Motivation

In recent years, differentiable fluid mechanics solvers like PhiFlow [1] and JAX-Fluids [2] have been developed to simplify the integration of Machine Learning (ML) workflows into Computational Fluid Dynamics (CFD) solvers and vice versa. One very promising application of differentiable solvers is their integration into design optimization and control workflows, for which gradients are often extremely advantageous. To extend the ecosystem of differentiable solvers, we have already implemented a Smoothed Particle Hydrodynamics solver in JAX using the formulation from [3], which solves the Navier-Stokes equations on point clouds rather than on grids, in contrast to the previously mentioned solvers.

In this work, we want to go one step further and use the solver for both shape design and flow control. The system under investigation is the 3D flow over a flat plate, where the flat plate exhibits constant energy influx and the fluid cools the plate by convection. The degrees of freedom for the control problem are the inflow properties of the fluid (e.g. velocity profile, mass flow rate, temperature distribution, etc.) and the degrees of freedom for the design problem are given by the surface structure of the flat plate. The main reference for this work will be the paper “Inverse Design for Fluid-Structure Interactions using Graph Network Simulators” by Allen et al. 2022 [4]. Following this paper, we also want to compare the performance of the optimization routine using graph neural network-based surrogates like the GNS model [5] and the EGNN model [6]. There are many potential industrial applications of such a design optimization process, for example battery cooling in electric cars.

Milestones

• Implementation of the approach from [4] and adaptation to our use case.
• Performance comparison when using the learned surrogates over the original differentiable solver.
• Investigation of further control and design strategies accommodating multiple objectives.

Datasets

Training data is only required for the training of the learned surrogate models and will be provided at the beginning of the project. It is comprised of multiple trajectories of the system under investigation.

Requirements

• Basics of Graph Neural Networks and JAX
• Interest in Fluid Mechanics
• Teamwork skills

References

[1] Learning to Control PDEs with Differentiable Physics, Holl et al., 2020
[2] JAX-Fluids: A fully-differentiable high-order computational fluid dynamics solver for compressible two-phase flows, Bezgin et al., 2022
[3] A transport-velocity formulation for smoothed particle hydrodynamics, Adami et al., 2013
[4] Inverse Design for Fluid-Structure Interactions using Graph Network Simulators, Allen et al., 2022
[5] Learning to Simulate Complex Physics with Graph Networks, Sanchez-Gonzalez et al., 2020
[6] Geometric and Physical Quantities Improve E(3) Equivariant Message Passing, Brandstetter et al., 2022