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Search: “pdes”

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

Latent-MoE adds domain-aware mixture-of-experts routing to PINNs, improving accuracy over an order of magnitude on multi-regime physics PDEs.

The paper shows standard coordinate networks used in physics-informed neural networks have translation-variant NTKs causing long-range gradient conflicts on PDEs with spatially varying physics. MoE architectures with centered compact-support routers produce a uniformly banded NTK that localizes learning. Latent-MoE interleaves domain-aware MoE blocks in a shared backbone, outperforming FB-PINNs and X-PINNs by over an order of magnitude on multi-stage time-variable physics benchmarks.

arXiv cs.AI / cs.LG / cs.CL · 9d agoAI research

Local gradient neural operator

Researchers propose LGNO, a lightweight interpretable neural operator using learnable local stencils, matching global-operator accuracy on PDE benchmarks with fewer parameters.

LGNO builds on nonlinear gradient discretization priors and uses multilayer perceptron convolutional layers to learn translation-invariant local kernels resembling discrete stencils. A zero consistent stencil factorization separates coefficient learning from field reconstruction, and network folding shares equivalent components to cut parameter counts for symmetric problems. Evaluations on linear and nonlinear, static and dynamic, and low- and high-dimensional PDE benchmarks show maintained accuracy, parameter efficiency, and rollout stability, with applicability to diffusion, flow, and quantum problems.

arXiv cs.AI / cs.LG / cs.CL · 9d agoAI research1