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Applications of Artificial Neural Networks to Solve Ordinary Differential Equations

Abstract: Applications of Neural Networks to numerical problems have gained increasing interest. Solving Ordinary Differential Equations can be realized with simple artificial neural network architectures. In this paper, first step is training a Neural Network to satisfy the condition required by a differential equation and then finding a function whose derivative satisfies the Ordinary Differential Equation condition. The method of solving differential equation is implemented in Python Programming using the TensorFlow library. Keywords: Neural Network, Differential Equation, Loss function, Train function, Mean Squared Error, TensorFlow.