IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v9y2021i17p2069-d623012.html
   My bibliography  Save this article

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
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/9/17/2069/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/9/17/2069/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    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).
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Vargas Alvarez, Hector & Fabiani, Gianluca & Kazantzis, Nikolaos & Kevrekidis, Ioannis G. & Siettos, Constantinos, 2024. "Nonlinear discrete-time observers with Physics-Informed Neural Networks," Chaos, Solitons & Fractals, Elsevier, vol. 186(C).
    2. 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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Simón A. Rella & Yuliya A. Kulikova & Emmanouil T. Dermitzakis & Fyodor A. Kondrashov, 2021. "Rates of SARS-COV-2 transmission and vaccination impact the fate of vaccine-resistant strains," Working Papers 2129, Banco de España.
    2. Prem Kumar, R. & Santra, P.K. & Mahapatra, G.S., 2023. "Global stability and analysing the sensitivity of parameters of a multiple-susceptible population model of SARS-CoV-2 emphasising vaccination drive," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 203(C), pages 741-766.
    3. Mendoza, Daniel E. & Ochoa-Sánchez, Ana & Samaniego, Esteban P., 2022. "Forecasting of a complex phenomenon using stochastic data-based techniques under non-conventional schemes: The SARS-CoV-2 virus spread case," Chaos, Solitons & Fractals, Elsevier, vol. 158(C).
    4. Đorđević, J. & Papić, I. & Šuvak, N., 2021. "A two diffusion stochastic model for the spread of the new corona virus SARS-CoV-2," Chaos, Solitons & Fractals, Elsevier, vol. 148(C).
    5. Xu, Changjin & Liu, Zixin & Pang, Yicheng & Akgül, Ali, 2023. "Stochastic analysis of a COVID-19 model with effects of vaccination and different transition rates: Real data approach," Chaos, Solitons & Fractals, Elsevier, vol. 170(C).
    6. 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.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:9:y:2021:i:17:p:2069-:d:623012. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.