Reconstructing Multi-Scale Physical Fields from Extremely Sparse Measurements with an Autoencoder-Diffusion Cascade

2025-12-01

AI Summary

This work addresses the ill-posed inverse problem of reconstructing multiscale physical fields from extremely sparse and randomly sampled measurements. We propose Cas-Sensing, a cascaded framework comprising (i) a neural operator autoencoder to capture global, coarse-scale structures, followed by (ii) a masked cascade conditional diffusion model to synthesize high-fidelity fine-scale details. To ensure measurement consistency, we introduce manifold-constrained gradient optimization; to enhance uncertainty quantification, we integrate Bayesian posterior sampling. The end-to-end architecture achieves high-accuracy reconstruction on both synthetic and real experimental data. It exhibits strong generalization across diverse sensor placements, complex boundary geometries, and varying physical parameters—effectively mitigating ill-posedness. Cas-Sensing is thus well-suited for practical applications in scientific computing and engineering monitoring.

Technology Category

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

Application Category

• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Security and Privacy: Large-scale security measurements
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

Reconstructing full fields from extremely sparse and random measurements is a longstanding ill-posed inverse problem. A powerful framework for addressing such challenges is hierarchical probabilistic modeling, where uncertainty is represented by intermediate variables and resolved through marginalization during inference. Inspired by this principle, we propose Cascaded Sensing (Cas-Sensing), a hierarchical reconstruction framework that integrates an autoencoder-diffusion cascade. First, a neural operator-based functional autoencoder reconstructs the dominant structures of the original field - including large-scale components and geometric boundaries - from arbitrary sparse inputs, serving as an intermediate variable. Then, a conditional diffusion model, trained with a mask-cascade strategy, generates fine-scale details conditioned on these large-scale structures. To further enhance fidelity, measurement consistency is enforced via the manifold constrained gradient based on Bayesian posterior sampling during the generation process. This cascaded pipeline substantially alleviates ill-posedness, delivering accurate and robust reconstructions. Experiments on both simulation and real-world datasets demonstrate that Cas-Sensing generalizes well across varying sensor configurations and geometric boundaries, making it a promising tool for practical deployment in scientific and engineering applications.

Problem

• Reconstructs full physical fields from extremely sparse measurements
• Uses autoencoder-diffusion cascade to handle ill-posed inverse problems
• Enhances fidelity with Bayesian posterior sampling for consistency

Innovation

• Autoencoder-diffusion cascade for hierarchical reconstruction
• Mask-cascade strategy trains conditional diffusion model
• Manifold constrained gradient enforces measurement consistency