Latent-MoE: Domain-Aware Mixture-of-Experts for PDEs with Multi-Regime Physics
Physics-informed neural networks (PINNs) struggle on PDEs whose governing physics varies across the domain. We trace this to a structural property of standard coordinate networks: their neural tangent kernel (NTK) is translation-variant and lets training points of large coordinate magnitude disproportionately influence predictions elsewhere, producing long-range coupling and gradient conflict during training. We show analytically and empirically that mixture-of-experts (MoE) architectures with centered, compact-support routers yield a uniformly banded NTK whose kernel-regression weights decay exponentially with distance, localizing the learning. Building on this, we propose \emph{Latent-M...
| Authors | Hanwen Wang, Paris Perdikaris |
|---|---|
| Primary category | cs.LG |
| Published | 7 September 2026 |
| Last updated at source | 7 September 2026 |
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