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

• URL: http://arxiv.org/abs/2301.00636v1
• Date: Thu, 29 Dec 2022 11:26:31 GMT
• Title: New Designed Loss Functions to Solve Ordinary Differential Equations with Artificial Neural Network
• Authors: Xiao Xiong
• Abstract summary: This paper investigates the use of artificial neural networks (ANNs) to solve differential equations (DEs) In section 2, the loss function is generalized to $ntextth$ order ordinary differential equation(ODE)
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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 $n^\text{th}$ order ordinary differential equation(ODE). Other methods of construction are examined in Section 3 and applied to three different models to assess their effectiveness.

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