Spacetime Neural Network for High Dimensional Quantum Dynamics

• URL: http://arxiv.org/abs/2108.02200v1
• Date: Wed, 4 Aug 2021 17:55:26 GMT
• Title: Spacetime Neural Network for High Dimensional Quantum Dynamics
• Authors: Jiangran Wang, Zhuo Chen, Di Luo, Zhizhen Zhao, Vera Mikyoung Hur, Bryan K. Clark
• Abstract summary: We develop a spacetime neural network method with second order optimization for solving quantum dynamics. We demonstrate the method in the Schr"odinger equation with a self-normalized autoregressive spacetime neural network construction.
• Score: 19.30780557470232
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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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