  In this work we apply a novel, accurate, fast, and robust physics-informed
neural network framework for data-driven parameters discovery of problems
modeled via parametric ordinary differential equations (ODEs) called the
Extreme Theory of Functional Connections (X-TFC). The proposed method merges
two recently developed frameworks for solving problems involving parametric
DEs, 1) the Theory of Functional Connections (TFC) and 2) the Physics-Informed
Neural Networks (PINN). 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 (SEIR). The results show
the low computational times, the high accuracy and effectiveness of the X-TFC
method in performing data-driven parameters discovery of systems modeled via
parametric ODEs using unperturbed and perturbed data.
