# NucleoNet: A Nuclear-Aware Determinant Ansatz for Multi-Geometry Neural Variational Monte Carlo

arXiv: https://arxiv.org/abs/2610.12985 · HTML: https://mlsanity.com/paper/2610.12985/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 13 of its 29 references that are in the map.
- First posted on arXiv 9 Oct 2026.

## Builds on (most cited first, 13 of 13)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [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)
- [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)
- [A Kaczmarz-inspired approach to accelerate the optimization of neural network wavefunctions](https://mlsanity.com/paper/2401.10190/) (2024)
- [Solving the electronic Schr"odinger equation for multiple nuclear geometries with weight-sharing deep neural networks](https://mlsanity.com/paper/2105.08351/) (2021)
- [An ab initio foundation model of wavefunctions that accurately describes chemical bond breaking](https://mlsanity.com/paper/2506.19960/) (2025)
- [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)
- [Spin-Adapted Neural Network Wavefunctions in Real Space](https://mlsanity.com/paper/2511.01671/) (2025)

## Abstract (arXiv)

Neural-network variational Monte Carlo provides an accurate route to solving the electronic Schr"odinger equation, but many neural wavefunctions are optimized for a single nuclear geometry, requiring separate calculations to map out a potential energy surface. We introduce NucleoNet, a nuclear-aware determinant ansatz in which electrons and nuclei form a unified particle set propagated through a shared electron--nucleus backbone that jointly evolves one-particle and two-particle representations. Nuclei carry learned representations that evolve alongside the electronic representations and condition orbital construction, while antisymmetry is imposed only by electronic determinants. On equilibrium small-molecule benchmarks, NucleoNet achieves accuracy comparable to established neural-wavefunction baselines with substantially fewer parameters. For each molecular system, a single model optimized jointly across geometries describes the N2 dissociation curve, Li displacement in LiCN, and the ethane and formamide minimum-energy paths for bond dissociation. Sparse-geometry training generalizes to unseen geometries for N2 and LiCN without further optimization, and N2 ablations show that nuclear streams substantially improve this interpolation. These results show that a compact wavefunction with jointly evolved nuclear representations can describe the geometries of a molecular system with a single set of parameters.