# Ab-initio quantum chemistry with neural-network wavefunctions

arXiv: https://arxiv.org/abs/2208.12590 · HTML: https://mlsanity.com/paper/2208.12590/

## Key facts

- Cited by 29 papers in the map (data through 14 Oct 2026).
- Builds on 42 of its 185 references that are in the map.
- First posted on arXiv 26 Aug 2022.

## Builds on (most cited first, 30 of 42)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [ImageNet Large Scale Visual Recognition Challenge](https://mlsanity.com/paper/1409.0575/) (2014)
- [Explaining and Harnessing Adversarial Examples](https://mlsanity.com/paper/1412.6572/) (2014)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [Variational Inference with Normalizing Flows](https://mlsanity.com/paper/1505.05770/) (2015)
- [WaveNet: A Generative Model for Raw Audio](https://mlsanity.com/paper/1609.03499/) (2016)
- [Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gauges](https://mlsanity.com/paper/2104.13478/) (2021)
- [Conditional Image Generation with PixelCNN Decoders](https://mlsanity.com/paper/1606.05328/) (2016)
- [Optimizing Neural Networks with Kronecker-factored Approximate Curvature](https://mlsanity.com/paper/1503.05671/) (2015)
- [Deep Learning in Neural Networks: An Overview](https://mlsanity.com/paper/1404.7828/) (2014)
- [Automatic chemical design using a data-driven continuous representation of molecules](https://mlsanity.com/paper/1610.02415/) (2016)
- [Tensor field networks: Rotation- and translation-equivariant neural networks for 3D point clouds](https://mlsanity.com/paper/1802.08219/) (2018)
- [E(3)-Equivariant Graph Neural Networks for Data-Efficient and Accurate Interatomic Potentials](https://mlsanity.com/paper/2101.03164/) (2021)
- [Equivariant Diffusion for Molecule Generation in 3D](https://mlsanity.com/paper/2203.17003/) (2022)
- [MACE: Higher Order Equivariant Message Passing Neural Networks for Fast and Accurate Force Fields](https://mlsanity.com/paper/2206.07697/) (2022)
- [Equivariant message passing for the prediction of tensorial properties and molecular spectra](https://mlsanity.com/paper/2102.03150/) (2021)
- [Identifying and attacking the saddle point problem in high-dimensional non-convex optimization](https://mlsanity.com/paper/1406.2572/) (2014)
- [The Loss Surfaces of Multilayer Networks](https://mlsanity.com/paper/1412.0233/) (2014)
- [Machine Learning Force Fields](https://mlsanity.com/paper/2010.07067/) (2020)
- [Ab-Initio Solution of the Many-Electron Schr"odinger Equation with Deep Neural Networks](https://mlsanity.com/paper/1909.02487/) (2019)
- [e3nn: Euclidean Neural Networks](https://mlsanity.com/paper/2207.09453/) (2022)
- [The Hardware Lottery](https://mlsanity.com/paper/2009.06489/) (2020)
- [Deep neural network solution of the electronic Schr"odinger equation](https://mlsanity.com/paper/1909.08423/) (2019)
- [Machine learning for molecular simulation](https://mlsanity.com/paper/1911.02792/) (2019)
- [Quantum Natural Gradient](https://mlsanity.com/paper/1909.02108/) (2019)
- [Unifying machine learning and quantum chemistry -- a deep neural network for molecular wavefunctions](https://mlsanity.com/paper/1906.10033/) (2019)
- [Deep autoregressive models for the efficient variational simulation of many-body quantum systems](https://mlsanity.com/paper/1902.04057/) (2019)
- [Relevance of Rotationally Equivariant Convolutions for Predicting Molecular Properties](https://mlsanity.com/paper/2008.08461/) (2020)
- [Ab-Initio Potential Energy Surfaces by Pairing GNNs with Neural Wave Functions](https://mlsanity.com/paper/2110.05064/) (2021)

