# Augmenting a Physics-Informed Neural Network for the 2D Burgers Equation by Addition of Solution Data Points

arXiv: https://arxiv.org/abs/2301.07824 · HTML: https://mlsanity.com/paper/2301.07824/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 3 of its 15 references that are in the map.
- First posted on arXiv 18 Jan 2023.

## Builds on (most cited first, 3 of 3)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [Integrating Scientific Knowledge with Machine Learning for Engineering and Environmental Systems](https://mlsanity.com/paper/2003.04919/) (2020)

## Built on by (most cited first, 5 of 5)

- [Redefining Super-Resolution: Fine-mesh PDE predictions without classical simulations](https://mlsanity.com/paper/2311.09740/) (2023)
- [Solving 2-D Helmholtz equation in the rectangular, circular, and elliptical domains using neural networks](https://mlsanity.com/paper/2503.20222/) (2025)
- [Equation identification for fluid flows via physics-informed neural networks](https://mlsanity.com/paper/2408.17271/) (2024)
- [DiffGrad for Physics-Informed Neural Networks](https://mlsanity.com/paper/2409.03239/) (2024)
- [Prediction of acoustic field in 1-D uniform duct with varying mean flow and temperature using neural networks](https://mlsanity.com/paper/2507.22370/) (2025)

## Abstract (arXiv)

We implement a Physics-Informed Neural Network (PINN) for solving the two-dimensional Burgers equations. This type of model can be trained with no previous knowledge of the solution; instead, it relies on evaluating the governing equations of the system in points of the physical domain. It is also possible to use points with a known solution during training. In this paper, we compare PINNs trained with different amounts of governing equation evaluation points and known solution points. Comparing models that were trained purely with known solution points to those that have also used the governing equations, we observe an improvement in the overall observance of the underlying physics in the latter. We also investigate how changing the number of each type of point affects the resulting models differently. Finally, we argue that the addition of the governing equations during training may provide a way to improve the overall performance of the model without relying on additional data, which is especially important for situations where the number of known solution points is limited.