# Burgers' pinns with implicit euler transfer learning

arXiv: https://arxiv.org/abs/2310.15343 · HTML: https://mlsanity.com/paper/2310.15343/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 2 of its 11 references that are in the map.
- First posted on arXiv 23 Oct 2023.

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

- [Deep Learning of Vortex Induced Vibrations](https://mlsanity.com/paper/1808.08952/) (2018)
- [Physics-Informed Neural Network Method for Solving One-Dimensional Advection Equation Using PyTorch](https://mlsanity.com/paper/2103.09662/) (2021)

## Built on by (most cited first, 2 of 2)

- [Fully-fused Multi-Layer Perceptrons on Intel Data Center GPUs](https://mlsanity.com/paper/2403.17607/) (2024)
- [Numerical simulation of transient heat conduction with moving heat source using Physics Informed Neural Networks](https://mlsanity.com/paper/2506.17726/) (2025)

## Abstract (arXiv)

The Burgers equation is a well-established test case in the computational modeling of several phenomena such as fluid dynamics, gas dynamics, shock theory, cosmology, and others. In this work, we present the application of Physics-Informed Neural Networks (PINNs) with an implicit Euler transfer learning approach to solve the Burgers equation. The proposed approach consists in seeking a time-discrete solution by a sequence of Artificial Neural Networks (ANNs). At each time step, the previous ANN transfers its knowledge to the next network model, which learns the current time solution by minimizing a loss function based on the implicit Euler approximation of the Burgers equation. The approach is tested for two benchmark problems: the first with an exact solution and the other with an alternative analytical solution. In comparison to the usual PINN models, the proposed approach has the advantage of requiring smaller neural network architectures with similar accurate results and potentially decreasing computational costs.