用可变形卷积让小模型精准模拟复杂物理流体。
Size is Not the Solution: Deformable Convolutions for Effective Physics Aware Deep Learning
- 引入可变形物理感知循环卷积，突破传统CNN刚性结构。
- 在多个方程上优于更大模型，精度显著提升。
- 适合追求高效高精度物理建模的研究者。
物理感知深度学习（PADL）可快速预测复杂物理系统，但现有卷积神经网络架构在高度非线性流动中表现受限。尽管扩大模型规模在通用AI中有效，但在物理建模中收益递减。受混合拉格朗日-欧拉数值方法启发，本文提出可变形物理感知循环卷积（D-PARC），以克服CNN的刚性问题。在Burgers方程、纳维-斯托克斯方程及反应流中，D-PARC性能优于显著更大的模型。分析显示，卷积核呈现反聚集行为，演化为一种学习得到的“主动滤波”策略，区别于传统的h-或p自适应。有效感受野分析表明，D-PARC能自主将计算资源集中于高应变区域，其余区域则粗化关注，类似计算力学中的自适应细化。结果表明，基于物理直觉的架构设计可超越参数量扩展，证明在轻量网络中进行策略性学习是实现高效物理建模的更优路径。
原文摘要 · Abstract (English)
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.
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