# Spacetime Neural Network for High Dimensional Quantum Dynamics

arXiv: https://arxiv.org/abs/2108.02200 · HTML: https://mlsanity.com/paper/2108.02200/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 19 references that are in the map.
- First posted on arXiv 4 Aug 2021.

## Builds on (most cited first, 5 of 5)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [DGM: A deep learning algorithm for solving partial differential equations](https://mlsanity.com/paper/1708.07469/) (2017)
- [Solving high-dimensional partial differential equations using deep learning](https://mlsanity.com/paper/1707.02568/) (2017)
- [Deep autoregressive models for the efficient variational simulation of many-body quantum systems](https://mlsanity.com/paper/1902.04057/) (2019)

## Built on by (most cited first, 9 of 9)

- [Gauge Equivariant Neural Networks for 2+1D U(1) Gauge Theory Simulations in Hamiltonian Formulation](https://mlsanity.com/paper/2211.03198/) (2022)
- [Simulating 2+1D Lattice Quantum Electrodynamics at Finite Density with Neural Flow Wavefunctions](https://mlsanity.com/paper/2212.06835/) (2022)
- [Pairing-based graph neural network for simulating quantum materials](https://mlsanity.com/paper/2311.02143/) (2023)
- [Predicting Properties of Quantum Systems with Conditional Generative Models](https://mlsanity.com/paper/2211.16943/) (2022)
- [L2M: Mutual Information Scaling Law for Long-Context Language Modeling](https://mlsanity.com/paper/2503.04725/) (2025)
- [Infinite Neural Network Quantum States: Entanglement and Training Dynamics](https://mlsanity.com/paper/2112.00723/) (2021)
- [TENG: Time-Evolving Natural Gradient for Solving PDEs With Deep Neural Nets Toward Machine Precision](https://mlsanity.com/paper/2404.10771/) (2024)
- [Artificial intelligence for artificial materials: moir'e atom](https://mlsanity.com/paper/2303.08162/) (2023)
- [TENG-BC: Unified Time-Evolving Natural Gradient for Neural PDE Solvers with General Boundary Conditions](https://mlsanity.com/paper/2603.00397/) (2026)

## Abstract (arXiv)

We develop a spacetime neural network method with second order optimization for solving quantum dynamics from the high dimensional Schr"odinger 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"odinger equation with a self-normalized autoregressive spacetime neural network construction. Future explorations for solving different high dimensional differential equations are discussed.