{"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/solving-neural-field-equations-using-physics","title":"Solving Neural Field Equations using Physics Informed Neural Networks","arxiv_id":null,"date":"2023-09-17","proceeding":"International Conference of Numerical Analysis and Applied Mathematics, ICNAAM 2023 9","authors":["Weronika Wojtak","Estela Bicho","Wolfram Erlhagen"],"abstract":"This article presents an approach for solving neural field equations (NFEs) using Physics Informed Neural Networks\r\n(PINNs). NFEs are integro-differential equations describing the spatio-temporal dynamics of neuronal populations in the cortex.\r\nThe traditional numerical methods for NFEs require significant computational effort due to the discretization of the spatial convolution.\r\nThe proposed approach leverages Fast Fourier Transforms (FFTs) to reduce the computational cost and improve efficiency. A\r\nPINN, consisting of a surrogate network and a residual network, is trained to approximate the solutions of NFEs. The effectiveness\r\nof the approach is demonstrated by solving the one-dimensional Amari equation, a commonly used neural field formulation. Our\r\nresults show that the accuracy of the PINN approach is comparable to traditional numerical methods. Future research directions include\r\noptimizing hyperparameters, incorporating input terms in NFEs, exploring transfer learning, addressing the inverse problem,\r\nand extending the approach to higher dimensions.","url_abs":"https://github.com/w-wojtak/solving-NFEs-using-PINNs/blob/main/ICNAAM_2023_Wojtak_final.pdf","url_pdf":"https://github.com/w-wojtak/solving-NFEs-using-PINNs/blob/main/ICNAAM_2023_Wojtak_final.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":"solving-neural-field-equations-using-physics","repo_url":"https://github.com/w-wojtak/solving-NFEs-using-PINNs","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":0,"framework":"pytorch","reach":null}],"tasks":[{"task_slug":"transfer-learning","task_name":"Transfer Learning"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}