{"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-numerical-study-of-chaotic-dynamics-of-k-s","title":"A Numerical Study of Chaotic Dynamics of K-S Equation with FNOs","arxiv_id":"2410.12280","date":"2024-10-16","proceeding":null,"authors":["Surbhi Khetrapal","Jaswin Kasi"],"abstract":"Solving non-linear partial differential equations which exhibit chaotic dynamics is an important problem with a wide-range of applications such as predicting weather extremes and financial market risk. Fourier neural operators (FNOs) have been shown to be efficient in solving partial differential equations (PDEs). In this work we demonstrate simulation of dynamics in the chaotic regime of the two-dimensional (2d) Kuramoto-Sivashinsky equation using FNOs. Particularly, we analyze the effect of Fourier mode cutoff on the results obtained by using FNOs vs those obtained using traditional PDE solvers. We compare the outputs using metrics such as the 2d power spectrum and the radial power spectrum. In addition we propose the normalised error power spectrum which measures the percentage error in the FNO model outputs. We conclude that FNOs capture the dynamics in the chaotic regime of the 2d K-S equation, provided the Fourier mode cutoff is kept sufficiently high.","url_abs":"https://arxiv.org/abs/2410.12280v1","url_pdf":"https://arxiv.org/pdf/2410.12280v1.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-numerical-study-of-chaotic-dynamics-of-k-s","repo_url":"https://github.com/skhetrapal/chaotic-pde-fno","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"pytorch","reach":{"status":"ok"}}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=2410.12280","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"2410.12280"}},"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/skhetrapal/chaotic-pde-fno","reach":{"status":"ok"}}],"summary":{"ran":1},"by_repo_kind":{"official":{"samples":1,"ran":1,"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":1,"samples":[{"code_sha256_prefix":"ff22c81e9f140b90","entry":"count_params","repo":"skhetrapal/chaotic-pde-fno","repo_kind":"official","path":"FNO2d_module/trainer.py","file_url":"https://github.com/skhetrapal/chaotic-pde-fno/blob/HEAD/FNO2d_module/trainer.py","link_basis":"first_harvest_node","language":"python","status":"ran","verification_level":1,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"NONE","inline_ok":false,"mcp_get_code":{"code_sha256":"ff22c81e9f140b90"}}]},"arxiv_metadata":null,"syntology_extracted_results":null}