DeepCFD: Efficient Steady-State Laminar Flow Approximation with Deep Convolutional Neural Networks

Ribeiro, Mateus Dias; Rehman, Abdul; Ahmed, Sheraz; Dengel, Andreas

doi:10.48550/arxiv.2004.08826

Cited by 28 publications

(40 citation statements)

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“…Reduction of computational cost is the main motivation of developing surrogate models. To appraise the time cost of all models used in this work, Table . 3 (Guo et al, 2016;Zhu and Zabaras, 2018;Bhatnagar et al, 2019;Ribeiro et al, 2020) The prediction of NN-p2p surrogate model respects physical laws in the training data. For example, the mass conservation for each cell in the mesh was calculated and the error is very small and comparable with the numerical error in SRH-2D.…”

Section: Computational Costmentioning

confidence: 99%

Surrogate Model for Shallow Water Equations Solvers with Deep Learning

Song¹,

Liu²

2021

Preprint

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Section: Computational Costmentioning

confidence: 99%

Surrogate Model for Shallow Water Equations Solvers with Deep Learning

Song¹,

Liu²

2021

Preprint

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“…In a different vein, many recent works [see, e.g. [23][24][25][26][27][28][29][30] used machine learning models to approximate global operators or surrogate models defined by the PDEs, which also hold the promise to nonlocal constitutive modeling. However, the objectivity of these modeling approaches, such as frame-independence and permutational invariance mentioned above, has rarely been discussed.…”

Section: A Invariance Properties Of Constitutive Modelsmentioning

confidence: 99%

VCNN-e: A vector-cloud neural network with equivariance for emulating Reynolds stress transport equations

Han¹,

Zhou²,

Xiao³

2022

Preprint

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Developing robust constitutive models is fundamental and a longstanding problem for accelerating the simulation of complicated physics. Machine learning provides promising tools to construct constitutive models based on various calibration data. In this work, we propose a new approach to emulate constitutive tensor transport equations for tensorial quantities through a vector-cloud neural network with equivariance (VCNN-e). The VCNN-e respects all the invariance properties desired by constitutive models and faithfully reflects the region of influence in physics. By design, the model guarantees that the predicted tensor is invariant to the frame translation and ordering (permutation) of the neighboring points. Furthermore, it is equivariant to the frame rotation, i.e., the output tensor co-rotates with the coordinate frame. We demonstrate its performance on Reynolds stress transport equations, showing that the VCNN-e can effectively emulate the Reynolds stress transport model for Reynolds-averaged Navier-Stokes (RANS) equations. Such a priori evaluations of the proposed network pave the way for developing and calibrating robust and nonlocal, non-equilibrium closure models for the RANS equations.

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“…(2) Another line of research aims to develop a variety of techniques to accelerate solving PDEs. Typically, these methods are developed for specific PDEs and a specific restricted range of problems: for example, fluid dynamics problems [39,16,56], with particular applications to cardiovascular modeling [25,19] and aerodynamics [53]; or solid mechanics simulation tasks, including stresses [29,24,27,15,22,23]. In cases where the governing equations are not given, the learning task becomes approximating them from data [30,7,1,9,2,28,3,43,44,46,45,52,35].…”

Section: Related Workmentioning

confidence: 99%

An Extensible Benchmark Suite for Learning to Simulate Physical Systems

Otness,

Gjoka,

Bruna

et al. 2021

Preprint

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Simulating physical systems is a core component of scientific computing, encompassing a wide range of physical domains and applications. Recently, there has been a surge in data-driven methods to complement traditional numerical simulations methods, motivated by the opportunity to reduce computational costs and/or learn new physical models leveraging access to large collections of data. However, the diversity of problem settings and applications has led to a plethora of approaches, each one evaluated on a different setup and with different evaluation metrics. We introduce a set of benchmark problems to take a step towards unified benchmarks and evaluation protocols. We propose four representative physical systems, as well as a collection of both widely used classical time integrators and representative data-driven methods (kernel-based, MLP, CNN, nearest neighbors). Our framework allows evaluating objectively and systematically the stability, accuracy, and computational efficiency of data-driven methods. Additionally, it is configurable to permit adjustments for accommodating other learning tasks and for establishing a foundation for future developments in machine learning for scientific computing.

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DeepCFD: Efficient Steady-State Laminar Flow Approximation with Deep Convolutional Neural Networks

Cited by 28 publications

References 0 publications

Surrogate Model for Shallow Water Equations Solvers with Deep Learning

Surrogate Model for Shallow Water Equations Solvers with Deep Learning

VCNN-e: A vector-cloud neural network with equivariance for emulating Reynolds stress transport equations

An Extensible Benchmark Suite for Learning to Simulate Physical Systems

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