Learnable Hodge-Laplacian Driven Mixture of Experts for Steady-PDE Surrogates on Coarse Unstructured Meshes
Current approaches for steady partial differential equations surrogate models on unstructured meshes apply a single mixing mechanism to the whole solution.
ProofPaper ↗
Key points
- This paper proposes an architecture that partitions the solution among vanilla transformer experts, each focused on a different spectral scale.
- The partition is built from a discrete Hodge Laplacian $L0=\star0^{-1} d0^{\top}\star1 d0$, that serves as a fitting layer measuring high-frequency content.
- AirFRANS is a steady Reynolds-averaged Navier--Stokes (RANS) airfoil benchmark.
- We evaluate our approach in a reduced remeshed version of the benchmark with each unstructured mesh counting 9.6K faces and 4.9K vertices.
Sources (1)
- [1]Learnable Hodge-Laplacian Driven Mixture of Experts for Steady-PDE Surrogates on Coarse Unstructured MeshesarXiv (AI, ML, NLP, CV, robotics, multi-agent) · Oct 14, 05:57 PM
Current approaches for steady partial differential equations surrogate models on unstructured meshes apply a single mixing mechanism to the whole solution.
This paper proposes an architecture that partitions the solution among vanilla transformer experts, each focused on a different spectral scale.
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