Bayesian optimization of sensor location in PINN-based inverse modeling of coupled hydro-poromechanical systems

Physics-Informed Neural Networks (PINNs) represent a powerful paradigm for solving inverse problems in coupled hydro-poromechanical systems. However, their application in real-world scenarios faces a critical hurdle: the accuracy of a PINN is highly dependent on observational data, yet acquiring this data through physical sensors can be extremely expensive and logistically challenging. This thesis addresses the challenge of optimal sensor placement by proposing a systematic framework based on Bayesian Optimization (BO). We employ a Gaussian Process (GP) to build an efficient surrogate model. This model learns the complex relationship between potential sensor configurations and a measure of the PINN's expected performance. An acquisition function then intelligently guides the search for the sensor layout that promises to yield the most informative data, maximizing the return on investment. The methodology is successfully demonstrated on 1D, showing that the BO-driven approach can identify sensor locations that significantly improve the accuracy and reliability of the inverse modeling compared to standard heuristics. This work provides a robust and computationally efficient strategy for optimizing experimental designs, ensuring that limited resources are used to their full potential in complex physical systems.