# Accurate Ab-initio Neural-network Solutions to Large-Scale Electronic Structure Problems

arXiv: https://arxiv.org/abs/2504.06087 · HTML: https://mlsanity.com/paper/2504.06087/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 70 references that are in the map.
- First posted on arXiv 8 Apr 2025.

## Builds on (most cited first, 15 of 15)

- [LLaMA: Open and Efficient Foundation Language Models](https://mlsanity.com/paper/2302.13971/) (2023)
- [Vision Transformers Need Registers](https://mlsanity.com/paper/2309.16588/) (2023)
- [Ab-Initio Solution of the Many-Electron Schr"odinger Equation with Deep Neural Networks](https://mlsanity.com/paper/1909.02487/) (2019)
- [Better Theory for SGD in the Nonconvex World](https://mlsanity.com/paper/2002.03329/) (2020)
- [A Self-Attention Ansatz for Ab-initio Quantum Chemistry](https://mlsanity.com/paper/2211.13672/) (2022)
- [So3krates: Equivariant attention for interactions on arbitrary length-scales in molecular systems](https://mlsanity.com/paper/2205.14276/) (2022)
- [Better, Faster Fermionic Neural Networks](https://mlsanity.com/paper/2011.07125/) (2020)
- [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)
- [Directional Message Passing on Molecular Graphs via Synthetic Coordinates](https://mlsanity.com/paper/2111.04718/) (2021)
- [Sampling-free Inference for Ab-Initio Potential Energy Surface Networks](https://mlsanity.com/paper/2205.14962/) (2022)
- [Accurate Computation of Quantum Excited States with Neural Networks](https://mlsanity.com/paper/2308.16848/) (2023)
- [Convergence Analysis of Stochastic Gradient Descent with MCMC Estimators](https://mlsanity.com/paper/2303.10599/) (2023)
- [Convergence of variational Monte Carlo simulation and scale-invariant pre-training](https://mlsanity.com/paper/2303.11602/) (2023)

## Built on by (most cited first, 8 of 8)

- [An ab initio foundation model of wavefunctions that accurately describes chemical bond breaking](https://mlsanity.com/paper/2506.19960/) (2025)
- [A Sketch-and-Project Analysis of Subsampled Natural Gradient Algorithms](https://mlsanity.com/paper/2508.21022/) (2025)
- [Spin-Adapted Neural Network Wavefunctions in Real Space](https://mlsanity.com/paper/2511.01671/) (2025)
- [Benchmarking Simulacra AI's Quantum Accurate Synthetic Data Generation for Chemical Sciences](https://mlsanity.com/paper/2511.07433/) (2025)
- [Excited Pfaffians: Generalized Neural Wave Functions Across Structure and State](https://mlsanity.com/paper/2603.14515/) (2026)
- [Hessian-informed machine learning interatomic potential towards bridging theory and experiments](https://mlsanity.com/paper/2603.25373/) (2026)
- [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)

## Abstract (arXiv)

We present finite-range embeddings (FiRE), a novel wave function ansatz for accurate large-scale ab-initio electronic structure calculations. Compared to contemporary neural-network wave functions, FiRE reduces the asymptotic complexity of neural-network variational Monte Carlo (NN-VMC) by ~ nel, the number of electrons. By restricting electron-electron interactions within the neural network, FiRE accelerates all key operations -- sampling, pseudopotentials, and Laplacian computations -- resulting in a real-world 10× acceleration in now-feasible 180-electron calculations. We validate our method's accuracy on various challenging systems, including biochemical compounds, conjugated hydrocarbons, and organometallic compounds. On these systems, FiRE's energies are consistently within chemical accuracy of the most reliable data, including experiments, even in cases where high-accuracy methods such as CCSD(T), AFQMC, or contemporary NN-VMC fall short. With these improvements in both runtime and accuracy, FiRE represents a new `gold-standard' method for fast and accurate large-scale ab-initio calculations, potentially enabling new computational studies in fields like quantum chemistry, solid-state physics, and material design.