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arXiv cs.LG
arXiv cs.LG
7/23/2026
Scale-Aware Learning of Chaotic Dynamics on Unstructured Meshes via Binned Spectral Losses

Scale-Aware Learning of Chaotic Dynamics on Unstructured Meshes via Binned Spectral Losses

Short summary

This work extends binned spectral power losses to unstructured-mesh surrogate modeling by replacing Fourier bands with graph-Laplacian frequency bands. The authors introduce GLEAM, a multilevel graph architecture applying scale-aware supervision across hierarchies, and use Chebyshev polynomial filters to avoid costly eigendecomposition. Results show improved long-horizon rollout fidelity and preserved statistical invariants for turbulent flow forecasting.

  • •Binned spectral loss extended to unstructured meshes via graph-Laplacian frequency bands
  • •GLEAM introduces multilevel scale-aware supervision across graph hierarchies
  • •Chebyshev polynomial filters avoid expensive eigendecomposition while improving rollout fidelity

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