{"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/sensitivity-constrained-fourier-neural","title":"Sensitivity-Constrained Fourier Neural Operators for Forward and Inverse Problems in Parametric Differential Equations","arxiv_id":"2505.08740","date":"2025-05-13","proceeding":null,"authors":["Abdolmehdi Behroozi","Chaopeng Shen and","Daniel Kifer"],"abstract":"Parametric differential equations of the form du/dt = f(u, x, t, p) are fundamental in science and engineering. While deep learning frameworks such as the Fourier Neural Operator (FNO) can efficiently approximate solutions, they struggle with inverse problems, sensitivity estimation (du/dp), and concept drift. We address these limitations by introducing a sensitivity-based regularization strategy, called Sensitivity-Constrained Fourier Neural Operators (SC-FNO). SC-FNO achieves high accuracy in predicting solution paths and consistently outperforms standard FNO and FNO with physics-informed regularization. It improves performance in parameter inversion tasks, scales to high-dimensional parameter spaces (tested with up to 82 parameters), and reduces both data and training requirements. These gains are achieved with a modest increase in training time (30% to 130% per epoch) and generalize across various types of differential equations and neural operators. Code and selected experiments are available at: https://github.com/AMBehroozi/SC_Neural_Operators","url_abs":"https://arxiv.org/abs/2505.08740v3","url_pdf":"https://arxiv.org/pdf/2505.08740v3.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":"sensitivity-constrained-fourier-neural","repo_url":"https://github.com/ambehroozi/sc_neural_operators","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"pytorch","reach":{"status":"ok"}}],"tasks":[{"task_slug":"sensitivity","task_name":"Sensitivity"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=2505.08740","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}