Structure-Preserving Neural Surrogates with Tractable Uncertainty Quantification
Recent advances in scientific machine learning provide a means of near-real-time solution to partial differential equations (PDEs), but lack the theoretical underpinnings of conventional simulators that support contemporary verification and validation. In this work, we construct data-driven reduced-order models that serve as structure-preserving, real-time surrogates. Remarkably, the exterior calculus that imposes physical conservation structure also exposes topological structure that we use to build a Gaussian process (GP) representation of uncertainty in state-flux relationships, ultimately yielding a Dirichlet-to-Neumann map for quantities of interest with closed-form expressions for p...
| Authors | Handi Zhang, Adrienne M. Propp, Brooks Kinch et al. |
|---|---|
| Primary category | cs.LG |
| Published | 10 June 2026 |
| Last updated at source | 10 June 2026 |
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