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

TL;DR

The ability of the 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.

Abstract

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.

Figures (6)

• Figure 1: Two popular approaches to deal with periodic boundary conditions, (a) Prior-knowledge and (b) direct incorporation of a loss into the final loss function
• Figure 2: Two neural network, in both networks the second layer is prior dictionary of periodic boundary condition shown in Fig.\ref{['PD']} and hidden intermediate layers(shown with dotted lines) are perceptrons with activation functions of choice, (a) vanilla PINN and (b) TENN
• Figure 3: The evolution of the vorticity field for the vanilla PINN is illustrated over time for two different Reynolds numbers: (a) $\text{Re} = 0.1$ and (b) $\text{Re} = 100$. The top row displays the vanilla PINN predictions, the middle row shows the ground truth, and the bottom row illustrates the error between the predicted and actual results.
• Figure 4: The evolution of the vorticity field over time for the Transport-Embedded Neural Network (TENN) is shown for two Reynolds numbers: (a) $\text{Re} = 100$ and (b) $\text{Re} = 10$. The top row displays the TENN predictions, the middle row shows the ground truth, and the bottom row illustrates the error between the predicted and actual results.
• Figure 5: The evolution of the vorticity field for the Transport-Enhanced Neural Network (TENN) is shown over time for two different Reynolds numbers: (a) $\text{Re} = 0.1$ and (b) $\text{Re} = 1$. The top row displays the TENN predictions, the middle row shows the ground truth, and the bottom row illustrates the error between the predicted and actual results.