Spacetime Neural Network for High Dimensional Quantum Dynamics
This addresses the computational challenge of simulating quantum systems in high dimensions for physics and chemistry applications, though it appears incremental as an extension of neural network methods to this domain.
The researchers tackled solving high-dimensional quantum dynamics from the Schrödinger equation by developing a spacetime neural network method with second-order optimization, which generates solutions for all spatial and temporal values simultaneously after optimization.
We develop a spacetime neural network method with second order optimization for solving quantum dynamics from the high dimensional Schrödinger 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 Schrödinger equation with a self-normalized autoregressive spacetime neural network construction. Future explorations for solving different high dimensional differential equations are discussed.