Physics-Informed Inversion of Process Parameters and Electro-Hydro-Chemical Fields in Soil Electrokinetic Remediation

Abstract Electrokinetic remediation (EKR) holds promise for in situ cleanup of heavy-metal-contaminated soils, yet rational design has been hampered by the undetectability of process parameters and physical fields. This study reported the inversion of EKR process parameters and electro-hydro-chemical (EHC) fields from limited-view and sparse data by physics-informed neural networks that embed the coupled Richards–Nernst–Planck equations (RNP-PINNs). Reaction-transport stiffness in the RNP equation was mitigated by local-equilibrium formulation, field-wise subnetworks, physics-based nondimensionalization, and sequentially coupled optimization. Pointwise pH values and endpoint total-Pb data were used for inversion of half-adsorption pH (pH50), dimensionless electroosmotic scaling factor (Keos), and H+ buffering coefficient (RH), together with the neural-network parameters. The parameters were tightly clustered across 500 bootstrap refits (Keos = 0.8–0.9, RH = 18.5–19.2, pH50 = 2.9–3.2), revealing weak pairwise compensation (absolute Pearson correlations ≤0.13). This allowed inversion of the spatiotemporal EHC fields with RMSEs of 1.3 × 10–1 mol m–3 d–1 for total-Pb transport and 2 × 10–3 d–1 for Richards equation residuals. The RNP-PINNs offered mechanistic insights into the way saturation reorganized pore-water transport, accelerated acid-front propagation, and promoted Pb redistribution and re-adsorption near the pH front. Compared with conventional theoretical numerical modeling or experimental investigation, this study provides a “theory + data” double-driven paradigm for the inversion of EKR processes.