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Physics-Informed Neural Networks and Functional Interpolation for Data-Driven Parameters Discovery of Epidemiological Compartmental Models

Author

Listed:
  • Enrico Schiassi

    (Systems & Industrial Engineering, University of Arizona, Tucson, AZ 85721, USA)

  • Mario De Florio

    (Systems & Industrial Engineering, University of Arizona, Tucson, AZ 85721, USA)

  • Andrea D’Ambrosio

    (Systems & Industrial Engineering, University of Arizona, Tucson, AZ 85721, USA
    School of Aerospace Engineering, Sapienza University of Rome, 00138 Rome, Italy)

  • Daniele Mortari

    (Aerospace Engineering, Texas A&M University, College Station, TX 77843-3141, USA)

  • Roberto Furfaro

    (Systems & Industrial Engineering, University of Arizona, Tucson, AZ 85721, USA
    Aerospace & Mechanical Engineering, University of Arizona, Tucson, AZ 85721, USA)

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 governing 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.

Suggested Citation

  • Enrico Schiassi & Mario De Florio & Andrea D’Ambrosio & Daniele Mortari & Roberto Furfaro, 2021. "Physics-Informed Neural Networks and Functional Interpolation for Data-Driven Parameters Discovery of Epidemiological Compartmental Models," Mathematics, MDPI, vol. 9(17), pages 1-17, August.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:17:p:2069-:d:623012
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    References listed on IDEAS

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    1. Daniele Mortari, 2017. "Least-Squares Solution of Linear Differential Equations," Mathematics, MDPI, vol. 5(4), pages 1-18, October.
    2. Adak, Debadatta & Majumder, Abhijit & Bairagi, Nandadulal, 2021. "Mathematical perspective of Covid-19 pandemic: Disease extinction criteria in deterministic and stochastic models," Chaos, Solitons & Fractals, Elsevier, vol. 142(C).
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    Cited by:

    1. Yassopoulos, Christopher & Reddy, J.N. & Mortari, Daniele, 2023. "Analysis of nonlinear Timoshenko–Ehrenfest beam problems with von Kármán nonlinearity using the Theory of Functional Connections," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 205(C), pages 709-744.

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