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

TL;DR

This paper enhances physics-informed neural networks for the 2D Burgers equation by integrating solution data points and governing equations, improving physical accuracy without requiring extensive data.

Contribution

It introduces a method to augment PINNs with solution data points, demonstrating improved physics adherence and performance when combining data with governing equations.

Findings

Adding governing equations improves physics compliance.

Combining solution points with governing equations enhances model accuracy.

Limited solution data can be compensated by equation-based training.

Abstract

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.