Simin Jiang | Searcharxiv

arXiv2025

PIS: A Generalized Physical Inversion Solver for Arbitrary Sparse Observations via Set Conditioned Flow Matching

The estimation of high-dimensional physical parameters constrained by partial differential equations (PDEs) from limited and indirect measurements is a highly ill-posed problem. Traditional methods face significant accuracy and efficiency bottlenecks, particularly when observations are sparse, irregularly sampled, and constrained by real-world sensor placement. We propose the Physical Inversion Solver (PIS), a unified framework that couples Set-Conditioned Flow Matching with a Cosine-Annealed Sparsity Curriculum (CASC) to enable stable inversion from arbitrary, off-grid sensors even under minimal guidance. By leveraging straight-path transport, PIS achieves instantaneous inference (50 NFEs), offering orders-of-magnitude speedup over iterative baselines. Extensive experiments demonstrate that PIS reduces error by up to 88.7% under extreme sparsity (<1%) across subsurface characterization, wave-based characterization, and structural health monitoring, while providing robust uncertainty quantification for optimal sensor placement.

cs.LG↗

arXiv2025

Diffusion-Inversion-Net (DIN): An End-to-End Direct Probabilistic Framework for Characterizing Hydraulic Conductivities and Quantifying Uncertainty

We propose the Diffusion-Inversion-Net (DIN) framework for inverse modeling of groundwater flow and solute transport processes. DIN utilizes an offline-trained Denoising Diffusion Probabilistic Model (DDPM) as a powerful prior leaner, which flexibly incorporates sparse, multi-source observational data, including hydraulic head, solute concentration, and hard conductivity data, through conditional injection mechanisms. These conditioning inputs subsequently guide the generative inversion process during sampling. Bypassing iterative forward simulations, DIN leverages stochastic sampling and probabilistic modeling mechanisms to directly generate ensembles of posterior parameter fields by repeatedly executing the reverse denoising process. Two representative posterior scenarios, Gaussian and non-Gaussian, are investigated. The results demonstrate that DIN can produce multiple constraint-satisfying realizations under identical observational conditions, accurately estimate hydraulic-conductivity fields, and achieve reliable uncertainty quantification. The framework exhibits strong generalization capability across diverse data distributions, offering a robust and unified alternative to conventional multi-stage inversion methodologies.

physics.geo-ph↗