Research on Deep Neural Network Solution of Ordinary Differential Equations and Its Application

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This article discusses the application of a single hidden layer neural network algorithm in solving numerical ordinary differential equations. Set the approximate solution with neural network structure to meet the initial boundary value conditions of ordinary differential equations, and discretize the weights of neural networks in the original equations. The optimization problem is transformed into the training problem of the neural network in the approximate solution, so that the approximate solution is close to the real solution. The changes in the structure, weights, and thresholds of the neural network are observed through network deduction. Numerical examples based on the python language prove the algorithm's performance Effectiveness.