{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/fourier-neural-differential-equations-for","title":"Fourier Neural Differential Equations for learning Quantum Field Theories","arxiv_id":"2311.17250","date":"2023-11-28","proceeding":null,"authors":["Isaac Brant","Alexander Norcliffe","Pietro Liò"],"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.","url_abs":"https://arxiv.org/abs/2311.17250v1","url_pdf":"https://arxiv.org/pdf/2311.17250v1.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"fourier-neural-differential-equations-for","repo_url":"https://github.com/2357e2/fnde","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"pytorch","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}