Fourier Neural Differential Equations for learning Quantum Field Theories

• URL: http://arxiv.org/abs/2311.17250v1
• Date: Tue, 28 Nov 2023 22:11:15 GMT
• Title: Fourier Neural Differential Equations for learning Quantum Field Theories
• Authors: Isaac Brant, Alexander Norcliffe and Pietro Li\`o
• Abstract summary: A Quantum Field Theory is defined by its interaction Hamiltonian, and linked to experimental data by the scattering matrix. In this paper, NDE models are used to learn theory, Scalar-Yukawa theory and Scalar Quantum Electrodynamics. The interaction Hamiltonian of a theory can be extracted from network parameters.
• Score: 57.11316818360655
• License: http://creativecommons.org/licenses/by/4.0/
• 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 $\phi^4$ 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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