{"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/a-novel-deeponet-model-for-learning-moving","title":"An enrichment approach for enhancing the expressivity of neural operators with applications to seismology","arxiv_id":"2306.04096","date":"2023-06-07","proceeding":null,"authors":["Ehsan Haghighat","Umair bin Waheed","George Karniadakis"],"abstract":"The Eikonal equation plays a central role in seismic wave propagation and hypocenter localization, a crucial aspect of efficient earthquake early warning systems. Despite recent progress, real-time earthquake localization remains challenging due to the need to learn a generalizable Eikonal operator. We introduce a novel deep learning architecture, Enriched-DeepONet (En-DeepONet), addressing the limitations of current operator learning models in dealing with moving-solution operators. Leveraging addition and subtraction operations and a novel `root' network, En-DeepONet is particularly suitable for learning such operators and achieves up to four orders of magnitude improved accuracy without increased training cost. We demonstrate the effectiveness of En-DeepONet in earthquake localization under variable velocity and arrival time conditions. Our results indicate that En-DeepONet paves the way for real-time hypocenter localization for velocity models of practical interest. The proposed method represents a significant advancement in operator learning that is applicable to a gamut of scientific problems, including those in seismology, fracture mechanics, and phase-field problems.","url_abs":"https://arxiv.org/abs/2306.04096v2","url_pdf":"https://arxiv.org/pdf/2306.04096v2.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":"a-novel-deeponet-model-for-learning-moving","repo_url":"https://github.com/ehsanhaghighat/en-deeponet","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":null},{"paper_slug":"a-novel-deeponet-model-for-learning-moving","repo_url":"https://github.com/ehsanhaghighat/x-deeponet","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[{"task_slug":"operator-learning","task_name":"Operator learning"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}