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

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.