# Refining Integration-by-Parts Reduction of Feynman Integrals with Machine Learning

arXiv: https://arxiv.org/abs/2502.05121 · HTML: https://mlsanity.com/paper/2502.05121/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 1 of its 19 references that are in the map.
- First posted on arXiv 7 Feb 2025.

## Builds on (most cited first, 1 of 1)

- [Transforming the Bootstrap: Using Transformers to Compute Scattering Amplitudes in Planar N = 4 Super Yang-Mills Theory](https://mlsanity.com/paper/2405.06107/) (2024)

## Built on by (most cited first, 6 of 6)

- [Learning-at-Criticality in Large Language Models for Quantum Field Theory and Beyond](https://mlsanity.com/paper/2506.03703/) (2025)
- [Symbolic Regression with Multimodal Large Language Models and Kolmogorov Arnold Networks](https://mlsanity.com/paper/2505.07956/) (2025)
- [Learning to Unscramble Feynman Loop Integrals with SAILIR](https://mlsanity.com/paper/2604.05034/) (2026)
- [Machine learning modularity](https://mlsanity.com/paper/2601.01779/) (2026)
- [FeynmanBench: Benchmarking Multimodal LLMs on Diagrammatic Physics Reasoning](https://mlsanity.com/paper/2604.03893/) (2026)
- [Efficient AI-Inspired Reduction of Feynman Integrals via Tube Seeding](https://mlsanity.com/paper/2606.10698/) (2026)

## Abstract (arXiv)

Integration-by-parts reductions of Feynman integrals pose a frequent bottle-neck in state-of-the-art calculations in theoretical particle and gravitational-wave physics, and rely on heuristic approaches for selecting integration-by-parts identities, whose quality heavily influences the performance. In this paper, we investigate the use of machine-learning techniques to find improved heuristics. We use funsearch, a genetic programming variant based on code generation by a Large Language Model, in order to explore possible approaches, then use strongly typed genetic programming to zero in on useful solutions. Both approaches manage to re-discover the state-of-the-art heuristics recently incorporated into integration-by-parts solvers, and in one example find a small advance on this state of the art.