Scalable learning of potentials to predict time-dependent Hartree-Fock dynamics
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866915047346798592 |
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| author | Bhat, Harish S. Gupta, Prachi Isborn, Christine M. |
| author_facet | Bhat, Harish S. Gupta, Prachi Isborn, Christine M. |
| contents | We propose a framework to learn the time-dependent Hartree-Fock (TDHF) inter-electronic potential of a molecule from its electron density dynamics. Though the entire TDHF Hamiltonian, including the inter-electronic potential, can be computed from first principles, we use this problem as a testbed to develop strategies that can be applied to learn a priori unknown terms that arise in other methods/approaches to quantum dynamics, e.g., emerging problems such as learning exchange-correlation potentials for time-dependent density functional theory. We develop, train, and test three models of the TDHF inter-electronic potential, each parameterized by a four-index tensor of size up to $60 \times 60 \times 60 \times 60$. Two of the models preserve Hermitian symmetry, while one model preserves an eight-fold permutation symmetry that implies Hermitian symmetry. Across seven different molecular systems, we find that accounting for the deeper eight-fold symmetry leads to the best-performing model across three metrics: training efficiency, test set predictive power, and direct comparison of true and learned inter-electronic potentials. All three models, when trained on ensembles of field-free trajectories, generate accurate electron dynamics predictions even in a field-on regime that lies outside the training set. To enable our models to scale to large molecular systems, we derive expressions for Jacobian-vector products that enable iterative, matrix-free training. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_04765 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Scalable learning of potentials to predict time-dependent Hartree-Fock dynamics Bhat, Harish S. Gupta, Prachi Isborn, Christine M. Chemical Physics Computational Physics Data Analysis, Statistics and Probability Machine Learning We propose a framework to learn the time-dependent Hartree-Fock (TDHF) inter-electronic potential of a molecule from its electron density dynamics. Though the entire TDHF Hamiltonian, including the inter-electronic potential, can be computed from first principles, we use this problem as a testbed to develop strategies that can be applied to learn a priori unknown terms that arise in other methods/approaches to quantum dynamics, e.g., emerging problems such as learning exchange-correlation potentials for time-dependent density functional theory. We develop, train, and test three models of the TDHF inter-electronic potential, each parameterized by a four-index tensor of size up to $60 \times 60 \times 60 \times 60$. Two of the models preserve Hermitian symmetry, while one model preserves an eight-fold permutation symmetry that implies Hermitian symmetry. Across seven different molecular systems, we find that accounting for the deeper eight-fold symmetry leads to the best-performing model across three metrics: training efficiency, test set predictive power, and direct comparison of true and learned inter-electronic potentials. All three models, when trained on ensembles of field-free trajectories, generate accurate electron dynamics predictions even in a field-on regime that lies outside the training set. To enable our models to scale to large molecular systems, we derive expressions for Jacobian-vector products that enable iterative, matrix-free training. |
| title | Scalable learning of potentials to predict time-dependent Hartree-Fock dynamics |
| topic | Chemical Physics Computational Physics Data Analysis, Statistics and Probability Machine Learning |
| url | https://arxiv.org/abs/2408.04765 |