{"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/surrogate-modeling-of-3d-rayleigh-benard","title":"Surrogate Modeling of 3D Rayleigh-Benard Convection with Equivariant Autoencoders","arxiv_id":"2505.13569","date":"2025-05-19","proceeding":null,"authors":["Fynn Fromme","Christine Allen-Blanchette","Hans Harder","Sebastian Peitz"],"abstract":"The use of machine learning for modeling, understanding, and controlling large-scale physics systems is quickly gaining in popularity, with examples ranging from electromagnetism over nuclear fusion reactors and magneto-hydrodynamics to fluid mechanics and climate modeling. These systems -- governed by partial differential equations -- present unique challenges regarding the large number of degrees of freedom and the complex dynamics over many scales both in space and time, and additional measures to improve accuracy and sample efficiency are highly desirable. We present an end-to-end equivariant surrogate model consisting of an equivariant convolutional autoencoder and an equivariant convolutional LSTM using $G$-steerable kernels. As a case study, we consider the three-dimensional Rayleigh-B\\'enard convection, which describes the buoyancy-driven fluid flow between a heated bottom and a cooled top plate. While the system is E(2)-equivariant in the horizontal plane, the boundary conditions break the translational equivariance in the vertical direction. Our architecture leverages vertically stacked layers of $D_4$-steerable kernels, with additional partial kernel sharing in the vertical direction for further efficiency improvement. Our results demonstrate significant gains both in sample and parameter efficiency, as well as a better scaling to more complex dynamics, that is, larger Rayleigh numbers. The accompanying code is available under https://github.com/FynnFromme/equivariant-rb-forecasting.","url_abs":"https://arxiv.org/abs/2505.13569v1","url_pdf":"https://arxiv.org/pdf/2505.13569v1.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":"surrogate-modeling-of-3d-rayleigh-benard","repo_url":"https://github.com/fynnfromme/equivariant-rb-forecasting","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"pytorch","reach":{"status":"ok","spdx":"MIT"}}],"tasks":[],"methods":[{"method_slug":"lstm","method_name":"LSTM"},{"method_slug":"sigmoid-activation","method_name":"Sigmoid Activation"},{"method_slug":"tanh-activation","method_name":"Tanh Activation"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":"https://app.syntology.ai/?focus=2505.13569","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"2505.13569"}},"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/fynnfromme/equivariant-rb-forecasting","reach":{"status":"ok","spdx":"MIT"}}],"summary":{"unverified":5},"by_repo_kind":{"official":{"samples":5,"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":"f50bb6e24d21ec44","entry":"conv_output_size","repo":"fynnfromme/equivariant-rb-forecasting","repo_kind":"official","path":"layers/conv/conv_utils.py","file_url":"https://github.com/fynnfromme/equivariant-rb-forecasting/blob/HEAD/layers/conv/conv_utils.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":"f50bb6e24d21ec44"}},{"code_sha256_prefix":"4258d8ae975dd7ea","entry":"count_trainable_params","repo":"fynnfromme/equivariant-rb-forecasting","repo_kind":"official","path":"experiments/models/model_utils.py","file_url":"https://github.com/fynnfromme/equivariant-rb-forecasting/blob/HEAD/experiments/models/model_utils.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":"4258d8ae975dd7ea"}},{"code_sha256_prefix":"a9894f860166fd14","entry":"get_hyperparameters","repo":"fynnfromme/equivariant-rb-forecasting","repo_kind":"official","path":"experiments/utils/model_building.py","file_url":"https://github.com/fynnfromme/equivariant-rb-forecasting/blob/HEAD/experiments/utils/model_building.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":"a9894f860166fd14"}},{"code_sha256_prefix":"4170a4a36bf2db15","entry":"load_json","repo":"fynnfromme/equivariant-rb-forecasting","repo_kind":"official","path":"experiments/evaluate.py","file_url":"https://github.com/fynnfromme/equivariant-rb-forecasting/blob/HEAD/experiments/evaluate.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":"4170a4a36bf2db15"}},{"code_sha256_prefix":"d5a686e829cac431","entry":"required_same_padding","repo":"fynnfromme/equivariant-rb-forecasting","repo_kind":"official","path":"layers/conv/conv_utils.py","file_url":"https://github.com/fynnfromme/equivariant-rb-forecasting/blob/HEAD/layers/conv/conv_utils.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":"d5a686e829cac431"}}]},"arxiv_metadata":null,"syntology_extracted_results":null}