Sparsely-Supervised Data Assimilation via Physics-Informed Schrödinger Bridge

2026-03-20

AI Summary

This work proposes a physics-informed conditional Schrödinger bridge (PICSB) framework to address the computational bottlenecks of traditional data assimilation methods, which rely on sample-wise optimization and struggle under sparse high-fidelity observations. PICSB establishes the first learnable data assimilation approach that does not require full-field high-fidelity supervision. It leverages low-fidelity simulations as a prior and employs a generative model to directly learn a high-fidelity posterior distribution consistent with both the governing partial differential equations (PDEs) and sparse observational data. The method integrates Schrödinger bridge generative modeling, PDE residual embedding, hard observation constraints, and an iterative surrogate endpoint update mechanism, ensuring physical consistency while enabling efficient inference. Evaluated on fluid dynamics PDE benchmarks, PICSB achieves reconstruction accuracy comparable to existing methods while significantly accelerating spatiotemporal field recovery.

Technology Category

• Reasoning under Uncertainty: Probabilistic Inference
• Search and Optimization: Sampling/Simulation-based Search
• Constraint Satisfaction and Optimization: Constraint Learning and Acquisition

Application Category

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

Abstract

Data assimilation (DA) for systems governed by partial differential equations (PDE) aims to reconstruct full spatiotemporal fields from sparse high-fidelity (HF) observations while respecting physical constraints. While full-grid low-fidelity (LF) simulations provide informative priors in multi-fidelity settings, recovering an HF field consistent with both sparse observations and the governing PDE typically requires per-instance test-time optimization, which becomes a major bottleneck in time-critical applications. To alleviate this, amortized reconstruction using generative models has recently been proposed; however, such approaches rely on full-field HF supervision during training, which is often impractical in real-world settings. From a more realistic perspective, we propose the Physics-Informed Conditional Schrödinger Bridge (PICSB), which transports an informative LF prior toward an observation-conditioned HF posterior without any additional inference-time guidance. To enable learning without HF endpoints, PICSB employs an iterative surrogate-endpoint refresh scheme, and directly incorporates PDE residuals into the training objective while enforcing observations via hard conditioning throughout sampling. Experiments on fluid PDE benchmarks demonstrate that PICSB enables extremely fast spatiotemporal field reconstruction while maintaining competitive accuracy under sparse HF supervision.

Problem

• Data Assimilation
• Partial Differential Equations
• Sparsely-Supervised Learning
• Multi-fidelity Modeling
• Spatiotemporal Reconstruction

Innovation

• Physics-Informed
• Schrödinger Bridge
• Data Assimilation
• Sparse Supervision
• Amortized Inference