Numerical Solutions of Stochastic Dynamics using Convolutional Neural Network Methods

Deep learning and machine learning are very popular and highly interactive across many different subjects; neural networks are usually used extensively in mathematics. We introduce a convolutional neural network (CNN) approach to solving ordinary differential equations and stochastic integral equations. We use an example of a typical first-order differential equation and stochastic integral equations to briefly explain the basic ideas of CNN and gradient computing. We use the control variable approach to compare several hyperparameters and different optimizers to investigate the adaptability and viability of our model. The creation of a convolutional neural network (CNN) for resolving the equations is the key goal here. This is made possible by using a single layer back-propagation learning technique with a logistic sigmoid function and Adam optimizer. To determine which loss best fits the output, multiple losses are created and the outcomes are analyzed for varying neuron counts.