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arXiv · 2311.17250

Fourier Neural Differential Equations for learning Quantum Field Theories

Isaac Brant·Alexander Norcliffe·Pietro Liò
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Abstract

A Quantum Field Theory is defined by its interaction Hamiltonian, and linked to experimental data by the scattering matrix. The scattering matrix is calculated as a perturbative series, and represented succinctly as a first order differential equation in time. Neural Differential Equations (NDEs) learn the time derivative of a residual network's hidden state, and have proven efficacy in learning differential equations with physical constraints. Hence using an NDE to learn particle scattering matrices presents a possible experiment-theory phenomenological connection. In this paper, NDE models are used to learn $ϕ^4$ theory, Scalar-Yukawa theory and Scalar Quantum Electrodynamics. A new NDE architecture is also introduced, the Fourier Neural Differential Equation (FNDE), which combines NDE integration and Fourier network convolution. The FNDE model demonstrates better generalisability than the non-integrated equivalent FNO model. It is also shown that by training on scattering data, the interaction Hamiltonian of a theory can be extracted from network parameters.

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Isaac Brant, Alexander Norcliffe, Pietro Liò. 2023-11-28. Fourier Neural Differential Equations for learning Quantum Field Theories. https://arxiv.org/abs/2311.17250

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