Neural Network Based Solution of Heat Equation for Thermography Modelling

We introduce a neural network-based solution of the heat conduction partial differential equation (PDE), to interpret the results of thermography, which is a non-destructive method for evaluating material structure. We are simulating a pulsed thermography system, in which transients of heat diffusion, following a heat pulse deposition on the material surface, are used to infer material internal properties. In this work we construct solutions for the PDE, using neural forms with the proper initial and boundary conditions embedded. As a benchmark problem, we solve the heat conduction equation in a one-dimensional rod of finite thickness, having both sides thermally insulated. The rod is initially brought at zero temperature, except for the front surface where a non-zero temperature distribution is specified. Future work will consider the extension of this neural network-based approach higher space dimensions and several different geometries.