A reduced order model framework suitable for geotechnical problems

Data-driven methods are of increasing popularity for solving problems in geotechnics, offering as they do, the possibility of high-fidelity results without the effort of a detailed deterministic numerical analysis (e.g. using finite elements). A wide range of approaches fall under the heading of Reduced Order Models (ROMs) which are created by processing data generated from high-fidelity models. The quality of these ROMs, and the computational cost of their construction, themselves depend heavily on the architecture chosen. In this study, we introduce a set of efficient frameworks for data-driven ROMs that can be applied to geotechnics problems in general. Our approach employs autoencoders and/or principal component analysis to reduce data dimensionality and to extract latent representations, followed by a Deep Operator Network (DeepONet) to learn nonlinear behaviour within this latent space. The architectures are demonstrated on the problem of the prediction of spatio-temporal responses in soil consolidation, and we demonstrate that the proposed efficient ROM architectures accurately predict responses for a range of problem specifications. The proposed framework provides a versatile methodology for large-scale complex geotechnical modelling applications.