Size is Not the Solution: Deformable Convolutions for Effective Physics Aware Deep Learning

Jack T Beerman; Shobhan Roy; H. S Udaykumar; Stephen S Baek

doi:10.48550/arxiv.2601.11657

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Size is Not the Solution: Deformable Convolutions for Effective Physics Aware Deep Learning

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Size is Not the Solution: Deformable Convolutions for Effective Physics Aware Deep Learning

Jack T Beerman, Shobhan Roy, H. S Udaykumar and Stephen S Baek

ArXiv.org

Cornell University

01/15/2026

DOI: 10.48550/arxiv.2601.11657

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Preprint (Author's original)This preprint has not been evaluated by subject experts through peer review. Preprints may undergo extensive changes and/or become peer-reviewed journal articles. Open Access

Abstract

Physics-aware deep learning (PADL) enables rapid prediction of complex physical systems, yet current convolutional neural network (CNN) architectures struggle with highly nonlinear flows. While scaling model size addresses complexity in broader AI, this approach yields diminishing returns for physics modeling. Drawing inspiration from Hybrid Lagrangian-Eulerian (HLE) numerical methods, we introduce deformable physics-aware recurrent convolutions (D-PARC) to overcome the rigidity of CNNs. Across Burgers' equation, Navier-Stokes, and reactive flows, D-PARC achieves superior fidelity compared to substantially larger architectures. Analysis reveals that kernels display anti-clustering behavior, evolving into a learned "active filtration" strategy distinct from traditional h- or p-adaptivity. Effective receptive field analysis confirms that D-PARC autonomously concentrates resources in high-strain regions while coarsening focus elsewhere, mirroring adaptive refinement in computational mechanics. This demonstrates that physically intuitive architectural design can outperform parameter scaling, establishing that strategic learning in lean networks offers a more effective path forward for PADL than indiscriminate network expansion.

Computer Science - Artificial Intelligence

Computer Science - Learning

Details

Title: Subtitle: Size is Not the Solution: Deformable Convolutions for Effective Physics Aware Deep Learning
Creators: Jack T Beerman
Shobhan Roy
H. S Udaykumar
Stephen S Baek
Resource Type: Preprint
Publication Details: ArXiv.org
DOI: 10.48550/arxiv.2601.11657
ISSN: 2331-8422
Publisher: Cornell University; Ithaca, New York
Language: English
Date posted: 01/15/2026
Academic Unit: Engineering Administration; IIHR--Hydroscience and Engineering; Injury Prevention Research Center; Chemical and Biochemical Engineering; Mechanical Engineering
Record Identifier: 9985130238202771

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