New Designed Loss Functions to Solve Ordinary Differential Equations with Artificial Neural Network

12/29/2022

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by   Xiao Xiong, et al.

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This paper investigates the use of artificial neural networks (ANNs) to solve differential equations (DEs) and the construction of the loss function which meets both differential equation and its initial/boundary condition of a certain DE. In section 2, the loss function is generalized to n^th order ordinary differential equation(ODE). Other methods of construction are examined in Section 3 and applied to three different models to assess their effectiveness.