CFDNet: a deep learning-based accelerator for fluid simulations

CFD is widely used in physical system design and optimization, where it is used to predict engineering quantities of interest, such as the lift on a plane wing or the drag on a motor vehicle. However, many systems of interest are prohibitively expensive for design optimization, due to the expense of evaluating CFD simulations. To render the computation tractable, reduced-order or surrogate models are used to accelerate simulations while respecting the convergence constraints provided by the higher-fidelity solution. This paper introduces CFDNet -- a physical simulation and deep learning coupled framework, for accelerating the convergence of Reynolds Averaged Navier-Stokes simulations. CFDNet is designed to predict the primary physical properties of the fluid including velocity, pressure, and eddy viscosity using a single convolutional neural network at its core. We evaluate CFDNet on a variety of use-cases, both extrapolative and interpolative, where test geometries are observed/not-observed during training. Our results show that CFDNet meets the convergence constraints of the domain-specific physics solver while outperforming it by 1.9 - 7.4x on both steady laminar and turbulent flows. Moreover, we demonstrate the generalization capacity of CFDNet by testing its prediction on new geometries unseen during training. In this case, the approach meets the CFD convergence criterion while still providing significant speedups over traditional domain-only models.Comment: It has been accepted and almost published in the International Conference in Supercomputing (ICS) 202

Deep Learning Algorithms for Accelerating Fluid Simulations

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.gi