Neural Network for Solving Ordinary Differential Equations

Deep learning and machine learning are immensely prevalent and highly interactive in a myriad of fields, typically neural networks is widely used in mathematics. We outline a technique for employing artificial neural networks (ANN) to solve ordinary differential equations. For better illustration, we present the basic logic and formula of ANN and gradient computation, following with one typical first order differential equation as example. In order to research the flexibility and feasibility of our model, we compare several hyperparameters and different optimizer using control variable method. Finally, our neural networks model is applied into the second order differential equations with innovative modification by analogy. In this article, we illustrate the relatively novel method to solve the ordinary differential equations and examine our model through adjustable parameters, then convert into the second order which shows a wide application range.