{"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/derivative-enhanced-deep-operator-network","title":"Derivative-enhanced Deep Operator Network","arxiv_id":"2402.19242","date":"2024-02-29","proceeding":null,"authors":["Yuan Qiu","Nolan Bridges","Peng Chen"],"abstract":"The deep operator networks (DeepONet), a class of neural operators that learn mappings between function spaces, have recently been developed as surrogate models for parametric partial differential equations (PDEs). In this work we propose a derivative-enhanced deep operator network (DE-DeepONet), which leverages derivative information to enhance the solution prediction accuracy and provides a more accurate approximation of solution-to-parameter derivatives, especially when training data are limited. DE-DeepONet explicitly incorporates linear dimension reduction of high dimensional parameter input into DeepONet to reduce training cost and adds derivative loss in the loss function to reduce the number of required parameter-solution pairs. We further demonstrate that the use of derivative loss can be extended to enhance other neural operators, such as the Fourier neural operator (FNO). Numerical experiments validate the effectiveness of our approach.","url_abs":"https://arxiv.org/abs/2402.19242v2","url_pdf":"https://arxiv.org/pdf/2402.19242v2.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":"derivative-enhanced-deep-operator-network","repo_url":"https://github.com/qy849/de-deeponet","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"pytorch","reach":null}],"tasks":[{"task_slug":"dimensionality-reduction","task_name":"Dimensionality Reduction"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":"https://app.syntology.ai/?focus=2402.19242","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}