# Renormalization-Inspired Effective Field Neural Networks for Scalable Modeling of Classical and Quantum Many-Body Systems

arXiv: https://arxiv.org/abs/2502.17665 · HTML: https://mlsanity.com/paper/2502.17665/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 11 of its 92 references that are in the map.
- First posted on arXiv 24 Feb 2025.

## Builds on (most cited first, 11 of 11)

- [E(3)-Equivariant Graph Neural Networks for Data-Efficient and Accurate Interatomic Potentials](https://mlsanity.com/paper/2101.03164/) (2021)
- [Machine Learning for Fluid Mechanics](https://mlsanity.com/paper/1905.11075/) (2019)
- [Ab-Initio Solution of the Many-Electron Schr"odinger Equation with Deep Neural Networks](https://mlsanity.com/paper/1909.02487/) (2019)
- [Physics-Informed Generative Adversarial Networks for Stochastic Differential Equations](https://mlsanity.com/paper/1811.02033/) (2018)
- [Lorentz Group Equivariant Neural Network for Particle Physics](https://mlsanity.com/paper/2006.04780/) (2020)
- [Equivariant flow-based sampling for lattice gauge theory](https://mlsanity.com/paper/2003.06413/) (2020)
- [Discovering Phase Transitions with Unsupervised Learning](https://mlsanity.com/paper/1606.00318/) (2016)
- [Physical Symmetries Embedded in Neural Networks](https://mlsanity.com/paper/1904.08991/) (2019)
- [Accelerate Monte Carlo Simulations with Restricted Boltzmann Machines](https://mlsanity.com/paper/1610.02746/) (2016)
- [Spin-Dependent Graph Neural Network Potential for Magnetic Materials](https://mlsanity.com/paper/2203.02853/) (2022)
- [Complex Spin Hamiltonian Represented by Artificial Neural Network](https://mlsanity.com/paper/2110.00724/) (2021)

## Abstract (arXiv)

We introduce Effective Field Neural Networks (EFNNs), a new architecture based on continued functions -- mathematical tools used in renormalization to handle divergent perturbative series. Our key insight is that neural networks can implement these continued functions directly, providing a principled approach to many-body interactions. Testing on three systems (a classical 3-spin infinite- range model, a continuous classical Heisenberg spin system, and a quantum double exchange model), we find that EFNN outperforms standard deep networks, ResNet, and DenseNet. Most striking is EFNN's generalization: trained on 10 × 10 lattices, it accurately predicts behavior on systems up to 40× 40 with no additional training -- and the accuracy improves with system size, with a computational time speed-up of 103 compared to ED for 40× 40 lattice. This demonstrates that EFNN captures the underlying physics rather than merely fitting data, making it valuable beyond many-body problems to any field where renormalization ideas apply.