## Built on by (most cited first, 29 of 29)

- [Introduction to Latent Variable Energy-Based Models: A Path Towards Autonomous Machine Intelligence](https://mlsanity.com/paper/2306.02572/) (2023)
- [A Self-Attention Ansatz for Ab-initio Quantum Chemistry](https://mlsanity.com/paper/2211.13672/) (2022)
- [Generalizing Neural Wave Functions](https://mlsanity.com/paper/2302.04168/) (2023)
- [Accurate Computation of Quantum Excited States with Neural Networks](https://mlsanity.com/paper/2308.16848/) (2023)
- [An ab initio foundation model of wavefunctions that accurately describes chemical bond breaking](https://mlsanity.com/paper/2506.19960/) (2025)
- [Operator SVD with Neural Networks via Nested Low-Rank Approximation](https://mlsanity.com/paper/2402.03655/) (2024)
- [Improving Energy Natural Gradient Descent through Woodbury, Momentum, and Randomization](https://mlsanity.com/paper/2505.12149/) (2025)
- [Wasserstein Quantum Monte Carlo: A Novel Approach for Solving the Quantum Many-Body Schr"odinger Equation](https://mlsanity.com/paper/2307.07050/) (2023)
- [Neural Pfaffians: Solving Many Many-Electron Schr"odinger Equations](https://mlsanity.com/paper/2405.14762/) (2024)
- [Ab-initio variational wave functions for the time-dependent many-electron Schr"odinger equation](https://mlsanity.com/paper/2403.07447/) (2024)
- [Quantum computing and artificial intelligence: status and perspectives](https://mlsanity.com/paper/2505.23860/) (2025)
- [Weighted Sobolev Approximation Rates for Neural Networks on Unbounded Domains](https://mlsanity.com/paper/2411.04108/) (2024)
- [Highly Accurate Real-space Electron Densities with Neural Networks](https://mlsanity.com/paper/2409.01306/) (2024)
- [Functional Neural Wavefunction Optimization](https://mlsanity.com/paper/2507.10835/) (2025)
- [First principles physics-informed neural network for quantum wavefunctions and eigenvalue surfaces](https://mlsanity.com/paper/2211.04607/) (2022)
- [Worth Their Weight: Randomized and Regularized Block Kaczmarz Algorithms without Preprocessing](https://mlsanity.com/paper/2502.00882/) (2025)
- [Waveflow: boundary-conditioned normalizing flows applied to fermionic wavefunctions](https://mlsanity.com/paper/2211.14839/) (2022)
- [On Training Derivative-Constrained Neural Networks](https://mlsanity.com/paper/2310.01649/) (2023)
- [Excited Pfaffians: Generalized Neural Wave Functions Across Structure and State](https://mlsanity.com/paper/2603.14515/) (2026)
- [A Fully GPU-Accelerated Framework for High-Performance Configuration Interaction Selection with Neural Network Quantum States](https://mlsanity.com/paper/2604.15768/) (2026)
- [A Score-Based Model for Learning Neural Wavefunctions](https://mlsanity.com/paper/2305.16540/) (2023)
- [Hybrid Ground-State Quantum Algorithms based on Neural Schr"odinger Forging](https://mlsanity.com/paper/2307.02633/) (2023)
- [Ground state phases of the two-dimension electron gas with a unified variational approach](https://mlsanity.com/paper/2405.19397/) (2024)
- [Operator Learning for Schr"odinger Equation: Unitarity, Error Bounds, and Time Generalization](https://mlsanity.com/paper/2505.18288/) (2025)
- [Solving excited states for long-range interacting trapped ions with neural networks](https://mlsanity.com/paper/2506.08594/) (2025)
- [Is Variational Monte Carlo Robust? Sharp Moment Thresholds and Heavy-tailed Stochastic Optimization](https://mlsanity.com/paper/2606.26009/) (2026)
- [Geometric Mean Pooling for Equal-Weight Multiplicative Coarse-Graining](https://mlsanity.com/paper/2609.21876/) (2026)
- [Foundation Neural-Network Quantum States for Molecular Potential Energy Surfaces in Second Quantization](https://mlsanity.com/paper/2609.37733/) (2026)
- [Generalization of Transformer-Based Neural Quantum States via In-Context Learning](https://mlsanity.com/paper/2610.03463/) (2026)

## Abstract (arXiv)

Machine learning and specifically deep-learning methods have outperformed human capabilities in many pattern recognition and data processing problems, in game playing, and now also play an increasingly important role in scientific discovery. A key application of machine learning in the molecular sciences is to learn potential energy surfaces or force fields from ab-initio solutions of the electronic Schr"odinger equation using datasets obtained with density functional theory, coupled cluster, or other quantum chemistry methods. Here we review a recent and complementary approach: using machine learning to aid the direct solution of quantum chemistry problems from first principles. Specifically, we focus on quantum Monte Carlo (QMC) methods that use neural network ansatz functions in order to solve the electronic Schr"odinger equation, both in first and second quantization, computing ground and excited states, and generalizing over multiple nuclear configurations. Compared to existing quantum chemistry methods, these new deep QMC methods have the potential to generate highly accurate solutions of the Schr"odinger equation at relatively modest computational cost.