design. Thin Solid Films 520, 5491–5499 (2012).

    Article  Google Scholar 

  163. Mohammadzadeh, S. & Lejeune, E. Predicting mechanically driven full-field quantities of interest with deep learning-based metamodels. Extrem. Mech. Lett. 50, 101566 (2022).

  164. Raissi, M., Perdikaris, P. & Karniadakis, G. E. Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations. J. Comput. Phys. 378, 686–707 (2019).

  165. Pun, G. P. P., Batra, R., Ramprasad, R. & Mishin, Y. Physically informed artificial neural networks for atomistic modeling of materials. Nat. Commun. 10, 2339 (2019).

    Article  Google Scholar 

  166. Wang, S., Wang, H. & Perdikaris, P. Learning the solution operator of parametric partial differential equations with physics-informed DeepONets. Sci. Adv. 7, eabi8605 (2021).

    Article  Google Scholar 

  167. You, H., Zhang, Q., Ross, C. J., Lee, C.-H. & Yu, Y. Learning deep implicit Fourier neural operators (IFNOs) with applications to heterogeneous material modeling. Comput. Methods Appl. Mech. Eng. https://doi.org/10.1016/j.cma.2022.115296 (2022).

  168. Guo, K., Yang, Z., Yu, C. H. & Buehler, M. J. Artificial intelligence and machine learning in design of mechanical materials. Mater. Horiz. 8, 1153–1172 (2021).

    Article  Google Scholar 

  169. Abueidda, D. W., Lu, Q. & Koric, S. Meshless physics-informed deep learning method for three-dimensional solid mechanics. Int. J. Numer. Methods Eng. 122, 7182–7201 (2021).

  170. Winkler, L., Müller, K. R. & Sauceda, H. E. High-fidelity molecular dynamics trajectory reconstruction with bi-directional neural networks. Mach. Learn. Sci. Technol. 3, 025011 (2022).

    Article  Google Scholar 

  171. Riniker, S., Wang, S., Bleiziffer, P., Böselt, L. & Esposito, C. Machine learning with and for molecular dynamics simulations. Chimia 73, 1024–1027 (2019).

    Article  Google Scholar 

  172. Pfaff, T., Fortunato, M., Sanchez-Gonzalez, A. & Battaglia, P. W. Learning mesh-based simulation with graph networks. Preprint at https://arxiv.org/abs/2010.03409 (2020).

  173. Wight, C. L. & Zhao, J. Solving Allen–Cahn and Cahn–Hilliard equations using the adaptive physics informed neural networks. Commun. Comput. Phys. 29, 930–954 (2021).

    Article  MathSciNet  MATH  Google Scholar 

  174. Attari, V. et al. Uncertainty propagation in a multiscale CALPHAD-reinforced elastochemical phase-field model. Acta Mater. 183, 452–470 (2020).

  175. Gierlich, C. & Palkovits, S. Featurizing chemistry for machine learning—methods and a coded example. Curr. Opin. Chem. Eng. 37, 100840 (2022).

    Article  Google Scholar 

  176. Kalidindi, S. R. Feature engineering of material structure for AI-based materials knowledge systems. J. Appl. Phys. 128, 41103 (2020).

    Article  Google Scholar 

  177. Schmidt, J., Marques, M. R. G., Botti, S. & Marques, M. A. L. Recent advances and applications of machine learning in solid-state materials science. npj Comput. Mater. 5, 83 (2019).

  178. Ojih, J., Al-Fahdi, M., Rodriguez, A. D. & Choudhary, K. Efficiently searching extreme mechanical properties via boundless objective-free exploration and minimal first-principles calculations. npj Comput. Mater. 8, 143 (2022).

    Article  Google Scholar 

Download references

Acknowledgements

The authors are grateful for financial support by the BIGmax research network of the Max-Planck Society (https://www.bigmax.mpg.de/).

Author information

Authors and Affiliations

Authors

Contributions

All authors contributed equally to the article, in terms of topical lines, discussion and writing.

Corresponding authors

Correspondence to Dierk Raabe, Jaber Rezaei Mianroodi or Jörg Neugebauer.

Ethics declarations

Competing interests

The authors declare no competing interests.

Peer review

Peer review information

Nature Computational Science thanks Stefano Curtarolo, Peng-Fei Guan and the other, anonymous, reviewer(s) for their contribution to the peer review of this work. Primary Handling Editor: Jie Pan, in collaboration with the Nature Computational Science team.

Additional information

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Raabe, D., Mianroodi, J.R. & Neugebauer, J. Accelerating the design of compositionally complex materials via physics-informed artificial intelligence. Nat Comput Sci 3, 198–209 (2023). https://doi.org/10.1038/s43588-023-00412-7

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/s43588-023-00412-7

This article is cited by

Search

Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing