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Latent-MoE: Domain-Aware Mixture-of-Experts for PDEs with Multi-Regime Physics

arXiv · AI, language, vision and robotics · article · Sep 7, 2026 · UTC

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

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