Machine learning–accelerated computational fluid dynamics

By Dmitrii Kochkov, Jamie A. Smith, Ayya Alieva, Qing Wang, Michael P. Brenner, Stephan Hoyer. Proceedings of the National Academy of Sciences of the United States of America, 2021

1,218 citations recorded by the source corpus.

Significance Accurate simulation of fluids is important for many science and engineering problems but is very computationally demanding. In contrast, machine-learning models can approximate physics very quickly but at the cost of accuracy. Here we show that using machine learning inside traditional fluid simulations can improve both accuracy and speed, even on examples very different from the training data. Our approach opens the door to applying machine learning to large-scale physical modeling tasks like airplane design and climate prediction. Numerical simulation of fluids plays an essential role in modeling many physical phenomena, such as weather, climate, aerodynamics, and plasma physics. Fluids are well described by the Navier–Stokes equations, but solving these equations at scale remains daunting, limited by the computational cost of resolving the smallest spatiotemporal features. This leads to unfavorable trade-offs between accuracy and tractability. Here we use end-to-end deep learning to improve approximations inside computational fluid dynamics for modeling two-dimensional turbulent flows. For both direct numerical simulation of turbulence and large-eddy simulation, our results are as accurate as baseline solvers with 8 to 10× finer resolution in each spatial dimension, resulting in 40- to 80-fold computational speedups. Our method remains stable during long simulations and generalizes to forcing functions and Reynolds numbers outside of the flows where it is trained, in contrast to black-box machine-learning approaches. Our approach exemplifies how scientific computing can leverage machine learning and hardware accelerators to improve simulations without sacrificing accuracy or generalization.

Subfields: Atmospheric Science, Computational Mechanics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/b62544d43edd402c23127b9e8c28d0f5b6b33db2

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Citations in the corpus

Enhancing computational fluid dynamics with machine learning (2021, background): “[25] for the twodimensional Kolmogorov flow [26], which maintains fluctuations via a forcing term.”
Multiwavelet-based Operator Learning for Differential Equations (2021, background): “In parallel, another stream of work focuses on constructing the PDE solution function as a NN architecture [31, 42, 57, 65].”
Monarch: Expressive Structured Matrices for Efficient and Accurate Training (2022, background): “Specific to the partial differential equations (PDEs) are approaches designed to learn solution operators (Raissi et al., 2019; Fan et al., 2020; Li et al., 2020), and hybridized solvers (Kochkov et al., 2021), evaluated primarily on classical fluid dynamics.”
Physics-Informed Neural Operator for Learning Partial Differential Equations (2021, neutral): “This setting consists of the ML-enhanced conventional solvers such as learned finite element, finite difference, and multigrid solvers [39–41], as well as purely neural network-based solvers such as the PINNs, Deep Galerkin Method, and Deep Ritz Method [14, 42, 43].”
Factorized Fourier Neural Operators (2021, methodology): “This means that if we double the grid size, the solver should take a step that is twice as small (we follow this approach to obtain DNS’s Pareto frontier in Fig.”
Deep Generative Models in Engineering Design: A Review (2021, methodology): “Shu et al. [70] take an iterative retraining approach by retraining a GAN on high performance models evaluated using Computational Fluid Dynamics (CFD) evaluation.”
ClimaX: A foundation model for weather and climate (2023, neutral): “These approaches are complemented by general machine learning models for fluid dynamics (Li et al., 2020; Kochkov et al., 2021; Lu et al., 2021; Brandstetter et al., 2022a;b).”
Fourier Neural Operator for Parametric Partial Differential Equations (2020, background): “Machine learning methods may hold the key to revolutionizing scientiﬁc disciplines by providing fast solvers that approximate or enhance traditional ones (Raissi et al., 2019; Jiang et al., 2020; Greenfeld et al., 2019; Kochkov et al., 2021).”
Learning the solution operator of parametric partial differential equations with physics-informed DeepONets (2021, positive): “Recent efforts [44, 16, 45, 46, 47] attempt to address some of these challenges by designing appropriate architectures and loss functions for learning discretized operators (i.”
Gradients are Not All You Need (2021, methodology): “This has been used to great effect in training of language models [Sutskever, 2013], learned optimizers [Andrychowicz et al., 2016, Wichrowska et al., 2017, Lv et al., 2017, Metz et al., 2019], and ﬂuid simulation [Kochkov et al., 2021].”
Neural operators for accelerating scientific simulations and design (2023, neutral): “Artificial intelligence (AI) is now transforming our ability to create fast, high-fidelity simulations of many complex multi-scale processes [5, 6].”