Análise sensitiva aplicada à solução de problemas diretos e inversos em química

Abstract

Problems in science are usually addressed in a direct scheme in which the output data (effects) are determined from an input (cause). However, studies can be done inverting the causality logic, and this approach is so called inverse problem. To solve this class of problems the experimental error must be considered, since it can cause problems to the inversion procedure. Therefore, robust methodologies are needed to figure them out, as the Tikhonov regularization and Hopfield neural network.An useful tool to solve inverse problems is the sensitivity analysis, which quantifies how the deviations on input parameters affect the output data. The subject of this thesis is the solution of direct and inverse problems and the use of sensitivity analysis to help solving them. Firstly, it will be proposed a new method for the solution of ill-posed inverseproblems, which is based on Tikhonov regularization and Hopfield neural network. The new method, which was labeled as regularized network, was applied to solve a simple problem and the inversion results were satisfactory. As a direct problem, the calculation of the quantum second virial coefficient for helium dimer was done at low temperatures. For this property determination, a recent potential for the system description were used. Moreover, the sensitivity of some potential parameters was evaluated in the calculation for the thermodynamic property.The results of this study provides a second virial coefficient within the experimental error. Using an inverse approach, the phonon distribution of aluminum was determined from experimental heat capacity. The inverted distribution has a better quality compared to experimental one, since the first provides the heat capacity within experimental error, unlike the experimental distribution. Lastly, the radial distribution function of the liquid argon was inverted from its structure factor. This study assessed mainly the influence of regularized network (developed in this work) to retrieve this property. For comparison, the same propertywas inverted using the Hopfield neural network and the Tikhonov regularization. As the radial distribution is a function with a many oscillations, the regularized network provided better results in its inversion.