Machine learning discovers a tube-seeding strategy for IBP reduction of Feynman integrals that scales linearly with numerator power, demonstrated on rank-20 2-loop 5-point integrals.
Zeng,Reinforcement Learning and Metaheuristics for Feynman Integral Reduction,2504.16045
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Two-loop Feynman integrals involve Riemann spheres, elliptic curves, hyperelliptic curves of genus 2 and 3, K3 surfaces, and a rationalizable Del Pezzo surface of degree 2.
Covariant differentiation on the dual vector space spanned by master integrals reduces a large class of Feynman integrals to masters, with connections reusable across mass configurations.
Inconsistency in spanning cuts for IBP reductions arises because cuts can make hidden terms in IBP relations finite via pinch singularities that cancel vanishing parameters, linked to hidden linear relations between propagators, for which an algorithm is provided.
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.
citing papers explorer
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Efficient AI-Inspired Reduction of Feynman Integrals via Tube Seeding
Machine learning discovers a tube-seeding strategy for IBP reduction of Feynman integrals that scales linearly with numerator power, demonstrated on rank-20 2-loop 5-point integrals.
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The spectrum of Feynman-integral geometries at two loops
Two-loop Feynman integrals involve Riemann spheres, elliptic curves, hyperelliptic curves of genus 2 and 3, K3 surfaces, and a rationalizable Del Pezzo surface of degree 2.
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Feynman integral reduction by covariant differentiation
Covariant differentiation on the dual vector space spanned by master integrals reduces a large class of Feynman integrals to masters, with connections reusable across mass configurations.
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On the spanning cuts consistency problem in the IBP reductions of Feynman integrals
Inconsistency in spanning cuts for IBP reductions arises because cuts can make hidden terms in IBP relations finite via pinch singularities that cancel vanishing parameters, linked to hidden linear relations between propagators, for which an algorithm is provided.
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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.