{"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/physics-informed-deep-super-resolution-for","title":"Physics-informed Deep Super-resolution for Spatiotemporal Data","arxiv_id":"2208.01462","date":"2022-08-02","proceeding":null,"authors":["Pu Ren","Chengping Rao","Yang Liu","Zihan Ma","Qi Wang","Jian-Xun Wang","Hao Sun"],"abstract":"High-fidelity simulation of complex physical systems is exorbitantly expensive and inaccessible across spatiotemporal scales. Recently, there has been an increasing interest in leveraging deep learning to augment scientific data based on the coarse-grained simulations, which is of cheap computational expense and retains satisfactory solution accuracy. However, the major existing work focuses on data-driven approaches which rely on rich training datasets and lack sufficient physical constraints. To this end, we propose a novel and efficient spatiotemporal super-resolution framework via physics-informed learning, inspired by the independence between temporal and spatial derivatives in partial differential equations (PDEs). The general principle is to leverage the temporal interpolation for flow estimation, and then introduce convolutional-recurrent neural networks for learning temporal refinement. Furthermore, we employ the stacked residual blocks with wide activation and sub-pixel layers with pixelshuffle for spatial reconstruction, where feature extraction is conducted in a low-resolution latent space. Moreover, we consider hard imposition of boundary conditions in the network to improve reconstruction accuracy. Results demonstrate the superior effectiveness and efficiency of the proposed method compared with baseline algorithms through extensive numerical experiments.","url_abs":"https://arxiv.org/abs/2208.01462v1","url_pdf":"https://arxiv.org/pdf/2208.01462v1.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":"physics-informed-deep-super-resolution-for","repo_url":"https://github.com/paulpuren/physr","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"pytorch","reach":{"status":"ok","spdx":"MIT"}}],"tasks":[{"task_slug":"super-resolution","task_name":"Super-Resolution"}],"methods":[{"method_slug":"pixelshuffle","method_name":"PixelShuffle"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=2208.01462","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"2208.01462"}},"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/paulpuren/physr","reach":{"status":"ok","spdx":"MIT"}}],"summary":{"unverified":17},"by_repo_kind":{"official":{"samples":17,"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":"b6257488a951d094","entry":"GetEachTerm","repo":"paulpuren/physr","repo_kind":"official","path":"Dataset/2DGS_FD_Solver[RK4].py","file_url":"https://github.com/paulpuren/physr/blob/HEAD/Dataset/2DGS_FD_Solver%5BRK4%5D.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":"b6257488a951d094"}},{"code_sha256_prefix":"d288ea72a943345f","entry":"LossGen","repo":"paulpuren/physr","repo_kind":"official","path":"Ablation/2DGS[no_convlstm].py","file_url":"https://github.com/paulpuren/physr/blob/HEAD/Ablation/2DGS%5Bno_convlstm%5D.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":"d288ea72a943345f"}},{"code_sha256_prefix":"d14bada57f01d250","entry":"LossGen","repo":"paulpuren/physr","repo_kind":"official","path":"Code/2DRB.py","file_url":"https://github.com/paulpuren/physr/blob/HEAD/Code/2DRB.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":"d14bada57f01d250"}},{"code_sha256_prefix":"237a3b35650bc0ae","entry":"apply_laplacian","repo":"paulpuren/physr","repo_kind":"official","path":"Dataset/2DGS_FD_Solver[RK4].py","file_url":"https://github.com/paulpuren/physr/blob/HEAD/Dataset/2DGS_FD_Solver%5BRK4%5D.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":"237a3b35650bc0ae"}},{"code_sha256_prefix":"180773dc5255ce55","entry":"apply_laplacian","repo":"paulpuren/physr","repo_kind":"official","path":"Dataset/3DGS_FD_Solver[RK4].py","file_url":"https://github.com/paulpuren/physr/blob/HEAD/Dataset/3DGS_FD_Solver%5BRK4%5D.