Courant: a State-Adaptive Perceiver-Based Neural Surrogate with Local Support and Interpretable Field Decomposition
This work provides a novel neural surrogate for scientific simulation that combines interpretability and adaptive refinement, benefiting researchers in scientific machine learning and computational physics.
Courant introduces a Perceiver-based neural surrogate with state-adaptive latent queries and local support, achieving competitive accuracy on steady and transient simulation benchmarks while enabling interpretable, multiscale field decomposition.
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.