Inverse physics-informed neural network framework for physics-consistent estimation of dispersion coefficient and mechanistic understanding of solute transport

doi:10.1016/j.compgeo.2026.108145

Inverse physics-informed neural network framework for physics-consistent estimation of dispersion coefficient and mechanistic understanding of solute transport

2026-04-16

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DOI：10.1016/j.compgeo.2026.108145

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A reliable estimation of the dispersion coefficient (D) is essential for predicting contaminant migration in low-permeability geomaterials. Although the conventional Ogata–Banks (OB) curve-fitting approach can statistically reproduce breakthrough curves, it often yields parameters that are physically inconsistent. This study develops and validates an inverse physics-informed neural network (iPiNN) framework that embeds the advection–dispersion equation (ADE) directly into the learning process, thereby ensuring physics-consistent parameter inversion. A series of saturated column tests on sand–illite mixtures was re-examined using this framework. The iPiNN achieved substantially higher statistical accuracy than the OB solution, reducing the root-mean-square error (RMSE) from 0.361 ± 0.160 to 0.175 ± 0.058 (approximately a 50% improvement) while maintaining high coefficients of determination (R2 = 0.996–0.998). The physics-consistency validation criteria confirmed that the iPiNN converged toward physically admissible D values. Mechanistic analysis of the reconstructed concentration fields further indicated that the iPiNN yields reduced apparent dispersion compared to OB-derived solutions. External validation was performed by forward prediction of breakthrough curves under an altered inlet boundary condition, supporting the transferability of the iPiNN framework. Moreover, extending the iPiNN to a two-parameter inversion involving advective velocity demonstrated that the framework remained robust under uncertain flow conditions, highlighting its potential as a generalizable tool for realistic transport scenarios. Overall, these findings demonstrate that physics-guided inversion effectively eliminates non-physical parameter estimates and provides a reliable framework for characterizing contaminant transport through geomaterials.

Keywords:

dispersion coefficient

physics-informed neural network

solute transport

advection-dispersion equation

parameter estimation

Inverse physics-informed neural network framework for physics-consistent estimation of dispersion coefficient and mechanistic understanding of solute transport

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