Learning Neural Operators from Partial Observations via Latent Autoregressive Modeling

2026-01-22

AI Summary

This work addresses the practical limitation of neural operators, which typically require full-field spatial observations and thus struggle in scenarios with partial observations due to sensor constraints or high measurement costs. To overcome this, we propose the first neural operator learning framework tailored for partial observations, integrating a masked prediction training scheme with a physics-informed, boundary-aware latent-space autoregressive propagator to reconstruct complete solution fields from sparse data. We also introduce POBench-PDE, a benchmark platform for systematic evaluation under partial observation settings. Experiments demonstrate that our method reduces relative L2 error by 18%–69% when missing regions are below 50%, and remains effective even at 75% missingness in real-world climate forecasting tasks, substantially alleviating the reliance on fully observed inputs inherent in conventional approaches.

Technology Category

• Search and Optimization: Learning to Search
• Intelligent Robots: State Estimation
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications

Abstract

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.

Problem

• partial observations
• neural operators
• incomplete data
• PDE learning
• scientific computing

Innovation

• Neural Operators
• Partial Observations
• Latent Autoregressive Modeling
• Mask-to-Predict
• Physics-Aware Latent Propagator