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

• URL: http://arxiv.org/abs/2605.25115v1
• Date: Sun, 24 May 2026 14:55:12 GMT
• Title: Courant: a State-Adaptive Perceiver-Based Neural Surrogate with Local Support and Interpretable Field Decomposition
• Abstract summary: "Courant" is a Perceiver-based encoder-processor-decoder surrogate model.<n>It has latent features exhibiting adaptive specialization and local support in the physical space.<n>We demonstrate that Courant's inductive biases yield latents that are interpretable by design.
• Score: 41.11599978669432
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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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