Abstract

A Quantum Field Theory (QFT) is defined by its interaction Hamiltonian and linked to experimental data by the scattering matrix – a relationship represented 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. To test the applicability of NDEs to QFTs, NDE models are used to learn φ4 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. It is shown that by training on scattering data, the interaction Hamiltonian of a theory can be extracted from learnt network parameters.