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

2026-09-07

AI Summary

为解决PINNs在物理特性多变的PDE上的表现不佳问题，提出Latent-MoE模型，通过领域感知的混合专家架构和共享骨干网络实现更有效的学习。

Abstract

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-MoE}, which interleaves domain-aware MoE blocks within a shared backbone. Unlike FB-PINNs or X-PINNs, which rigidly partition both the domain and the parameters so that the parameters on different subdomains are updated independently, Latent-MoE is designed to preserve the localization benefit of domain-aware routing while allowing capacity to flow across regions through the shared backbone. On standard homogeneous-physics benchmarks Latent-MoE is competitive with established baselines; on benchmarks with multi-stage time-variable physics, where global models and rigid domain decompositions both fall into spurious solutions, it improves over them by more than an order of magnitude, with markedly reduced gradient conflict during training.

Problem

• Physics-informed neural networks
• PDEs
• Multi-Regime Physics
• Gradient Conflict
• Domain-Aware

Innovation

• Latent-MoE
• Domain-Aware Routing
• Shared Backbone
• Mixture-of-Experts (MoE)
• Gradient Conflict