In recent years, differentiable fluid mechanics solvers like FhiFlow, JAX-CFD, and JAX-Fluids have been developed to simplify the integration of Machine Learning (ML) building block into Computational Fluid Dynamics (CFD) solvers. The workhorse of all these frameworks are automatic differentiation Python libraries like PyTorch and JAX. However, what these three libraries implement are grid-based solvers, and to the best of our knowledge there is no differentiable particle-based CFD solver yet. To address this shortcoming, we will implement a working Smoothed Particle Hydrodynamics solver in JAX using the formulations by Morris et al. 1997 as well as Adami et al. 2013.
Afterwards, we want to extend on this code base in two ways: (1) by implementing classical SPH turbulence models and (2) comparing them against state-of-the-art Graph Neural Network (GNN) surrogates.
On the first part (1), we emphasize that turbulence modeling in SPH is by far not as we studied as grid-based turbulence closure models. Thus, a thorough literature research is needed to identify the 2-3 most promising turbulence models, see Adami et al. 2012 and Monaghan 2009, and implement them.
On the GNN part (2), we will implement the GNS model (Sanchez-Gonzalez et at. 2020) and the SEGNN model (Brandstetter et al. 2022) in JAX and then, we will train and compare the results. The physical system we will mainly investigate is the decaying 3D Taylor-Green vortex (TGV)(Brachet et al. 1983). If the results look promising, we will submit them to a fluid mechanics journal.