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Simulating solute transport in heterogeneous porous media poses computationalchallenges due to the high-resolution meshing required for traditional solvers.To overcome these challenges, this study explores a mesh-free method based ondeep learning to accelerate solute transport simulation. We employPhysics-informed Neural Networks (PiNN) with a periodic activation function tosolve solute transport problems in both homogeneous and heterogeneous porousmedia governed by the advection-dispersion equation. Unlike traditional neuralnetworks that rely on large training datasets, PiNNs use strong-formmathematical models to constrain the network in the training phase andsimultaneously solve for multiple dependent or independent field variables,such as pressure and solute concentration fields. To demonstrate theeffectiveness of using PiNNs with a periodic activation function to resolvesolute transport in porous media, we construct PiNNs using two activationfunctions, sin and tanh, for seven case studies, including 1D and 2D scenarios.The accuracy of the PiNNs' predictions is then evaluated using absolute pointerror and mean square error metrics and compared to the ground truth solutionsobtained analytically or numerically. Our results demonstrate that the PiNNwith sin activation function, compared to tanh activation function, is up totwo orders of magnitude more accurate and up to two times faster to train,especially in heterogeneous porous media. Moreover, PiNN's simultaneouspredictions of pressure and concentration fields can reduce computationalexpenses in terms of inference time by three orders of magnitude compared toFEM simulations for two-dimensional cases.

Physics-informed Neural Networks with Periodic Activation Functions for Solute Transport in Heterogeneous Porous Media