{"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/new-designed-loss-functions-to-solve-ordinary","title":"New Designed Loss Functions to Solve Ordinary Differential Equations with Artificial Neural Network","arxiv_id":"2301.00636","date":"2022-12-29","proceeding":null,"authors":["Xiao Xiong"],"abstract":"This paper investigates the use of artificial neural networks (ANNs) to solve differential equations (DEs) and the construction of the loss function which meets both differential equation and its initial/boundary condition of a certain DE. In section 2, the loss function is generalized to $n^\\text{th}$ order ordinary differential equation(ODE). Other methods of construction are examined in Section 3 and applied to three different models to assess their effectiveness.","url_abs":"https://arxiv.org/abs/2301.00636v1","url_pdf":"https://arxiv.org/pdf/2301.00636v1.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":"new-designed-loss-functions-to-solve-ordinary","repo_url":"https://github.com/xiaosherry/a-new-designed-loss-function-to-solve-ordinary-differential-equations-with-artificial-neural-network","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","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}