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Lakshmi Sireesha Ch.

SSVKSS Jyothiraditya

Shriya Vadavalli

Jayaditya Peddisetti

Abstract

In this paper we propose a supervised Neural Network architecture for solving Singularly Perturbed 1D Reaction-Diffusion Equations (SPRDE). By Taylor series expansion, first we transform SPRDE to a Singularly Perturbed Differential Equation (SPDE). Using the ordinary differential equation (ODE) framework, in the algorithm we formulate and train an NN architecture comprising five fully connected layers with a ReLU activation function and a Mean Squared Error (MSE) loss function. Next we employ the Adam optimizer on the model for optimization and convergence of the solutions to SPRDE. The optimizer is implemented using Tensor Flow’s Neural Network architecture. This architecture helps for sequential stacking of layers thus enabling the construction of deep neural networks. The results presented in graphs, using the proposed ReLU based architecture demonstrate high accuracy of solutions.

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