The application of differentiable programming frameworks to computational fluid dynamics

The application of differentiable programming frameworks to computational fluid dynamics

Vos, Bart (TU Delft Electrical Engineering, Mathematics and Computer Science; TU Delft Delft Institute of Applied Mathematics)

Verlaan, M. (mentor)
Nuttall, Jonathan (mentor)
Budko, N.V. (graduation committee)

Delft University of Technology

Applied Mathematics

2021-02-19

In recent years many automatic differentiable programming frameworks have been developed in which numerical programs can be differentiated through automatic differentiation (AD). Examples of these frameworks are Theano, TensorFlow and Pytorch. These frameworks are widely used in Machine Learning. AD also finds applications in the field of computational fluid dynamics (CFD). It is used to develop discrete adjoint CFD code for research concerning for instance sensitivity analysis, data assimilation and design optimization. However, the use of the automatic differentiable programming frameworks in the field of CFD is limited. One can find some examples in the literature on how to find a numerical solution to an initial value problem using a differentiable programming framework. In this work it will be clarified how one can implement an semiimplicit
time integration scheme for a staggered grid to simulate the propagation of long waves in water with a free surface in TensorFlow. A main advantage of the automatic differentiable programming frameworks is the user friendly application
programming interface (API) for AD. No research has been conducted to use this API in the field of CFD. In this work an example will be given how one can use TensorFlow for research concerning sensitivity analysis. AD requires a significant allocation of memory on a CPU/GPU when working with fine meshes and/or long simulations and since CPU/GPU memory is finite, the method checkpointing is
proposed to make it feasible to perform sensitivity analysis when working with fine meshes and/or long simulations. Another main advantage of the differentiable programming framework TensorFlow is the use of compute unified device architecture (CUDA) of a NVIDIA GPU in order to perform computations in parallel, which results in a significant reduction in computation time. A Benchmark will be given that indicates the computational efficiency of TensorFlow compared to a loop over grid implementation in NumPy and a Fortran CPU scalar implementation.

Computational Fluid Dynamics (CFD)
Tensorflow
Shallow Water Equations
Automatic Differentiation
Sensitivity Analysis
Checkpointing
Adjoint-based optimization
Partial Differential Equations solver
Differentiable programming

http://resolver.tudelft.nl/uuid:e5da7c83-7e6c-43d2-80b6-7e9d9dd34706

Student theses

bachelor thesis

© 2021 Bart Vos