Contributed Talk
Physics-informed neural networks for multiscale hyperbolic models for the spatial spread of infectious diseases
University of Ferrar, Italy
Abstract
The purpose of this talk is to present some recent results in the mathematical modeling of epidemic phenomena through the use of kinetic equations and their numerical solution with physics-informed machine learning techniques. When studying real epidemic scenarios, the model parameters, necessary to simulate the predictive dynamics of the propagation of the virus of interest, require a delicate calibration phase, often made even more challenging by the scarcity of observed data reported by official sources. Moreover, one of the main problems in studying the propagation of epidemics consists in the great uncertainty of available data, such as the real number of infected individuals (as demonstrated by the recent COVID-19 pandemic, especially in its early phase). Thus, we are commonly forced to draw conclusions and make decisions having only partial and random information at our disposal. A class of multiscale hyperbolic transport models is introduced to study the propagation of an infectious disease described by the diffusive behavior characterizing a part of the population acting over an urban scale and the transport mechanism related to individuals traveling in extra-urban scales. Recently developed asymptotic-preserving (AP) physics-informed neural networks (PINNs) for hyperbolic transport models of epidemic spread are designed to solve the inverse and the forward problem of interest without losing the ability to describe the multiscale dynamics of the phenomenon. Given the large uncertainty on epidemic data reported by official sources, noisy and stochastic data are also taken into account. Several numerical experiments are discussed to confirm the validity of the proposed methodology.
This is part of joint works with S. Jin (Shanghai Jiao Tong University), C. Lu (Iowa University), L. Pareschi (University of Ferrara), and X. Zhu (Iowa University).