Hong Wang
Publications
Learning Neural Operators from Partial Observations via Latent Autoregressive Modeling
Real-world scientific applications frequently encounter incomplete observational data due to sensor limitations, geographic constraints, or measurement costs. Although neural operators significantly advanced PDE solving in terms of computational efficiency and accuracy, their underlying assumption of fully-observed spatial inputs severely restricts applicability in real-world applications. We introduce the first systematic framework for learning neural operators from partial observation. We identify and formalize two fundamental obstacles: (i) the supervision gap in unobserved regions that prevents effective learning of physical correlations, and (ii) the dynamic spatial mismatch between incomplete inputs and complete solution fields. Specifically, our proposed Latent Autoregressive Neural Operator(LANO) introduces two novel components designed explicitly to address the core difficulties of partial observations: (i) a mask-to-predict training strategy that creates artificial supervision by strategically masking observed regions, and (ii) a Physics-Aware Latent Propagator that reconstructs solutions through boundary-first autoregressive generation in latent space. Additionally, we develop POBench-PDE, a dedicated and comprehensive benchmark designed specifically for evaluating neural operators under partial observation conditions across three PDE-governed tasks. LANO achieves state-of-the-art performance with 18--69$\%$ relative L2 error reduction across all benchmarks under patch-wise missingness with less than 50$\%$ missing rate, including real-world climate prediction. Our approach effectively addresses practical scenarios involving up to 75$\%$ missing rate, to some extent bridging the existing gap between idealized research settings and the complexities of real-world scientific computing.
HGATSolver: A Heterogeneous Graph Attention Solver for Fluid-Structure Interaction
Fluid-structure interaction (FSI) systems involve distinct physical domains, fluid and solid, governed by different partial differential equations and coupled at a dynamic interface. While learning-based solvers offer a promising alternative to costly numerical simulations, existing methods struggle to capture the heterogeneous dynamics of FSI within a unified framework. This challenge is further exacerbated by inconsistencies in response across domains due to interface coupling and by disparities in learning difficulty across fluid and solid regions, leading to instability during prediction. To address these challenges, we propose the Heterogeneous Graph Attention Solver (HGATSolver). HGATSolver encodes the system as a heterogeneous graph, embedding physical structure directly into the model via distinct node and edge types for fluid, solid, and interface regions. This enables specialized message-passing mechanisms tailored to each physical domain. To stabilize explicit time stepping, we introduce a novel physics-conditioned gating mechanism that serves as a learnable, adaptive relaxation factor. Furthermore, an Inter-domain Gradient-Balancing Loss dynamically balances the optimization objectives across domains based on predictive uncertainty. Extensive experiments on two constructed FSI benchmarks and a public dataset demonstrate that HGATSolver achieves state-of-the-art performance, establishing an effective framework for surrogate modeling of coupled multi-physics systems.