# An AI-powered Technology Stack for Solving Many-Electron Field Theory

arXiv: https://arxiv.org/abs/2403.18840 · HTML: https://mlsanity.com/paper/2403.18840/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 9 of its 111 references that are in the map.
- First posted on arXiv 28 Feb 2024.

## Builds on (most cited first, 9 of 9)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Variational Inference with Normalizing Flows](https://mlsanity.com/paper/1505.05770/) (2015)
- [Automatic differentiation in machine learning: a survey](https://mlsanity.com/paper/1502.05767/) (2015)
- [Neural Spline Flows](https://mlsanity.com/paper/1906.04032/) (2019)
- [Neural Importance Sampling](https://mlsanity.com/paper/1808.03856/) (2018)
- [normflows: A PyTorch Package for Normalizing Flows](https://mlsanity.com/paper/2302.12014/) (2023)
- [Cubic-Spline Flows](https://mlsanity.com/paper/1906.02145/) (2019)
- [i-flow: High-dimensional Integration and Sampling with Normalizing Flows](https://mlsanity.com/paper/2001.05486/) (2020)
- [Flow-based sampling for multimodal and extended-mode distributions in lattice field theory](https://mlsanity.com/paper/2107.00734/) (2021)

## Abstract (arXiv)

Quantum field theory (QFT) for interacting many-electron systems is fundamental to condensed matter physics, yet achieving accurate solutions confronts computational challenges in managing the combinatorial complexity of Feynman diagrams, implementing systematic renormalization, and evaluating high-dimensional integrals. We present a unifying framework that integrates QFT computational workflows with an AI-powered technology stack. A cornerstone of this framework is representing Feynman diagrams as computational graphs, which structures the inherent mathematical complexity and facilitates the application of optimized algorithms developed for machine learning and high-performance computing. Consequently, automatic differentiation, native to these graph representations, delivers efficient, fully automated, high-order field-theoretic renormalization procedures. This graph-centric approach also enables sophisticated numerical integration; our neural-network-enhanced Monte Carlo method, accelerated via massively parallel GPU implementation, efficiently evaluates challenging high-dimensional diagrammatic integrals. Applying this framework to the uniform electron gas, we determine the quasiparticle effective mass to a precision significantly surpassing current state-of-the-art simulations. Our work demonstrates the transformative potential of integrating AI-driven computational advances with QFT, opening systematic pathways for solving complex quantum many-body problems across disciplines.