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

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.

Accelerating Hybrid Agent-Based Models and Fuzzy Cognitive Maps: How to Combine Agents who Think Alike?

While Agent-Based Models can create detailed artificial societies based on individual differences and local context, they can be computationally intensive. Modelers may offset these costs through a parsimonious use of the model, for example by using smaller population sizes (which limits analyses in sub-populations), running fewer what-if scenarios, or accepting more uncertainty by performing fewer simulations. Alternatively, researchers may accelerate simulations via hardware solutions (e.g., GPU parallelism) or approximation approaches that operate a tradeoff between accuracy and compute time. In this paper, we present an approximation that combines agents who `think alike', thus reducing the population size and the compute time. Our innovation relies on representing agent behaviors as networks of rules (Fuzzy Cognitive Maps) and empirically evaluating different measures of distance between these networks. Then, we form groups of think-alike agents via community detection and simplify them to a representative agent. Case studies show that our simplifications remain accuracy.