Warp-DG: A Differentiable Discontinuous Galerkin Solver for Compressible Flows

The rapid growth in machine learning and deep learning has opened numerous opportunities to advance computational fluid dynamics for compressible flows. The goal of this work is to reduce the gap between the state-of-the-art CFD techniques and latest advancement in the learning community by developing a differentiable PDE platform for complex geometry. Existing works that either rely on low-order finite volume or high-order finite-difference discretization face challenges when higher numerical accuracy over complex geometry is desired. Thus, we build a high-order discontinuous Galerkin (DG) solver under the framework of differentiable programming from Nvidia Warp.

In this presentation, we will show the convergence results of the developed solver over several classical PDE examples over both structured and unstructured grids. Finally, an end-to-end learning of the hyperparameters in the DG scheme will be demonstrated to show the effectiveness of the proposed framework on advancing CFD for compressible flows with machine learning techniques.