# Forward Laplacian: A New Computational Framework for Neural Network-based Variational Monte Carlo

arXiv: https://arxiv.org/abs/2307.08214 · HTML: https://mlsanity.com/paper/2307.08214/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 53 references that are in the map.
- First posted on arXiv 17 Jul 2023.

## Builds on (most cited first, 17 of 17)

- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [Ab-Initio Solution of the Many-Electron Schr"odinger Equation with Deep Neural Networks](https://mlsanity.com/paper/1909.02487/) (2019)
- [Deep neural network solution of the electronic Schr"odinger equation](https://mlsanity.com/paper/1909.08423/) (2019)
- [A Self-Attention Ansatz for Ab-initio Quantum Chemistry](https://mlsanity.com/paper/2211.13672/) (2022)
- [Ab-Initio Potential Energy Surfaces by Pairing GNNs with Neural Wave Functions](https://mlsanity.com/paper/2110.05064/) (2021)
- [Better, Faster Fermionic Neural Networks](https://mlsanity.com/paper/2011.07125/) (2020)
- [NetKet 3: Machine Learning Toolbox for Many-Body Quantum Systems](https://mlsanity.com/paper/2112.10526/) (2021)
- [Generalizing Neural Wave Functions](https://mlsanity.com/paper/2302.04168/) (2023)
- [Gold-standard solutions to the Schr"odinger equation using deep learning: How much physics do we need?](https://mlsanity.com/paper/2205.09438/) (2022)
- [Discovering Quantum Phase Transitions with Fermionic Neural Networks](https://mlsanity.com/paper/2202.05183/) (2022)
- [Solving the electronic Schr"odinger equation for multiple nuclear geometries with weight-sharing deep neural networks](https://mlsanity.com/paper/2105.08351/) (2021)
- [Learning Physics-Informed Neural Networks without Stacked Back-propagation](https://mlsanity.com/paper/2202.09340/) (2022)
- [Is L2 Physics-Informed Loss Always Suitable for Training Physics-Informed Neural Network?](https://mlsanity.com/paper/2206.02016/) (2022)
- [Electronic excited states in deep variational Monte Carlo](https://mlsanity.com/paper/2203.09472/) (2022)
- [Sampling-free Inference for Ab-Initio Potential Energy Surface Networks](https://mlsanity.com/paper/2205.14962/) (2022)
- [Explicitly antisymmetrized neural network layers for variational Monte Carlo simulation](https://mlsanity.com/paper/2112.03491/) (2021)
- [Towards a Foundation Model for Neural Network Wavefunctions](https://mlsanity.com/paper/2303.09949/) (2023)

## Built on by (most cited first, 6 of 6)

- [Kronecker-Factored Approximate Curvature for Physics-Informed Neural Networks](https://mlsanity.com/paper/2405.15603/) (2024)
- [Stochastic Taylor Derivative Estimator: Efficient amortization for arbitrary differential operators](https://mlsanity.com/paper/2412.00088/) (2024)
- [Transferable Neural Wavefunctions for Solids](https://mlsanity.com/paper/2405.07599/) (2024)
- [QERNEL: a Scalable Large Electron Model](https://mlsanity.com/paper/2604.26018/) (2026)
- [On Representing Electronic Wave Functions with Sign Equivariant Neural Networks](https://mlsanity.com/paper/2403.05249/) (2024)
- [Is attention all you need to solve the correlated electron problem?](https://mlsanity.com/paper/2502.05383/) (2025)

## Abstract (arXiv)

Neural network-based variational Monte Carlo (NN-VMC) has emerged as a promising cutting-edge technique of ab initio quantum chemistry. However, the high computational cost of existing approaches hinders their applications in realistic chemistry problems. Here, we report the development of a new NN-VMC method that achieves a remarkable speed-up by more than one order of magnitude, thereby greatly extending the applicability of NN-VMC to larger systems. Our key design is a novel computational framework named Forward Laplacian, which computes the Laplacian associated with neural networks, the bottleneck of NN-VMC, through an efficient forward propagation process. We then demonstrate that Forward Laplacian is not only versatile but also facilitates more developments of acceleration methods across various aspects, including optimization for sparse derivative matrix and efficient neural network design. Empirically, our approach enables NN-VMC to investigate a broader range of atoms, molecules and chemical reactions for the first time, providing valuable references to other ab initio methods. The results demonstrate a great potential in applying deep learning methods to solve general quantum mechanical problems.