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The robust and efficient numerical solution of coupled hydro-poromechanical problems is of paramount importance in many application fields, in particular in geomechanics and biomechanics. Even though the solution by means of the Finite Elements Method (FEM) still remains the preferred option, Physics-Informed Neural Networks (PINNs) are rapidly gaining attention as a powerful and promising approach. By involving the residual of the governing PDEs as a constraint in the training, PINNs combine a physics-driven approach together with a data-driven one, leveraging on deep learning techniques. This work focuses on coupled hydro-poromechanical processes, where a PINN-based approach is implemented and investigated in classical benchmarks. An analysis of the influence of the hyper-parameter selection has been performed to study the model sensitivity to PINN architecture and identify the most appropriate one. To take advantage of PINN ability to integrate data and reduce the complexity of the solution of the coupled hydro-poromechanical problem, a "sensor-driven" training is proposed where data are provided at locations inside the domain even to solve a forward problem. The goal is to assess and validate the approach, thus contributing to the foundation of this method in coupled hydro-poromechanics. • Development of PINN models for hydro-poromechanics governed by coupled equations. • Definition of the problem-based hyper-parameter setting for the PINN architecture. • Model application to problems simulating the presence of data recorded from sensors. [ABSTRACT FROM AUTHOR]

Due to the complex behavior arising from non-uniqueness, symmetry, and bifurcations in the solution space, solving inverse problems of nonlinear differential equations (DEs) with multiple solutions is a challenging task. To address this, we propose homotopy physics-informed neural networks (HomPINNs), a novel framework that leverages homotopy continuation and neural networks (NNs) to solve inverse problems. The proposed framework begins with the use of NNs to simultaneously approximate unlabeled observations across diverse solutions while adhering to DE constraints. Through homotopy continuation, the proposed method solves the inverse problem by tracing the observations and identifying multiple solutions. The experiments involve testing the performance of the proposed method on one-dimensional DEs and applying it to solve a two-dimensional Gray-Scott simulation. Our findings demonstrate that the proposed method is scalable and adaptable, providing an effective solution for solving DEs with multiple solutions and unknown parameters. Moreover, it has significant potential for various applications in scientific computing, such as modeling complex systems and solving inverse problems in physics, chemistry, biology, etc. • Physics-informed neural networks are used to estimate unknown parameters with physical constraints. • HomPINNs helps to identify multiple solutions and solve inverse problems. • Numerical examples demonstrate its scalability and adaptability. • HomPINNs facilitates the discovery of previously unknown solutions. [ABSTRACT FROM AUTHOR]