Physics-informed neural networks and functional interpolation for data-driven parameters discovery of epidemiological compartmental models

Enrico Schiassi, Mario De Florio, Andrea D’ambrosio, Daniele Mortari, Roberto Furfaro

Research output: Contribution to journalArticlepeer-review

Abstract

In this work, we apply a novel and accurate Physics-Informed Neural Network Theory of Functional Connections (PINN-TFC) based framework, called Extreme Theory of Functional Connections (X-TFC), for data-physics-driven parameters’ discovery of problems modeled via Ordinary Differential Equations (ODEs). The proposed method merges the standard PINNs with a functional interpolation technique named Theory of Functional Connections (TFC). In particular, this work focuses on the capability of X-TFC in solving inverse problems to estimate the parameters govern-ing the epidemiological compartmental models via a deterministic approach. The epidemiological compartmental models treated in this work are Susceptible-Infectious-Recovered (SIR), Susceptible-Exposed-Infectious-Recovered (SEIR), and Susceptible-Exposed-Infectious-Recovered-Susceptible (SEIRS). The results show the low computational times, the high accuracy, and effectiveness of the X-TFC method in performing data-driven parameters’ discovery systems modeled via parametric ODEs using unperturbed and perturbed data.

Original languageEnglish (US)
Article number2069
JournalMathematics
Volume9
Issue number17
DOIs
StatePublished - Sep 2021

Keywords

  • COVID-19
  • Epidemiological compartmental models
  • Extreme learning machine
  • Functional interpolation
  • Physics-informed neural networks
  • Theory of functional connections

ASJC Scopus subject areas

  • Mathematics(all)

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