Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Estimate Epidemiological Parameters given Partial Observations based on Algebraically Observable PINNs

Mizuka Komatsu

TL;DR

This work tackles parameter estimation in SEIR-like epidemiological models from partial observations using physics-informed neural networks (PINNs). It introduces algebraic observability, deriving polynomial relationships (e.g., $S = \frac{\ddot{I} + (\epsilon + \gamma)\dot{I} + \epsilon\gamma I}{\beta\epsilon I}$ and $E = \frac{\dot{I} + \gamma I}{\epsilon}$) to recover unobserved states from observed $I$ and its derivatives via Gröbner-basis elimination. The authors propose Algebraically Observable PINNs, leveraging these relations to generate data for unobserved variables and employing a Gaussian process–Bayesian optimization (GP-BO) outer loop to estimate the unknown parameter $\epsilon$ by minimizing test error. The approach achieves accurate trajectory predictions and improved parameter estimation under partial data, offering a practical framework for epidemic inference when observations are limited.

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.

Estimate Epidemiological Parameters given Partial Observations based on Algebraically Observable PINNs

TL;DR

This work tackles parameter estimation in SEIR-like epidemiological models from partial observations using physics-informed neural networks (PINNs). It introduces algebraic observability, deriving polynomial relationships (e.g., and ) to recover unobserved states from observed and its derivatives via Gröbner-basis elimination. The authors propose Algebraically Observable PINNs, leveraging these relations to generate data for unobserved variables and employing a Gaussian process–Bayesian optimization (GP-BO) outer loop to estimate the unknown parameter by minimizing test error. The approach achieves accurate trajectory predictions and improved parameter estimation under partial data, offering a practical framework for epidemic inference when observations are limited.

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.
Paper Structure (6 sections, 4 equations, 4 figures, 1 table)

This paper contains 6 sections, 4 equations, 4 figures, 1 table.

Table of Contents

  1. Introduction
  2. Target scenario
  3. Loss function of vanilla PINNs
  4. The algebraic observability of SEIR model
  5. Algebraically Observable PINNs
  6. Results

Figures (4)

  • Figure 1: The values of the loss function of the GP-BO.
  • Figure 2: Comparison of trajectories (Ground truth versus prediction by the proposed method.)
  • Figure 3: Comparison of trajectories (Ground truth versus prediction by the baseline method at 2000 epoch) The same legend as Figure \ref{['fig:pred-base-2000']} is applied.
  • Figure 4: Comparison of trajectories (Ground truth versus prediction by the baseline method at 26000 epoch.) The same legend as Figure \ref{['fig:pred-base-26000']} is applied.