# Sampling-free Inference for Ab-Initio Potential Energy Surface Networks

arXiv: https://arxiv.org/abs/2205.14962 · HTML: https://mlsanity.com/paper/2205.14962/

## Key facts

- Cited by 19 papers in the map (data through 14 Oct 2026).
- Builds on 19 of its 67 references that are in the map.
- First posted on arXiv 30 May 2022.

## Builds on (most cited first, 19 of 19)

- [Gaussian Error Linear Units (GELUs)](https://mlsanity.com/paper/1606.08415/) (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)
- [Directional Message Passing for Molecular Graphs](https://mlsanity.com/paper/2003.03123/) (2020)
- [Equivariant message passing for the prediction of tensorial properties and molecular spectra](https://mlsanity.com/paper/2102.03150/) (2021)
- [High-Performance Large-Scale Image Recognition Without Normalization](https://mlsanity.com/paper/2102.06171/) (2021)
- [GemNet: Universal Directional Graph Neural Networks for Molecules](https://mlsanity.com/paper/2106.08903/) (2021)
- [Fast and Uncertainty-Aware Directional Message Passing for Non-Equilibrium Molecules](https://mlsanity.com/paper/2011.14115/) (2020)
- [Ab-Initio Solution of the Many-Electron Schr"odinger Equation with Deep Neural Networks](https://mlsanity.com/paper/1909.02487/) (2019)
- [Spherical Message Passing for 3D Graph Networks](https://mlsanity.com/paper/2102.05013/) (2021)
- [Deep neural network solution of the electronic Schr"odinger equation](https://mlsanity.com/paper/1909.08423/) (2019)
- [Characterizing signal propagation to close the performance gap in unnormalized ResNets](https://mlsanity.com/paper/2101.08692/) (2021)
- [OrbNet: Deep Learning for Quantum Chemistry Using Symmetry-Adapted Atomic-Orbital Features](https://mlsanity.com/paper/2007.08026/) (2020)
- [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)
- [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)
- [Explicitly antisymmetrized neural network layers for variational Monte Carlo simulation](https://mlsanity.com/paper/2112.03491/) (2021)

## Built on by (most cited first, 19 of 19)

- [A Self-Attention Ansatz for Ab-initio Quantum Chemistry](https://mlsanity.com/paper/2211.13672/) (2022)
- [Ab-initio quantum chemistry with neural-network wavefunctions](https://mlsanity.com/paper/2208.12590/) (2022)
- [Generalizing Neural Wave Functions](https://mlsanity.com/paper/2302.04168/) (2023)
- [Uncertainty Estimation for Molecules: Desiderata and Methods](https://mlsanity.com/paper/2306.14916/) (2023)
- [Variational Monte Carlo on a Budget -- Fine-tuning pre-trained Neural Wavefunctions](https://mlsanity.com/paper/2307.09337/) (2023)
- [Neural Pfaffians: Solving Many Many-Electron Schr"odinger Equations](https://mlsanity.com/paper/2405.14762/) (2024)
- [Accurate Ab-initio Neural-network Solutions to Large-Scale Electronic Structure Problems](https://mlsanity.com/paper/2504.06087/) (2025)
- [Towards a Foundation Model for Neural Network Wavefunctions](https://mlsanity.com/paper/2303.09949/) (2023)
- [Forward Laplacian: A New Computational Framework for Neural Network-based Variational Monte Carlo](https://mlsanity.com/paper/2307.08214/) (2023)
- [Learning Equivariant Non-Local Electron Density Functionals](https://mlsanity.com/paper/2410.07972/) (2024)
- [MolCrystalFlow: Molecular Crystal Structure Prediction via Flow Matching](https://mlsanity.com/paper/2602.16020/) (2026)
- [Large Electron Model: A Universal Ground State Predictor](https://mlsanity.com/paper/2603.02346/) (2026)
- [On Representing Electronic Wave Functions with Sign Equivariant Neural Networks](https://mlsanity.com/paper/2403.05249/) (2024)
- [Ab-initio simulation of excited-state potential energy surfaces with transferable deep quantum Monte Carlo](https://mlsanity.com/paper/2503.19847/) (2025)
- [Excited Pfaffians: Generalized Neural Wave Functions Across Structure and State](https://mlsanity.com/paper/2603.14515/) (2026)
- [A Score-Based Model for Learning Neural Wavefunctions](https://mlsanity.com/paper/2305.16540/) (2023)
- [Enabling ab initio geometry optimization of strongly correlated systems with transferable deep quantum Monte Carlo](https://mlsanity.com/paper/2603.25381/) (2026)
- [Is Variational Monte Carlo Robust? Sharp Moment Thresholds and Heavy-tailed Stochastic Optimization](https://mlsanity.com/paper/2606.26009/) (2026)
- [Foundation Neural-Network Quantum States for Molecular Potential Energy Surfaces in Second Quantization](https://mlsanity.com/paper/2609.37733/) (2026)

## Abstract (arXiv)

Recently, it has been shown that neural networks not only approximate the ground-state wave functions of a single molecular system well but can also generalize to multiple geometries. While such generalization significantly speeds up training, each energy evaluation still requires Monte Carlo integration which limits the evaluation to a few geometries. In this work, we address the inference shortcomings by proposing the Potential learning from ab-initio Networks (PlaNet) framework, in which we simultaneously train a surrogate model in addition to the neural wave function. At inference time, the surrogate avoids expensive Monte-Carlo integration by directly estimating the energy, accelerating the process from hours to milliseconds. In this way, we can accurately model high-resolution multi-dimensional energy surfaces for larger systems that previously were unobtainable via neural wave functions. Finally, we explore an additional inductive bias by introducing physically-motivated restricted neural wave function models. We implement such a function with several additional improvements in the new PESNet++ model. In our experimental evaluation, PlaNet accelerates inference by 7 orders of magnitude for larger molecules like ethanol while preserving accuracy. Compared to previous energy surface networks, PESNet++ reduces energy errors by up to 74%.