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

arXiv: https://arxiv.org/abs/2301.00636 · HTML: https://mlsanity.com/paper/2301.00636/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 2 of its 10 references that are in the map.
- First posted on arXiv 29 Dec 2022.

## Builds on (most cited first, 2 of 2)

- [DGM: A deep learning algorithm for solving partial differential equations](https://mlsanity.com/paper/1708.07469/) (2017)
- [A unified deep artificial neural network approach to partial differential equations in complex geometries](https://mlsanity.com/paper/1711.06464/) (2017)

## Abstract (arXiv)

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 nth order ordinary differential equation(ODE). Other methods of construction are examined in Section 3 and applied to three different models to assess their effectiveness.