{"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/competitive-physics-informed-networks","title":"Competitive Physics Informed Networks","arxiv_id":"2204.11144","date":"2022-04-23","proceeding":null,"authors":["Qi Zeng","Yash Kothari","Spencer H. Bryngelson","Florian Schäfer"],"abstract":"Neural networks can be trained to solve partial differential equations (PDEs) by using the PDE residual as the loss function. This strategy is called \"physics-informed neural networks\" (PINNs), but it currently cannot produce high-accuracy solutions, typically attaining about $0.1\\%$ relative error. We present an adversarial approach that overcomes this limitation, which we call competitive PINNs (CPINNs). CPINNs train a discriminator that is rewarded for predicting mistakes the PINN makes. The discriminator and PINN participate in a zero-sum game with the exact PDE solution as an optimal strategy. This approach avoids squaring the large condition numbers of PDE discretizations, which is the likely reason for failures of previous attempts to decrease PINN errors even on benign problems. Numerical experiments on a Poisson problem show that CPINNs achieve errors four orders of magnitude smaller than the best-performing PINN. We observe relative errors on the order of single-precision accuracy, consistently decreasing with each epoch. To the authors' knowledge, this is the first time this level of accuracy and convergence behavior has been achieved. Additional experiments on the nonlinear Schr\\\"odinger, Burgers', and Allen-Cahn equation show that the benefits of CPINNs are not limited to linear problems.","url_abs":"https://arxiv.org/abs/2204.11144v2","url_pdf":"https://arxiv.org/pdf/2204.11144v2.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":"competitive-physics-informed-networks","repo_url":"https://github.com/comp-physics/cpinn","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"pytorch","reach":{"status":"ok","spdx":"MIT"}}],"tasks":[],"methods":[{"method_slug":"adam","method_name":"Adam"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=2204.11144","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"2204.11144"}},"developers":"https://syntology.ai/developers","read_at":"2026-09-24T18:15:14+00:00","read_at_is":"when the build read Syntology's graph, not when any sample ran","claim":"Per-sample execution status on synthesized fixtures; not a correctness claim about the paper. Samples come from repositories linked to the paper, official or community; repo_kind says which.","repos":[{"provenance":"external:paperswithcode_snapshot_2025-07-28","url":"https://github.com/comp-physics/cpinn","reach":{"status":"ok","spdx":"MIT"}}],"summary":{"unverified":1},"by_repo_kind":{"official":{"samples":1,"ran":0,"repositories":1}},"repo_kind_vocabulary":{"official":"The archive marks this repository official for the paper","named_in_paper":"The archive records that the paper mentions this repository; it is not marked official","listed":"In the archive's code links for this paper, not marked official and not recorded as mentioned in the paper","found_in_text":"Syntology found this repository in the paper's own text; whether it is the authors' implementation is not asserted","community":"Not in the archive's code links for this paper; a community repository Syntology harvested"},"n_pointer_only_for_licence":0,"samples":[{"code_sha256_prefix":"861928d6a426fba5","entry":"testingData","repo":"comp-physics/cpinn","repo_kind":"official","path":"WAN/train_WAN_2D_Poisson_comb_activation_algo1_no_log.py","file_url":"https://github.com/comp-physics/cpinn/blob/HEAD/WAN/train_WAN_2D_Poisson_comb_activation_algo1_no_log.py","link_basis":"harvester_set","language":"python","status":"unverified","verification_level":0,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"861928d6a426fba5"}}]},"arxiv_metadata":null,"syntology_extracted_results":null}