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

TL;DR

This paper introduces deformable convolutions inspired by numerical methods to improve physics-aware deep learning, outperforming larger models by adaptively focusing on complex regions in fluid flow simulations.

Contribution

Proposes deformable physics-aware recurrent convolutions (D-PARC) that adaptively focus on high-strain regions, surpassing larger CNNs in modeling complex physical systems.

Findings

D-PARC outperforms larger architectures in Burgers', Navier-Stokes, and reactive flows.

Kernels develop anti-clustering behavior, acting as learned active filters.

D-PARC autonomously concentrates resources in high-strain regions.

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.