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

arXiv: https://arxiv.org/abs/2601.11657 · HTML: https://mlsanity.com/paper/2601.11657/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 22 references that are in the map.
- First posted on arXiv 15 Jan 2026.

## Builds on (most cited first, 7 of 7)

- [Scaling Laws for Neural Language Models](https://mlsanity.com/paper/2001.08361/) (2020)
- [EfficientNet: Rethinking Model Scaling for Convolutional Neural Networks](https://mlsanity.com/paper/1905.11946/) (2019)
- [Deformable Convolutional Networks](https://mlsanity.com/paper/1703.06211/) (2017)
- [Learning to Simulate Complex Physics with Graph Networks](https://mlsanity.com/paper/2002.09405/) (2020)
- [Understanding the Effective Receptive Field in Deep Convolutional Neural Networks](https://mlsanity.com/paper/1701.04128/) (2017)
- [Compute Trends Across Three Eras of Machine Learning](https://mlsanity.com/paper/2202.05924/) (2022)
- [PARCv2: Physics-aware Recurrent Convolutional Neural Networks for Spatiotemporal Dynamics Modeling](https://mlsanity.com/paper/2402.12503/) (2024)

## Built on by (most cited first, 1 of 1)

- [G-PARC: Graph-Physics Aware Recurrent Convolutional Neural Networks for Spatiotemporal Dynamics on Unstructured Meshes](https://mlsanity.com/paper/2604.16533/) (2026)

## Abstract (arXiv)

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.