Physics-Embedded Probabilistic Inverse Learning of Heterogeneous Consolidation Parameters from Sparse Multisource Data

Abstract

Abstract Geotechnical properties that govern consolidation behavior, such as the coefficient of consolidation, are spatially heterogeneous and exhibit strong site-specific variability. Reliable estimation of their spatial distribution from sparse field measurements remains a major challenge in reclamation design and performance analysis, particularly for inverse consolidation problems that are ill-posed under limited monitoring data. Conventional data-driven and Bayesian approaches often struggle to integrate sparse multisource observations while simultaneously enforcing consolidation physics. To address this challenge, this study proposes a physics-informed inverse analysis framework for identifying heterogeneous consolidation parameter fields from limited measurements. The consolidation parameter field is represented using a sparse and low-order basis expansion, and the governing consolidation equation is enforced through a finite-difference scheme. This quasi-analytic and physics-informed formulation enables stable inverse identification of heterogeneous consolidation parameters with quantified uncertainty, even under severe data sparsity. The performance of the proposed method is illustrated using two benchmark consolidation problems and a field-scale case study in Japan. Results demonstrate that the method can reliably reconstruct heterogeneous consolidation parameter fields and resolve inverse problems that are otherwise difficult to solve with physics-informed neural networks. Owing to the strong physical consistency and low data demand, the proposed framework provides a practical tool for inverse consolidation analysis.