High-dimensional inverse modeling of hydraulic tomography by physics informed neural network (HT-PINN)

A hydraulic tomography – physics informed neural network (HT-PINN) is developed for inverting two-dimensional large-scale spatially distributed transmissivity. HT-PINN involves a neural network model of transmissivity and a series of neural network models to describe transient or steady-state sequential pumping tests. All the neural network models are jointly trained by minimizing the total loss function including data fitting errors and PDE constraints. Batch training of collocation points is used to amplify the advantage of the mesh-free property of neural networks, thereby limiting the number of collocation points per training iteration and reducing the total training time. The developed HT-PINN accurately and efficiently inverts two-dimensional Gaussian transmissivity fields with more than a million unknowns (1024 × 1024 resolution), and the inversion map accuracy exceeds 95 %. The effects of batch sampling methods, batch number and size, and data requirements for direct and indirect measurements are systematically investigated. In addition, the developed HT-PINN exhibits great scalability and structure robustness in inverting fields with different resolutions ranging from coarse (64 × 64) to fine (1024 × 1024). Specifically, data requirements do not increase with the problem dimensionality, and the computational cost of HT-PINN remains almost unchanged due to its mesh-free nature while maintaining high inversion accuracy when increasing the field resolution.