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Inverse Modelling in Hydro-Poromechanics with PINN
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A Physics-Informed Neural Network (PINN) application is presented to simulate coupled flow and deformation processes in geological porous media, with the aim at solving the governing PDEs and integrating additional data information at the same time. Indeed, PINN is a machine learning technique that makes it possible to introduce the knowledge of some physical principles to a standard data-driven training. These particular neural networks are trained not only to fit available data of a monitored process, but also to satisfy the governing equations, via the minimization of the residual [1]. In this context, PINNs can be used for either predicting the space- and time-dependent quantities of interest or approximating the unknown material parameters characterizing the problem. These properties suggest PINN-based model application when the physical understanding of the process is limited and some recorded measurements are available. In this work, Biot’s coupled differential equations of hydro-poromechanics are solved via a PINN-based approach so that available data are used to identify the involved unknown hydraulic and geomechanical parameters. By leveraging previous work results [2], the coupled PDEs with unknown material coefficients along with available data are used to train the model in order to estimate parameter values and simultaneously approximate pressure and displacements in the domain. The performance of the method is investigated on different problems, ranging from one- to three- dimensions either in homogeneous or in heterogeneous settings. Moreover, the effect of different assumptions – e.g. quantity, location, noisiness of available data – on the identification accuracy is analysed, for the purpose of validating the approach capability to deal with problems in hydro-poromechanics, thus making it possible to use PINN-based models in real-world geophysical applications.