Estimation of initial condition in heat conduction by neural network

This article describes a methodology for using neural networks in an inverse heat conduction problem. Three neural network (NN) models are used to determine the initial temperature profile on a slab with adiabatic boundary condition, given a transient temperature distribution at a given time. This is an ill-posed one-dimensional parabolic inverse problem, where the initial condition has to be estimated. Three neural network models addressed the problem: a feedforward network with backpropagation, radial basis functions (RBF), and cascade correlation. The input for the NN is the temperature profile obtained from a set of probes equally spaced in the one-dimensional domain. The NNs were trained considering a 5% of noise in the experimental data. The training was performed considering 500 similar test-functions and 500 different test-functions. Good reconstructions have been obtained with the proposed methodology.