Scalable Machine Learning for Predicting the Electronic Structure of Matter

I will present our recent progress in significantly scaling up density functional theory calculations with machine learning [1], for which we have developed the Materials Learning Algorithms (MALA) framework [2]. We have demonstrated the transferability of our machine learning model across phase boundaries, such as metals at their melting point [3] and electronic temperature [4]. In addition, our use of automated machine learning has led to a significant reduction in the computational resources required to identify optimal neural network architectures [5]. Most importantly, I will present our recent breakthrough in enabling fast neural-network driven electronic structure calculations for ultra-large systems unattainable by conventional density functional theory calculations [6]. I will mention in passing our other efforts in solving the Kohn-Sham equations of time-dependent density functional theory in terms of physics-informed neural networks [7], and in developing a robust framework for inverting the Kohn-Sham equations in terms of Fourier neural operators [8].

[1] L. Fiedler, K. Shah, M. Bussmann, A. Cangi, Phys. Rev. Materials, 6, 040301 (2022).
[2] A. Cangi, S. Rajamanickam, B. Brzoza, T. J. Callow, J. A. Ellis, O. Faruk, L. Fiedler, J. Fox, N. Hoffmann, K. D. Miller, D. Kotik, S. Kulkarni, N. Modine, P. Mohammed, V. Oles, G. A. Popoola, F. Pöschel, J. Romero, S. Schmerler, J. A. Stephens, H. Tahmasbi, A. P. Thompson, S. Verma, D. J. Vogel, Materials Learning Algorithms (MALA), doi.org/10.5281/zenodo.5557254, (2023).
[3] J. Ellis, L. Fiedler, G. Popoola, N. Modine, J. Stephens, A. Thompson, A. Cangi, S. Rajamanickam, Phys. Rev. B, 104, 035120 (2021).
[4] L. Fiedler, N. A. Modine, K. D. Miller, A. Cangi, Phys. Rev. B 108, 125146 (2023).
[5] L. Fiedler, N. Hoffmann, P. Mohammed, G. Popoola, T. Yovell, V. Oles, J. Austin Ellis, S. Rajamanickam, A. Cangi, Mach. Learn.: Sci. Technol., 3, 045008 (2022).
[6] L. Fiedler, N. Modine, S. Schmerler, D. Vogel, G. Popoola, A. Thompson, S. Rajamanickam, A. Cangi, npj. Comput. Mater., 9, 115 (2023).
[7] K. Shah, P. Stiller, N. Hoffmann, A. Cangi, Physics-Informed Neural Networks as Solvers for the Time-Dependent Schrödinger Equation, NeurIPS Workshop Machine Learning and the Physical Sciences, arXiv:2210.12522 (2022).
[8] V. Martinetto, K. Shah, A. Cangi, A. Pribram-Jones, Inverting the Kohn-Sham equations with physics-informed machine learning, arXiv:2312.15301 (2023).