TY - JOUR
T1 - Physics-informed neural networks and functional interpolation for data-driven parameters discovery of epidemiological compartmental models
AU - Schiassi, Enrico
AU - De Florio, Mario
AU - D’ambrosio, Andrea
AU - Mortari, Daniele
AU - Furfaro, Roberto
N1 - Publisher Copyright:
© 2021 by the authors. Licensee MDPI, Basel, Switzerland.
PY - 2021/9
Y1 - 2021/9
N2 - 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 govern-ing 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.
AB - 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 govern-ing 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.
KW - COVID-19
KW - Epidemiological compartmental models
KW - Extreme learning machine
KW - Functional interpolation
KW - Physics-informed neural networks
KW - Theory of functional connections
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U2 - 10.3390/math9172069
DO - 10.3390/math9172069
M3 - Article
AN - SCOPUS:85114263779
SN - 2227-7390
VL - 9
JO - Mathematics
JF - Mathematics
IS - 17
M1 - 2069
ER -