Uso da rede neural fracionária de Hopfield na solução de problemas inversos em química

Abstract

Usually, the laboratory routine is summed up to observing a phenomenon and determining its causative agent, in other words, it seeks to relate the cause to an e ect. This relationship can be expressed through matrices as Kf = g, where f represents the cause and it is not directly accessible, g represents an e ect that can be measured and, nally, K, the mathematical operator that relates the two parameters. Finding f through K and g is known as inverse problem. This is a very recurring subject in several areas and has complications in its resolution, such as the ampli cation of the error in the result, leading to a solution inconsistent with the physical interpretation. There are numerous studies that investigate e cient methods to obtain a result, among them, the Arti cial Neural Networks stand out. The use of these networks has generated great scienti c advance for the optimization of such problems. In order to generalize the Integer Order Arti cial Neural Network model, which is named after being described by an integer derivative, studies have proposed the implementation of the Arti cial Neural Network with Fractional Calculus, where the order of the derivative is fractional, incorporating the set of rational numbers, obtaining excellent results when compared to the traditional Calculus. The methodology used in this work can circumvent di culties that are not tractable by traditional means. The originality of this project lies in the implementation of Hop eld Neural Networks with Fractional Calculus (FHNN) to solve the density of phonon states of heat capacity, using the MATLAB software to aid in numerical analysis, with an improvement at the speed of convergence of results. This methodology was also used to solve simpler problems, in order to introduce concepts and evaluate the performance of the FHNN, which was also e cient regarding the speed of convergence of the solution. This method provided accurate solutions, being 202 times faster than the Hop eld Neural Network, signi cantly decreasing the processing time.