Inverse Physics-Informed Neural Networks for transport models in porous materials
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This work proposes an adaptive inverse PINN applied to different transport models, from diffusion to advection–diffusion–reaction, and mobile–immobile transport models for porous materials. Once a suitable PINN is established to solve the forward problem, the transport parameters are added as trainable parameters and the reference data is added to the cost function. We find that, for the inverse problem to converge to the correct solution, the different components of the loss function (data misfit, initial conditions, boundary conditions and residual of the transport equation) need to be weighted adaptively as a function of the training iteration (epoch). Similarly, gradients of trainable parameters are scaled at each epoch accordingly. Several examples are presented for different test cases to support our PINN architecture and its scalability and robustness. In particular, an anomalous transport phenomenon is investigated.