Mario De Florio

TL;DR: The results show that, for most of the problems considered, X-TFC achieves high accuracy with low computational time, even for large scale PDEs, without suffering the curse of dimensionality.

TL;DR: This work aims at accurately solve a thermal creep flow in a plane channel problem, as a class of rarefied-gas dynamics problems, using Physics-Informed Neural Networks (PINNs), where the solution of the problem is represented by the Constrained Expressions prescribed by the recently introduced Theory of Functional Connections (TFC).

TL;DR: 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 and shows 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.

TL;DR: In this paper, a novel approach to solving Chandrasekhar's problem in radiative transfer using the recently developed Theory of Functional Connections is presented, which is designed to elegantly and accurately solve the Linear Boundary Value Problem from the angular discretization of the integrodifferential Boltzmann equation for Radiative Transfer.

TL;DR: This work presents a recently developed approach based on physics-informed neural networks (PINNs) for the solution of initial value problems (IVPs), focusing on stiff chemical kinetic problems with governing equations of stiff ordinary differential equations (ODEs).