Learnable Hodge-Laplacian Driven Mixture of Experts for Steady-PDE Surrogates on Coarse Unstructured Meshes

Stavros Nousias, Akis Nousias, Konstantinos Gkrispanis|October 14, 2026arXiv

Key Takeaway

Using spectral decomposition via Hodge-Laplacian to route different frequency scales to specialized experts improves PDE surrogate accuracy by 31-47% compared to single-mechanism approaches.

Summary

This paper proposes a neural network architecture for predicting solutions to steady partial differential equations on unstructured meshes. The key innovation is using a Hodge-Laplacian operator to partition the solution into different frequency components, each handled by separate transformer experts.

architecture reasoning

Key Terms

mixture-of-experts hodge-laplacian pde-solver unstructured-mesh spectral-decomposition