AJS - Caterina Millevoi

Speaker: Caterina Millevoi (University of Padova)

Title: From Porous Media to Pandemics: Harnessing Physics-Informed Neural Networks

Abstract: In many engineering fields traditionally dominated by discretization methods for the numerical solution of differential equations, neural network models are increasingly playing a significant role in advancing scientific research. One such technique, Physics-Informed Neural Networks (PINNs), incorporates information from governing equations of a phenomenon into the data, including the residual as a constraint in the training process. These models are particularly promising for problems involving poorly understood processes, where it is computationally impractical to run simulations at desired spatial and temporal resolutions, or where some noisy data can be recorded in addition to initial and boundary conditions. This seminar will discuss various applications of PINNs for solving differential equation-based problems.
First, a PINN-based approach will be explored for reproducing coupled flow and deformation processes in geological porous media and identifying hydraulic and geomechanical parameters characterizing material properties in the governing hydro-poromechanical equations. A sensor-driven approach is introduced to accelerate convergence and enhance accuracy by integrating field data automatically during the training process. The investigation also considers the technique's application to parameter estimation in various settings, laying the groundwork for complex real-world applications like reservoir modeling.
Second, a synthetic SIR compartmental model of the COVID-19 pandemic will be presented featuring a PINN model. This model's potential to approximate the Susceptible, Infectious, and Recovered classes of the population during the epidemic is examined and the PINN's capability to solve an ill-posed inverse problem by estimating the reproduction number using real infectious data recorded in Italy during the COVID-19 pandemic is demonstrated. Additionally, the method is tested on short-term forecasting. In this context, a split-PINN approach, involving a two-step training process, is proposed. This method proves to be a computationally efficient alternative, outperforming traditional PINN training in terms of both accuracy and speed. The goal is to establish this technique in epidemiology to apply it to more complex models, providing quick, accurate answers to aid decision-making during pandemic events.

This seminar aims to provide a comprehensive overview of the versatility and potential of PINNs in addressing complex problems in hydro-poromechanics and epidemiology, highlighting the integration of deep learning with physics-based models to enhance predictive capabilities in these fields.