# Transport-Embedded Neural Architecture: Redefining the Landscape of physics aware neural models in fluid mechanics

arXiv: https://arxiv.org/abs/2410.04114 · HTML: https://mlsanity.com/paper/2410.04114/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 9 of its 31 references that are in the map.
- First posted on arXiv 5 Oct 2024.

## Builds on (most cited first, 9 of 9)

- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Characterizing possible failure modes in physics-informed neural networks](https://mlsanity.com/paper/2109.01050/) (2021)
- [Lagrangian Neural Networks](https://mlsanity.com/paper/2003.04630/) (2020)
- [A Method for Representing Periodic Functions and Enforcing Exactly Periodic Boundary Conditions with Deep Neural Networks](https://mlsanity.com/paper/2007.07442/) (2020)
- [Neural Conservation Laws: A Divergence-Free Perspective](https://mlsanity.com/paper/2210.01741/) (2022)
- [Physics-informed neural networks for solving Reynolds-averaged Navierunicodex2013Stokes equations](https://mlsanity.com/paper/2107.10711/) (2021)
- [Accelerating Physics-Informed Neural Network Training with Prior Dictionaries](https://mlsanity.com/paper/2004.08151/) (2020)
- [Investigating and Mitigating Failure Modes in Physics-informed Neural Networks (PINNs)](https://mlsanity.com/paper/2209.09988/) (2022)
- [How to Avoid Trivial Solutions in Physics-Informed Neural Networks](https://mlsanity.com/paper/2112.05620/) (2021)

## Abstract (arXiv)

This work introduces a new neural model which follows the transport equation by design. A physical problem, the Taylor-Green vortex, defined on a bi-periodic domain, is used as a benchmark to evaluate the performance of both the standard physics-informed neural network and our model (transport-embedded neural network). Results exhibit that while the standard physics-informed neural network fails to predict the solution accurately and merely returns the initial condition for the entire time span, our model successfully captures the temporal changes in the physics, particularly for high Reynolds numbers of the flow. Additionally, the ability of our model to prevent false minima can pave the way for addressing multiphysics problems, which are more prone to false minima, and help them accurately predict complex physics.