pdes

This paper identifies a capacity-induced failure mode in physics-informed neural networks (PINNs) where overparameterized networks develop functional modularity that hinders convergence, and proposes Modular-Sparsity Synchronization (ModSync), a framework that penalizes task-exclusive connections to maintain cross-objective interaction and achieve state-of-the-art accuracy.

This paper introduces Separable Neural Architecture (SNA), a function class that combines neural approximation with tensor decomposition to efficiently solve parametric PDEs. The method achieves dramatic speedups (up to 150,000×) over traditional grid-based methods in engineering applications like laser powder bed fusion and material property prediction.