Obtaining the solutions of initial and boundary value problems with TLBO approach

Objective: In this study, our goal is to obtain Artificial Neural Network (ANN) solutions of linear or nonlinear ordinary differential equations under initial value and Dirichlet boundary conditions. It is aimed to use derivative-free optimisation methods for the training of the ANN. Material and Methods: This study uses the Teaching-Learning Based Algorithm, a meta-heuristic optimisation approach inspired by the teaching-learning process. Results: The artificial neural network models proposed in the research and trained by the TLBO method have been found to be a suitable method for the solution of both initial value problems and Dirichlet boundary value problems. Comparisons with Particle Swarm Optimisation (PSO), which is set as the gold standard in this thesis, show that although TLBO approaches do not converge to the solution with the desired rate of error, they significantly shorten the training time of the neural network model. Conclusions: In this study, it is concluded that artificial neural network models that can predict numerical solutions of differential equations can be developed and the proposed model can be trained without calculating the derivative values. Keywords: Global optimization, Neural networks, Teaching-Learning based optimization, Dirichlet Boundary Value Problem