{"paper":{"title":"ViT-K: A Few-Shot Learning Model for Coupled Fluid-Porous Media Flows with Interface Conditions","license":"http://creativecommons.org/licenses/by/4.0/","headline":"ViT-K learns stable long-term predictions for coupled fluid-porous flows from few examples by linearizing dynamics with a Koopman operator.","cross_cats":["cs.NA","physics.flu-dyn"],"primary_cat":"math.NA","authors_text":"Changxin Qiu, Menghui Xu, Mengjia Chen, Zhiping Mao","submitted_at":"2026-05-13T08:27:17Z","abstract_excerpt":"The numerical simulation of interaction between free flow and porous media, governed by coupled Stokes/Navier--Stokes--Darcy flows, is critical for understanding fluid filtration and physiological transport, yet it is hindered by the high computational cost of resolving interface heterogeneities and the instability of long-term predictions. While deep learning offers surrogate modeling potential, existing frameworks often suffer from exponential error accumulation and poor convergence in multi-physics regimes. To address these limitations, we propose ViT-K, a novel few-shot learning model desi"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"By lifting nonlinear dynamics into a globally linear observable space, the ViT-K model provides stability by design, ensuring that prediction errors grow linearly rather than exponentially over time.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"That the Koopman operator can be learned effectively from sparse data to linearize the full coupled Stokes/Navier-Stokes-Darcy system including interface conditions without losing essential nonlinear physics or requiring extensive hyperparameter tuning.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"ViT-K uses Vision Transformers and Koopman operators to learn stable long-term spatiotemporal dynamics of coupled fluid-porous media flows from sparse data.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"ViT-K learns stable long-term predictions for coupled fluid-porous flows from few examples by linearizing dynamics with a Koopman operator.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"52516da8fea9676c4973cf8d46c0121d380c43f2a8f40e234f5195db37825439"},"source":{"id":"2605.13912","kind":"arxiv","version":1},"verdict":{"id":"3f47fbc8-4713-49e1-944b-ef8eb0848bd6","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-15T02:55:15.665863Z","strongest_claim":"By lifting nonlinear dynamics into a globally linear observable space, the ViT-K model provides stability by design, ensuring that prediction errors grow linearly rather than exponentially over time.","one_line_summary":"ViT-K uses Vision Transformers and Koopman operators to learn stable long-term spatiotemporal dynamics of coupled fluid-porous media flows from sparse data.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"That the Koopman operator can be learned effectively from sparse data to linearize the full coupled Stokes/Navier-Stokes-Darcy system including interface conditions without losing essential nonlinear physics or requiring extensive hyperparameter tuning.","pith_extraction_headline":"ViT-K learns stable long-term predictions for coupled fluid-porous flows from few examples by linearizing dynamics with a Koopman operator."},"references":{"count":53,"sample":[{"doi":"","year":null,"title":"Advances in neural information processing systems , volume=","work_id":"9c5780d0-d7c4-4f73-a274-a7b00c883750","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2016,"title":"Journal of Hydrology , volume=","work_id":"6c117c05-8d3f-4e44-973b-b8b67e40c043","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2004,"title":"Domain decomposition methods for the coupling of surface and groundwater flows , author=. 2004 , type=","work_id":"bf898650-88b3-428e-a936-0cdd6e8b139b","ref_index":3,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2007,"title":"Computational issues related to iterative coupling of subsurface and channel flows , author=. 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