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

Transport processes are integral to a variety of flow problems, describing the movement of quantities like mass or energy within the flow. These equations are robust local representations of fundamental conservation laws in physics and appear in numerous applications, from heat transfer[Bergman et al., 2011] to drug delivery in biofluidic flows[Longest et al., 2019]. Depending on the specific quantity being transported, they are known by different names, such as convection-diffusion equations for species and energy transport or Navier-Stokes equations for momentum transport. With recent advancements in computational fluid dynamics (CFD), several methods, including finite element[Lewis et al., 2004], finite volume[Moukalled et al., 2016] and meshless techniques[Katz, 2009] have been developed. However, these methods struggle to effectively integrate real-world data into their frameworks.