UC Irvine

Computational fluid dynamics (CFD) is the de-facto method for solving the Navier-Stokes equations, the set of partial differential equations that describe most laminar and turbulent flow problems. Solving this system of equations requires extensive computational resources; hence significant progress for scaling CFD simulations has been made with advancements in high-performance computing. However, the CFD community has mainly focused on developing high-order accurate methods instead of designing algorithms that harness the full potential of the new hardware. Moreover, current CFD solvers do not effectively utilize heterogeneous systems, where graphics processing units (GPUs) accelerate multi-core central processing units. At the same time, deep learning (DL) algorithms, whose training and inference stages map well to GPUs, have revolutionized the fields of computer vision and natural language processing. In this dissertation, we explore and propose novel algorithms to improve the performance and productivity of CFD solvers using DL.

First, we present CFDNet, a new convolutional neural network-based framework that accelerates laminar and turbulent flow simulations. Early works on DL+CFD approaches proposed surrogates that predict the flow field without any guarantees of satisfying the physical laws. Instead, we design CFDNet as an accelerator that reaches the same convergence guarantees as traditional first principles-based methods with fewer iterations. As a result, CFDNet achieves 1.9 − 7.4× speedups without compromising the quality of the solution of the physical solver in both laminar and turbulent flow problems for different configurations (such as channel flow and flow around an airfoil). CFDNet is the first DL-based accelerator for fluid simulations and presents three advantages: (a) it can be used in tandem with other acceleration techniques, such as multigrid solvers and parallelization, (b) it is amenable to any time-marching scheme, and (c) it is a DL module that can be plugged into any existing physical solver.

Like classical DL algorithms, CFDNet relies on training on large-scale datasets. Hence, it becomes impractical for high-resolution problems due to computationally prohibitive data collection and training. To overcome this limitation, we employ the idea of transfer learn- ing (that is, reusing a model trained with a large number of samples for a task where data is scarce) and propose SURFNet: a transfer learning-based framework to accelerate high-resolution simulations. SURFNet performs data collection and training mostly at low resolution (64 × 256) while being evaluated at high resolutions (up to 2048 × 2048), improving the scalability of DL algorithms for CFD. SURFNet achieves a constant 2× acceleration across different unseen-during-training flow configurations (such as symmetric and non-symmetric airfoils), and resolutions, showcasing resolution-invariance up to 2048 × 2048 spatial resolutions - significantly larger than those attempted in the literature.

SURFNet accelerates fluid simulations based on uniform meshes. However, since different regions of the domain present different flow complexity, we do not require uniform numerical accuracy throughout the domain. Adaptive mesh refinement (AMR) is an iterative technique that refines the mesh only in those regions that require higher numerical accuracy, and CFD solvers use it extensively for scalability. We propose ADARNet, a DL algorithm that predicts a non-uniform output and decides the final resolution of different domain regions in a single shot. Hence, ADARNet marries the advantages of DL (one-shot prediction) and AMR solvers (non-uniform refinement) to present a novel algorithm that outperforms both. Due to ADARNet’s ability to super-resolve only regions of interest, it predicts the same target 1024 × 1024 spatial resolution 7 − 28.5× faster than state-of-the-art DL methods (which perform uniform super-resolution) and reduces the memory usage by 4.4 − 7.7×, showcasing improved scalability.

CFDNet, SURFNet, and ADARNet are hybrid DL-CFD frameworks that collectively im- prove the state-of-the-art. First, CFDNet is a DL-based accelerator for iterative numerical schemes. Second, SURFNet scales CFDNet to high resolutions and allows acceleration of real-world aerospace design scenarios. Third, ADARNet is a direct method for AMR that of- fers high-resolution accuracy with significantly less compute and memory resources. The code for these frameworks is open-source and can be found in: https://github.com/oobiols/staidy.git