{"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/revisiting-pinns-generative-adversarial","title":"Revisiting PINNs: Generative Adversarial Physics-informed Neural Networks and Point-weighting Method","arxiv_id":"2205.08754","date":"2022-05-18","proceeding":null,"authors":["Wensheng Li","Chao Zhang","Chuncheng Wang","Hanting Guan","DaCheng Tao"],"abstract":"Physics-informed neural networks (PINNs) provide a deep learning framework for numerically solving partial differential equations (PDEs), and have been widely used in a variety of PDE problems. However, there still remain some challenges in the application of PINNs: 1) the mechanism of PINNs is unsuitable (at least cannot be directly applied) to exploiting a small size of (usually very few) extra informative samples to refine the networks; and 2) the efficiency of training PINNs often becomes low for some complicated PDEs. In this paper, we propose the generative adversarial physics-informed neural network (GA-PINN), which integrates the generative adversarial (GA) mechanism with the structure of PINNs, to improve the performance of PINNs by exploiting only a small size of exact solutions to the PDEs. Inspired from the weighting strategy of the Adaboost method, we then introduce a point-weighting (PW) method to improve the training efficiency of PINNs, where the weight of each sample point is adaptively updated at each training iteration. The numerical experiments show that GA-PINNs outperform PINNs in many well-known PDEs and the PW method also improves the efficiency of training PINNs and GA-PINNs.","url_abs":"https://arxiv.org/abs/2205.08754v1","url_pdf":"https://arxiv.org/pdf/2205.08754v1.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":"revisiting-pinns-generative-adversarial","repo_url":"https://github.com/Liwgreat/GA-PINN","is_official":1,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"pytorch","reach":null},{"paper_slug":"revisiting-pinns-generative-adversarial","repo_url":"https://github.com/Max-Hi/GenerativePINNs","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":0,"framework":"pytorch","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}