Data-Driven Deep Learning Methods for Physically-Based Simulations

In this doctoral thesis, we study and analyze Deep Learning applications to learn physically-based simulations’ results. The first type of application is focused on underground flow analysis problems modeled through Discrete Fracture Networks, training Deep Learning models as reduced models for Uncertainty Quantification. In particular, we look for trained Neural Networks able to predict the outflowing fluxes of a Discrete Fracture Network model. These Neural Networks are also exploited to define a new backbone identification method for a network of underground fractures. The second type of application deals with the parametric design optimization processes; specifically, we train Deep Learning models to speed up the objective function calls. These applications are described after a novel and sound formalization of the main concepts of supervised Machine Learning and Deep Neural Networks (the quintessence of Deep Learning). A numerical approach characterizes this new formalization of the learning problem; furthermore, we describe how the learning techniques evolved in history to reach the current state of the art. We test different kinds of Neural Network architectures in this thesis, such as the multitask Neural Networks and the residual Neural Networks. Moreover, we develop two new Neural Network layers: the Graph Informed layer and the Discontinuous layer. The first one is defined to embed Neural Network architectures with graphs and improve prediction abilities on graph-structured data (as the Discrete Fracture Network models). The second one introduces learnable discontinuities into Neural Networks, to approximate discontinuous functions and identify discontinuity interfaces. The last chapter of this thesis is dedicated to the definition and description of the Discontinuous layers.