Bridging Data and Dynamics: Physics-Informed Neural Networks in the SEIR Model

Abstract

Neural networks are powerful tools for learning from data and

capturing complex relationships between inputs and outputs. In many

situations, especially when the physical laws governing a system are

unknown or hard to describe, neural networks can help us build useful

models directly from data. However, in the study of dynamical systems,

we often do have equations that describe how systems evolve over time.

What we may lack are accurate parameter values, or ways to combine

those equations with real-world data. In this talk, we explore the

concept of physics-informed neural networks (PINNs), a recent approach

that combines the strengths of neural networks with known physical

models. PINNs incorporate differential equations directly into the

learning process, allowing us to estimate parameters and quantify

uncertainty, all while respecting the structure of the underlying

system. We will illustrate this approach using the SEIR

epidemiological model, highlighting the potential and challenges of

PINNs in combining data and physical models within a unified

framework.

Bio:

Dr. Abel Palafox González holds a PhD in Computational Science from the Center for Research in Mathematics (CIMAT A.C.) since 2016. He holds a Master of Science degree specializing in Computing and Mathematics for Industry. He has worked in the private sector in the development of computational systems and the implementation of models for ocean circulation studies. Since 2018, he has been an associate professor in the Department of Mathematics at the University of Guadalajara, CUCEI campus. He is a level 1 member of the National System of Researchers (SNII), and he has made contributions in the area of ​​inverse problems, with case studies in geophysics, mathematical epidemiology, and wave dispersion. His research interests include Bayesian inverse problems, high-performance computing, and numerical methods for partial differential equations.