A Parameter Sensitivity Investigation Of Neural Networks In Solving Differential Equations

A couple of decades ago,I.Lagaris and A.Likas presented a new numerical method making use of feedforward neural networks to solve differential equations.This method can be used to solve initial and boundary value problems and has shown to provide accurate solution when used with single hidden layered net of fixed ar-chitecture.However,not many results have been presented on the choice of the hyperparameters of the network and how it influences the computed solution.This thesis aims at answering those questions by numerical study of this method.The first investigation looks at how the error of the numercial solution decreases as the number of points used to train the nerwork increases.Then,the some similar tests are performed for the complexity of the network and its depth.Lastly,it will be shown that the choice of activation function does not matter as long as the function is regular enough and non-linear.