mlsanityData to 7 Oct 2026

Courant: a State-Adaptive Perceiver-Based Neural Surrogate with Local Support and Interpretable Field Decomposition

arXiv 2605.25115 ↗First posted 24 May 2026cs.LG cs.AI cs.CEcited by 0

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Abstract (arXiv)

We introduce "Courant", a Perceiver-based encoder-processor-decoder surrogate model that has latent features exhibiting adaptive specialization and local support in the physical space, enabling functionality akin to an adaptive hp-refinement scheme, an attribute that is highly desirable in traditional numerical solvers and scientific machine learning broadly. The proposed architecture combines a shared random Fourier feature coordinate embedding, state-adapted latent queries, and a light-weight decoder. Courant is trained end-to-end with steady or transient simulation data and only a standard L_2 prediction loss in the physical space, achieving competitive accuracy on benchmarks. We demonstrate that Courant's inductive biases yield latents that are interpretable by design: they develop multiscale geometric specialization in the simulation domain and track coherent structures in the time-dependent case, acting analogously to time-evolving spatial basis functions and allowing for decoding a compact, geometry-anchored, partition-of-unity-like decomposition of the simulated field.

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References · 32

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  8. 2025Geometry Aware Operator Transformer as an Efficient and Accurate Neural Surrogate for PDEs on Arbitrary Domainscited by 56
  9. 2024AROMA: Preserving Spatial Structure for Latent PDE Modeling with Local Neural Fieldscited by 38
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  13. 2025GeoTransolver: Learning Physics on Irregular Domains Using Multi-scale Geometry Aware Physics Attention Transformercited by 20
  14. 2026Transolver-3: Scaling Up Transformer Solvers to Industrial-Scale Geometriescited by 20
  15. 2024Grounding Continuous Representations in Geometry: Equivariant Neural Fieldscited by 19
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  18. 2023Interpretable A-posteriori Error Indication for Graph Neural Network Surrogate Modelscited by 6
  19. 2025Interpreting CFD Surrogates through Sparse Autoencoderscited by 3
  20. 2025FIGNN: Feature-Specific Interpretability for Graph Neural Network Surrogate Modelscited by 2

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