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.
Highlights
We show that solving these problems via Physics-Informed Neural Network (PINN) methods, such as X-Theory of Functional Connections (TFC), mitigates the ill-posedness of the inverse problems toward modeling errors and noisy data
We propose to employ a different and more robust PINN model, the Extreme Theory of Functional Connections (X-TFC), that merges Neural Networks (NNs) and the Theory of Functional Connections (TFC) [23,37]
To test the ability of the X-TFC in performing data-driven parameters discovery of epidemiological compartmental models, we have created synthetic datasets according to the three models presented above (SIR, SEIR, and SEIRS)
Summary
Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. The concern for viruses’ spread has been in the researchers’ spotlight for many years [1,2,3,4]. In the last year and a half, due to the COVID-19 pandemic, this concern has become a hot topic in many research fields [5,6,7,8,9,10,11,12,13]. Many models exist to study the spread of viruses. The first categorization between these models can be made for deterministic and stochastic models [14,15,16,17]
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