Estimate Epidemiological Parameters given Partial Observations based on Algebraically Observable PINNs

TL;DR

This paper introduces algebraically observable PINNs to estimate epidemiological parameters from partial, noisy data, enabling accurate parameter estimation and prediction of unobserved variables in epidemic models.

Contribution

The paper proposes a novel algebraic observability concept integrated into PINNs for improved epidemiological parameter estimation from incomplete data.

Findings

Algebraically observable PINNs effectively estimate parameters from partial data.

The method accurately predicts unobserved epidemic variables.

Numerical experiments validate the approach's robustness and accuracy.

Abstract

In this study, we considered the problem of estimating epidemiological parameters based on physics-informed neural networks (PINNs). In practice, not all trajectory data corresponding to the population estimated by epidemic models can be obtained, and some observed trajectories are noisy. Learning PINNs to estimate unknown epidemiological parameters using such partial observations is challenging. Accordingly, we introduce the concept of algebraic observability into PINNs. The validity of the proposed PINN, named as an algebraically observable PINNs, in terms of estimation parameters and prediction of unobserved variables, is demonstrated through numerical experiments.