Computational Intelligence and Tikhonov Regularization with Reduced Dimension Model: Applications in Health, Renewable Energy and Climate Heat Transfer Inverse Problems

In this chapter we present a method to predict the optimal value of the Tikhonov’s regularization parameter by solving simplified versions of the inverse problems considered. This can be of great benefit since methods such as the L-curve and the Fixed Point Iteration require the inverse problem to be solved several times in order to determine the optimal value for the regularization parameter. The main idea that supports the proposed approach is to solve the problem of interest using a low set of dimensions to represent the function to be estimated and, then, this solution is used to obtain an estimate for the regularization parameter of the complete model, based on the Fixed Point Iteration method. Tests are performed on three inverse heat transfer problems: estimation of the variable thermal conductivity of a biological tissue, estimation of the inlet temperature in parallel plates channel, and the estimation of the variable scattering albedo of a radiative transfer participating medium. The results obtained demonstrate the feasibility of the technique in three problems with potential practical applications in bioengineering, renewable energy and climate in alignment with the Sustainable Development Goals (SDG) 3, 4, 7, 9, 13, and 17 of the United Nations 2030 Agenda established in 2015.