Physics informed neural networks for solving inverse thermal wave coupled boundary-value problems

Abstract

As one of the essential parameters in thermophysical analysis, effective measurement of thermal diffusivity is necessary. This paper utilizes the Physics-Informed Neural Networks (PINN) framework to simulate the diffusion of thermal waves. The governing equations / boundary-value problem (BVP) for the thermal waves are expressed in a coupled partial differential form, derived using the method of separation of variables. The inverse problem associated with the coupled partial differential equations is solved using a dimensionless equation / BVP with a loss function that incorporates physical information. Even in the presence of experimental system errors, the neural network (NN) method introduced in this work (“new NN method”) was shown to be capable of robustly solving the thermal wave inverse problem without nonlinear DC components at different spatial locations, for determining the unknown thermal diffusivity of green (unsintered) metal powder compact materials. The results indicate that the coupled partial differential equations for the amplitude and phase of thermal waves within the PINN framework represent a promising strategy for determining thermophysical parameters.