Development of a hydro-mechanical model for layered subsurface media based on physics informed neural networks (PINNs)

In recent years, physics-informed neural networks (PINNs) have garnered significant interest in the field of engineering. PINNs are a class of deep learning algorithms that predict the physical response of a system by optimizing a loss functional constructed by directly embedding well-established governing physical laws. This approach makes PINNs more computationally efficient and better at generalizing than traditional machine learning models, which rely solely on observed data. PINNs offer a flexible mesh-free alternative to conventional numerical methods (e.g., finite element method or finite difference method) for solving complex problems constrained by physical laws. Moreover, the use of automatic differentiation enables PINNs to naturally handle inverse problems, which are often prohibitively expensive to solve using traditional numerical techniques.

Despite their promise, the application of PINNs in geotechnical engineering remains limited. This is largely due to the inherent complexity of soil systems, which often consist of multiple layers with varying material properties, as well as the heterogeneous and non-linear behaviour of subsurface media. In addition, general geotechnical problems often, involve irregular boundaries and complex domain geometries, posing significant challenges for PINNs in achieving accurate and reliable solutions.

To extend the applicability of PINNs in geotechnical engineering, this project aims to develop a PINNs-based framework for both forward and inverse analysis of the hydro-mechanical behaviour of layered subsurface media, with potential applications to field-scale problems in geotechnical engineering. To achieve this, the following objectives are proposed:

• Development of a PINNs framework incorporating effective domain decomposition strategies and its application to irregular boundary/domain geometries.

• Development of a PINNs solver for fluid flow in layered soils/rocks.

• Development of a PINNs solver for predicting soil/rock deformation by incorporating the linear/non-linear constitutive laws into the proposed PINN framework.

• Development of a coupled hydro-mechanical solver to analyse the behaviour of layered rocks.

• Application of the model to noisy data and real-world applications and improvement of the model’s robustness.