Sparse‐Well Diffusion Reconstructions Enable Groundwater Transport Equation Recovery and Plume Refinement

Abstract Groundwater contamination assessments based on sparse wells rarely provide continuous hydraulic head and contaminant concentration fields for plume interpretation. Visually plausible reconstructions may not retain the transport information needed for physical diagnosis. We develop a Sparse‐Well Diffusion‐SINDy Residual Refinement (SW‐DSRR) framework that couples diffusion reconstruction, Sparse Identification of Nonlinear Dynamics transport equation recovery and consistency assessment, and consistency‐guided plume refinement to test whether sparse‐well reconstructions preserve transport structure. This information is then used to reduce plume error. Tests cover normal and extreme well layouts under baseline, source/sink, and heterogeneous permeability conditions. Reconstructed fields retain dominant terms, generating parameter scales, and hidden contaminant source structure. Recovered equations reproduce observed‐well and full‐field evolution while preserving mass, centroid migration, and nonnegative concentrations. Relative to initial diffusion reconstructions, plume refinement reduces concentration errors. SW‐DSRR connects field reconstruction with equation‐level assessment and targeted plume correction that can support plume delineation, source assessment, and remediation planning.