{"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/fourier-mionet-fourier-enhanced-multiple","title":"Fourier-MIONet: Fourier-enhanced multiple-input neural operators for multiphase modeling of geological carbon sequestration","arxiv_id":"2303.04778","date":"2023-03-08","proceeding":null,"authors":["Zhongyi Jiang","Min Zhu","Lu Lu"],"abstract":"Geologic carbon sequestration (GCS) is a safety-critical technology that aims to reduce the amount of carbon dioxide in the atmosphere, which also places high demands on reliability. Multiphase flow in porous media is essential to understand CO$_2$ migration and pressure fields in the subsurface associated with GCS. However, numerical simulation for such problems in 4D is computationally challenging and expensive, due to the multiphysics and multiscale nature of the highly nonlinear governing partial differential equations (PDEs). It prevents us from considering multiple subsurface scenarios and conducting real-time optimization. Here, we develop a Fourier-enhanced multiple-input neural operator (Fourier-MIONet) to learn the solution operator of the problem of multiphase flow in porous media. Fourier-MIONet utilizes the recently developed framework of the multiple-input deep neural operators (MIONet) and incorporates the Fourier neural operator (FNO) in the network architecture. Once Fourier-MIONet is trained, it can predict the evolution of saturation and pressure of the multiphase flow under various reservoir conditions, such as permeability and porosity heterogeneity, anisotropy, injection configurations, and multiphase flow properties. Compared to the enhanced FNO (U-FNO), the proposed Fourier-MIONet has 90% fewer unknown parameters, and it can be trained in significantly less time (about 3.5 times faster) with much lower CPU memory ($<$ 15%) and GPU memory ($<$ 35%) requirements, to achieve similar prediction accuracy. In addition to the lower computational cost, Fourier-MIONet can be trained with only 6 snapshots of time to predict the PDE solutions for 30 years. The excellent generalizability of Fourier-MIONet is enabled by its adherence to the physical principle that the solution to a PDE is continuous over time.","url_abs":"https://arxiv.org/abs/2303.04778v2","url_pdf":"https://arxiv.org/pdf/2303.04778v2.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":"fourier-mionet-fourier-enhanced-multiple","repo_url":"https://github.com/lu-group/fourier-mionet","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":{"status":"ok","spdx":"Apache-2.0"}},{"paper_slug":"fourier-mionet-fourier-enhanced-multiple","repo_url":"https://github.com/lululxvi/deepxde","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"tf","reach":{"status":"ok","spdx":"LGPL-2.1"}}],"tasks":[{"task_slug":null,"task_name":"CPU"},{"task_slug":null,"task_name":"GPU"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":"https://syntology.ai/paper/2303.04778","atlas_url":"https://app.syntology.ai/?focus=2303.04778","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"2303.04778"}},"developers":"https://syntology.ai/developers","read_at":"2026-09-25T09:33:49+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/lu-group/fourier-mionet","reach":{"status":"ok","spdx":"Apache-2.0"}},{"provenance":"external:paperswithcode_snapshot_2025-07-28","url":"https://github.com/lululxvi/deepxde","reach":{"status":"ok","spdx":"LGPL-2.1"}}],"summary":{"ran":2,"unverified":4},"by_repo_kind":{"official":{"samples":6,"ran":2,"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":"a97adb13c6ea7483","entry":"Rsquare_plume_tegother","repo":"lu-group/fourier-mionet","repo_kind":"official","path":"baselines/MIONet_FNN_SG.py","file_url":"https://github.com/lu-group/fourier-mionet/blob/HEAD/baselines/MIONet_FNN_SG.py","link_basis":"harvester_set","language":"python","status":"ran","verification_level":1,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"Apache-2.0","inline_ok":true,"mcp_get_code":{"code_sha256":"a97adb13c6ea7483"}},{"code_sha256_prefix":"23c51c8250128178","entry":"get_data","repo":"lu-group/fourier-mionet","repo_kind":"official","path":"baselines/MIONet_FNN_dP.py","file_url":"https://github.com/lu-group/fourier-mionet/blob/HEAD/baselines/MIONet_FNN_dP.py","link_basis":"harvester_set","language":"python","status":"ran","verification_level":1,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"Apache-2.0","inline_ok":true,"mcp_get_code":{"code_sha256":"23c51c8250128178"}},{"code_sha256_prefix":"d02ccde5af40a256","entry":"Rsquare_plume_tegother","repo":"lu-group/fourier-mionet","repo_kind":"official","path":"baselines/MIONet_FNN_dP.py","file_url":"https://github.com/lu-group/fourier-mionet/blob/HEAD/baselines/MIONet_FNN_dP.py","link_basis":"harvester_set","language":"python","status":"unverified","verification_level":0,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"Apache-2.0","inline_ok":true,"mcp_get_code":{"code_sha256":"d02ccde5af40a256"}},{"code_sha256_prefix":"dff83504d3c6e5bc","entry":"get_data","repo":"lu-group/fourier-mionet","repo_kind":"official","path":"Fourier-MIONet_dP.py","file_url":"https://github.com/lu-group/fourier-mionet/blob/HEAD/Fourier-MIONet_dP.py","link_basis":"harvester_set","language":"python","status":"unverified","verification_level":0,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"Apache-2.0","inline_ok":true,"mcp_get_code":{"code_sha256":"dff83504d3c6e5bc"}},{"code_sha256_prefix":"1f70d7a8ef17d69f","entry":"get_data","repo":"lu-group/fourier-mionet","repo_kind":"official","path":"Fourier-MIONet_sg.py","file_url":"https://github.com/lu-group/fourier-mionet/blob/HEAD/Fourier-MIONet_sg.py","link_basis":"harvester_set","language":"python","status":"unverified","verification_level":0,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"Apache-2.0","inline_ok":true,"mcp_get_code":{"code_sha256":"1f70d7a8ef17d69f"}},{"code_sha256_prefix":"87d9396f5d165ecf","entry":"get_data","repo":"lu-group/fourier-mionet","repo_kind":"official","path":"baselines/MIONet_FNN_SG.py","file_url":"https://github.com/lu-group/fourier-mionet/blob/HEAD/baselines/MIONet_FNN_SG.py","link_basis":"harvester_set","language":"python","status":"unverified","verification_level":0,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"Apache-2.0","inline_ok":true,"mcp_get_code":{"code_sha256":"87d9396f5d165ecf"}}]},"arxiv_metadata":null,"syntology_extracted_results":null}