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Refining Integration-by-Parts Reduction of Feynman Integrals with Machine Learning
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Refining Integration-by-Parts Reduction of Feynman Integrals with Machine Learning
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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.
Forward citations
Cited by 9 Pith papers
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FeynmanBench: Benchmarking Multimodal LLMs on Diagrammatic Physics Reasoning
Across 19 multimodal LLMs, local Feynman-diagram recognition stays high while topological reconstruction and full amplitude derivation collapse.
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AMFlow 2.0: significant algorithmic and software improvements for Feynman integral evaluation
AMFlow 2.0 cuts symbolic and numerical cost of multi-loop Feynman integral evaluation via an FT recursion mode, a C++ DE solver, and modern IBP reducers, demonstrated on a three-loop five-point family.
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