A Modified PINN Approach for Identifiable Compartmental Models in Epidemiology with Applications to COVID-19

TL;DR

This paper introduces a modified Physics-Informed Neural Network approach to analyze COVID-19 epidemiological data, addressing challenges of incomplete information and parameter identifiability, with applications to US testing effectiveness.

Contribution

It proposes novel modifications to PINN loss functions for better performance with incomplete data and assesses model parameter identifiability in epidemiological modeling.

Findings

Modified PINN can handle incomplete COVID-19 data effectively.

The approach enables estimation of testing effectiveness across US states.

Wavelet transform denoising improves data quality for modeling.

Abstract

A variety of approaches using compartmental models have been used to study the COVID-19 pandemic and the usage of machine learning methods with these models has had particularly notable success. We present here an approach toward analyzing accessible data on Covid-19's U.S. development using a variation of the "Physics Informed Neural Networks" (PINN) which is capable of using the knowledge of the model to aid learning. We illustrate the challenges of using the standard PINN approach, then how with appropriate and novel modifications to the loss function the network can perform well even in our case of incomplete information. Aspects of identifiability of the model parameters are also assessed, as well as methods of denoising available data using a wavelet transform. Finally, we discuss the capability of the neural network methodology to work with models of varying parameter values, as well as a concrete application in estimating how effectively cases are being tested for in a population, providing a ranking of U.S. states by means of their respective testing.