{"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-universal-pinns-method-for-solving-partial","title":"A Universal PINNs Method for Solving Partial Differential Equations with a Point Source","arxiv_id":null,"date":"2022-07-23","proceeding":"Proceedings of the Thirty-First International Joint Conference on Artificial Intelligence 2022 7","authors":["Xiang Huang","Hongsheng Liu","Beiji Shi","Zidong Wang","Kang Yang","Yang Li","Min Wang","Haotian Chu","Jing Zhou","Fan Yu","Bei Hua","Bin Dong","Lei Chen"],"abstract":"In recent years, deep learning technology has been used to solve partial differential equations (PDEs), among which the physics-informed neural networks (PINNs)method emerges to be a promising method for solving both forward and inverse PDE problems. PDEs with a point source that is expressed as a Dirac delta function in the governing equations are mathematical models of many physical processes. However, they cannot be solved directly by conventional PINNs method due to the singularity brought by the Dirac delta function. In this paper, we propose a universal solution to tackle this problem by proposing three novel techniques. Firstly the Dirac delta function is modeled as a continuous probability density function to eliminate the singularity at the point source; secondly a lower bound constrained uncertainty weighting algorithm is proposed to balance the physics-informed loss terms of point source area and the remaining areas; and thirdly a multi-scale deep neural network with periodic activation function is used to improve the accuracy and convergence speed. We evaluate the proposed method with three representative PDEs, and the experimental results show that our method outperforms existing deep learning based methods with respect to the accuracy, the efficiency and the versatility.","url_abs":"https://www.ijcai.org/proceedings/2022/533","url_pdf":"https://www.ijcai.org/proceedings/2022/0533.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-universal-pinns-method-for-solving-partial","repo_url":"https://github.com/xiuyu0000/new_papers_codes/tree/main/time_domain_maxwell","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":0,"framework":"mindspore","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}