New Designed Loss Functions to Solve Ordinary Differential Equations with Artificial Neural Network
This work addresses the problem of solving ODEs numerically for researchers and engineers, but it appears incremental as it focuses on loss function variations without claiming major breakthroughs.
The paper tackles solving ordinary differential equations (ODEs) using artificial neural networks by designing new loss functions that incorporate both the differential equation and its initial/boundary conditions, and it tests these methods on three models to evaluate effectiveness.
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.