Exploring the Efficiency of Neural Networks for Solving Dynamic Process Problems: The Fisher Equation Investigation

The numerical solution of problems based on ordinary and partial differential equations has been a subject of extensive research. While several methods, such as the finite difference, finite element, and finite volume methods, have been developed, each has its own strengths and limitations. This paper presents a different approach that utilizes feedforward neural networks to approximate functions, resulting in a differentiable analytical expression. Compared to other methods, this approach requires significantly fewer model parameters, leading to reduced computational requirements. The study examines the influence of a neural network’s loss function configuration on the accuracy and convergence rate of solving partial differential equations for functions of two variables: coordinate and time, using the example of the Fisher’s equation.