Dynamic Learning of Correlation Potentials for a Time-Dependent Kohn-Sham System

Harish S. Bhat, Kevin Collins, Prachi Gupta, Christine M. Isborn
Proceedings of The 4th Annual Learning for Dynamics and Control Conference, PMLR 168:546-558, 2022.

Abstract

We develop methods to learn the correlation potential for a time-dependent Kohn-Sham (TDKS) system in one spatial dimension. We start from a low-dimensional two-electron system for which we can numerically solve the time-dependent Schrödinger equation; this yields electron densities suitable for training models of the correlation potential. We frame the learning problem as one of optimizing a least-squares objective subject to the constraint that the dynamics obey the TDKS equation. Applying adjoints, we develop efficient methods to compute gradients and thereby learn models of the correlation potential. Our results show that it is possible to learn values of the correlation potential such that the resulting electron densities match ground truth densities. We also show how to learn correlation potential functionals with memory, demonstrating one such model that yields reasonable results for trajectories outside the training set.

Cite this Paper

BibTeX
@InProceedings{pmlr-v168-bhat22a, title = {Dynamic Learning of Correlation Potentials for a Time-Dependent Kohn-Sham System}, author = {Bhat, Harish S. and Collins, Kevin and Gupta, Prachi and Isborn, Christine M.}, booktitle = {Proceedings of The 4th Annual Learning for Dynamics and Control Conference}, pages = {546--558}, year = {2022}, editor = {Firoozi, Roya and Mehr, Negar and Yel, Esen and Antonova, Rika and Bohg, Jeannette and Schwager, Mac and Kochenderfer, Mykel}, volume = {168}, series = {Proceedings of Machine Learning Research}, month = {23--24 Jun}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v168/bhat22a/bhat22a.pdf}, url = {https://proceedings.mlr.press/v168/bhat22a.html}, abstract = {We develop methods to learn the correlation potential for a time-dependent Kohn-Sham (TDKS) system in one spatial dimension. We start from a low-dimensional two-electron system for which we can numerically solve the time-dependent Schrödinger equation; this yields electron densities suitable for training models of the correlation potential. We frame the learning problem as one of optimizing a least-squares objective subject to the constraint that the dynamics obey the TDKS equation. Applying adjoints, we develop efficient methods to compute gradients and thereby learn models of the correlation potential. Our results show that it is possible to learn values of the correlation potential such that the resulting electron densities match ground truth densities. We also show how to learn correlation potential functionals with memory, demonstrating one such model that yields reasonable results for trajectories outside the training set.} }
Endnote
%0 Conference Paper %T Dynamic Learning of Correlation Potentials for a Time-Dependent Kohn-Sham System %A Harish S. Bhat %A Kevin Collins %A Prachi Gupta %A Christine M. Isborn %B Proceedings of The 4th Annual Learning for Dynamics and Control Conference %C Proceedings of Machine Learning Research %D 2022 %E Roya Firoozi %E Negar Mehr %E Esen Yel %E Rika Antonova %E Jeannette Bohg %E Mac Schwager %E Mykel Kochenderfer %F pmlr-v168-bhat22a %I PMLR %P 546--558 %U https://proceedings.mlr.press/v168/bhat22a.html %V 168 %X We develop methods to learn the correlation potential for a time-dependent Kohn-Sham (TDKS) system in one spatial dimension. We start from a low-dimensional two-electron system for which we can numerically solve the time-dependent Schrödinger equation; this yields electron densities suitable for training models of the correlation potential. We frame the learning problem as one of optimizing a least-squares objective subject to the constraint that the dynamics obey the TDKS equation. Applying adjoints, we develop efficient methods to compute gradients and thereby learn models of the correlation potential. Our results show that it is possible to learn values of the correlation potential such that the resulting electron densities match ground truth densities. We also show how to learn correlation potential functionals with memory, demonstrating one such model that yields reasonable results for trajectories outside the training set.
APA
Bhat, H.S., Collins, K., Gupta, P. & Isborn, C.M.. (2022). Dynamic Learning of Correlation Potentials for a Time-Dependent Kohn-Sham System. Proceedings of The 4th Annual Learning for Dynamics and Control Conference, in Proceedings of Machine Learning Research 168:546-558 Available from https://proceedings.mlr.press/v168/bhat22a.html.

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