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arXiv · 2108.02200

Spacetime Neural Network for High Dimensional Quantum Dynamics

Jiangran Wang·Zhuo Chen·Di Luo·Zhizhen Zhao·Vera Mikyoung Hur·Bryan K. Clark
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Abstract

We develop a spacetime neural network method with second order optimization for solving quantum dynamics from the high dimensional Schr\"{o}dinger equation. In contrast to the standard iterative first order optimization and the time-dependent variational principle, our approach utilizes the implicit mid-point method and generates the solution for all spatial and temporal values simultaneously after optimization. We demonstrate the method in the Schr\"{o}dinger equation with a self-normalized autoregressive spacetime neural network construction. Future explorations for solving different high dimensional differential equations are discussed.

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Jiangran Wang, Zhuo Chen, Di Luo, Zhizhen Zhao, Vera Mikyoung Hur, Bryan K. Clark. 2021-08-04. Spacetime Neural Network for High Dimensional Quantum Dynamics. https://arxiv.org/abs/2108.02200

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