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Approximating Grassmann valued path integrals with radial basis function neural networks

Gábor Balassa*

  • Department of Physics, Yonsei University, Seoul 03722, South Korea and Institute for Particle and Nuclear Physics, HUN-REN Wigner Research Centre for Physics, 29-33 Konkoly-Thege Miklós út, Budapest 1121, Hungary

  • *Contact author: balassa.gabor@yonsei.ac.kr
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Phys. Rev. D 114, 036024 – Published 24 August, 2026

DOI: https://doi.org/10.1103/c918-1gq1

Abstract

Solving path integrals in quantum field theories often involves the numerical handling of noncommuting Grassmann fields, which is in many cases a highly nontrivial and numerically inefficient task, especially in large systems and at higher dimensions. In this paper a radial basis function type neural network construction is used to approximate fermionic path integrals that include local couplings in their hopping terms. By isolating the interaction terms from the purely fermionic components using a radial basis function expansion, the path integral can be approximated by a few percent accuracy even for very large lattice sizes. The method has been developed and tested using staggered fermions in one, and in two dimensions, through calculating the partition functions, and expectation values.

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Phys. Rev. D 114, 036024– Published 24 August, 2026
  • Received 9 February 2026
  • Accepted 10 August 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP3.

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