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In this work we apply a novel, accurate, fast, and robust physics-informedneural network framework for data-driven parameters discovery of problemsmodeled via parametric ordinary differential equations (ODEs) called theExtreme Theory of Functional Connections (X-TFC). The proposed method mergestwo recently developed frameworks for solving problems involving parametricDEs, 1) the Theory of Functional Connections (TFC) and 2) the Physics-InformedNeural Networks (PINN). In particular, this work focuses on the capability ofX-TFC in solving inverse problems to estimate the parameters governing theepidemiological compartmental models via a deterministic approach. Theepidemiological compartmental models treated in this work areSusceptible-Infectious-Recovered (SIR),Susceptible-Exposed-Infectious-Recovered (SEIR), andSusceptible-Exposed-Infectious-Recovered-Susceptible (SEIR). The results showthe low computational times, the high accuracy and effectiveness of the X-TFCmethod in performing data-driven parameters discovery of systems modeled viaparametric ODEs using unperturbed and perturbed data.

Physics-Informed Extreme Theory of Functional Connections Applied to Data-Driven Parameters Discovery of Epidemiological Compartmental Models