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":"180773dc5255ce55"}},{"code_sha256_prefix":"434c702bbdf3336b","entry":"frobenius_norm","repo":"paulpuren/physr","repo_kind":"official","path":"Baseline/quadlinear_3dgs.py","file_url":"https://github.com/paulpuren/physr/blob/HEAD/Baseline/quadlinear_3dgs.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":"434c702bbdf3336b"}},{"code_sha256_prefix":"4bd6b46bf27ff16c","entry":"test","repo":"paulpuren/physr","repo_kind":"official","path":"Ablation/2DGS[no_phy_loss].py","file_url":"https://github.com/paulpuren/physr/blob/HEAD/Ablation/2DGS%5Bno_phy_loss%5D.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":"4bd6b46bf27ff16c"}},{"code_sha256_prefix":"ce8717d8e0064f87","entry":"train","repo":"paulpuren/physr","repo_kind":"official","path":"Ablation/2DGS[no_phy_loss].py","file_url":"https://github.com/paulpuren/physr/blob/HEAD/Ablation/2DGS%5Bno_phy_loss%5D.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":"ce8717d8e0064f87"}},{"code_sha256_prefix":"16c1dc634664a934","entry":"train","repo":"paulpuren/physr","repo_kind":"official","path":"Ablation/2DGS[no_convlstm].py","file_url":"https://github.com/paulpuren/physr/blob/HEAD/Ablation/2DGS%5Bno_convlstm%5D.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":"16c1dc634664a934"}},{"code_sha256_prefix":"706163c796a494dd","entry":"train","repo":"paulpuren/physr","repo_kind":"official","path":"Code/2DGS.py","file_url":"https://github.com/paulpuren/physr/blob/HEAD/Code/2DGS.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":"706163c796a494dd"}},{"code_sha256_prefix":"7f6cc40fc108a234","entry":"train","repo":"paulpuren/physr","repo_kind":"official","path":"Code/2DRB.py","file_url":"https://github.com/paulpuren/physr/blob/HEAD/Code/2DRB.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":"7f6cc40fc108a234"}},{"code_sha256_prefix":"f8a80544a3264dab","entry":"update","repo":"paulpuren/physr","repo_kind":"official","path":"Dataset/2DGS_FD_Solver[RK4].py","file_url":"https://github.com/paulpuren/physr/blob/HEAD/Dataset/2DGS_FD_Solver%5BRK4%5D.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":"f8a80544a3264dab"}},{"code_sha256_prefix":"dab0180fa32337d1","entry":"update","repo":"paulpuren/physr","repo_kind":"official","path":"Dataset/3DGS_FD_Solver[RK4].py","file_url":"https://github.com/paulpuren/physr/blob/HEAD/Dataset/3DGS_FD_Solver%5BRK4%5D.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":"dab0180fa32337d1"}},{"code_sha256_prefix":"5a4da65afd3c04a0","entry":"update_rk4","repo":"paulpuren/physr","repo_kind":"official","path":"Dataset/3DGS_FD_Solver[RK4].py","file_url":"https://github.com/paulpuren/physr/blob/HEAD/Dataset/3DGS_FD_Solver%5BRK4%5D.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":"5a4da65afd3c04a0"}},{"code_sha256_prefix":"03d5ce0e3812fd42","entry":"validate","repo":"paulpuren/physr","repo_kind":"official","path":"Ablation/2DGS[no_phy_loss].py","file_url":"https://github.com/paulpuren/physr/blob/HEAD/Ablation/2DGS%5Bno_phy_loss%5D.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":"03d5ce0e3812fd42"}},{"code_sha256_prefix":"f2c8ecbebaaedeb0","entry":"validate","repo":"paulpuren/physr","repo_kind":"official","path":"Ablation/2DGS[no_convlstm].py","file_url":"https://github.com/paulpuren/physr/blob/HEAD/Ablation/2DGS%5Bno_convlstm%5D.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":"f2c8ecbebaaedeb0"}},{"code_sha256_prefix":"ed892bfd2432fc9d","entry":"validate","repo":"paulpuren/physr","repo_kind":"official","path":"Code/2DGS.py","file_url":"https://github.com/paulpuren/physr/blob/HEAD/Code/2DGS.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":"ed892bfd2432fc9d"}}]},"arxiv_metadata":null,"syntology_extracted_results":null}