A Large Scale Benchmark for the Incompressible Navier-Stokes Equations

Huang, Zizhou; Schneider, Teseo; Li, Minchen; Jiang, Chenfanfu; Zorin, Denis; Panozzo, Daniele

doi:10.2139/ssrn.4030476

Cited by 5 publications

(5 citation statements)

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“…It has been proved that neural networks can be used to solve nonlinear PDEs [20], including the classical Navier-Stokes equation in fluid mechanics, but little work has been done to train and test real flow problems [22,45]. CFDBench is designed for training and testing existing neural models for flow problems under different operating conditions based on solving the N-S equation of incompressible fluid.…”

Section: Cfdbenchmentioning

confidence: 99%

CFDBench: A Comprehensive Benchmark for Machine Learning Methods in Fluid Dynamics

Luo,

Chen,

Zhang

2023

Preprint

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In recent years, applying deep learning to solve physics problems has attracted much attention. Data-driven deep learning methods produce operators that can learn solutions to the whole system of partial differential equations. However, the existing methods are only evaluated on simple flow equations (e.g., Burger's equation), and only consider the generalization ability on different initial conditions. In this paper, we construct CFDBench, a benchmark with four classic problems in computational fluid dynamics (CFD): lid-driven cavity flow, laminar boundary layer flow in circular tubes, dam flows through the steps, and periodic Karman vortex street. Each flow problem includes data with various boundary conditions, fluid physical properties, and domain geometries. Compared to existing datasets, the advantages of CFDBench are (1) comprehensive. It contains common physical parameters such as velocity, pressure, and cavity fraction. (2) realistic. It is very suitable for deep learning solutions of fluid mechanics equations. (3) challenging. It has a certain learning difficulty, prompting to find models with strong learning ability. (4) standardized. CFDBench facilitates a comprehensive and fair comparison of different deep learning methods for CFD. We make appropriate modifications to popular deep neural networks to apply them to CFDBench and enable the accommodation of more changing inputs. The evaluation on CFDBench reveals some new shortcomings of existing works and we propose possible directions for solving such problems.

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Section: Cfdbenchmentioning

confidence: 99%

CFDBench: A Comprehensive Benchmark for Machine Learning Methods in Fluid Dynamics

Luo,

Chen,

Zhang

2023

Preprint

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“…Each set of governing equations or experiment design assumptions leads to a distinct dataset of PDE samples. Recent works in PDEs have attempted to produce standardised datasets covering well-known challenges [44,19,51]. [19] targets non-ML uses.…”

Section: Related Workmentioning

confidence: 99%

“…Recent works in PDEs have attempted to produce standardised datasets covering well-known challenges [44,19,51]. [19] targets non-ML uses. [51] is specialised for particular classes of equations.…”

Section: Related Workmentioning

confidence: 99%

PDEBENCH: An Extensive Benchmark for Scientific Machine Learning

Takamoto¹,

Praditia²,

Leiteritz³

et al. 2022

Preprint

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Machine learning-based modeling of physical systems has experienced increased interest in recent years. Despite some impressive progress, there is still a lack of benchmarks for Scientific ML that are easy to use but still challenging and representative of a wide range of problems. We introduce PDEBENCH, a benchmark suite of time-dependent simulation tasks based on Partial Differential Equations (PDEs). PDEBENCH comprises both code and data to benchmark the performance of novel machine learning models against both classical numerical simulations and machine learning baselines. Our proposed set of benchmark problems contribute the following unique features: (1) A much wider range of PDEs compared to existing benchmarks, ranging from relatively common examples to more realistic and difficult problems; (2) much larger ready-to-use datasets compared to prior work, comprising multiple simulation runs across a larger number of initial and boundary conditions and PDE parameters; (3) more extensible source codes with user-friendly APIs for data generation and baseline results with popular machine learning models (FNO, U-Net, PINN, Gradient-Based Inverse Method). PDEBENCH allows researchers to extend the benchmark freely for their own purposes using a standardized API and to compare the performance of new models to existing baseline methods. We also propose new evaluation metrics with the aim to provide a more holistic understanding of learning methods in the context of Scientific ML. With those metrics we identify tasks which are challenging for recent ML methods and propose these tasks as future challenges for the community. The code is available at https://github.com/pdebench/PDEBench.

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“…By a unit test , it is meant that each operation, or function, of the library, is tested individually; by contrast, benchmarks can be used to test a whole program that utilizes the library, and will not be addressed here. We refer to Reference 3 for an example of such a benchmark. In our preliminary work, 4 we presented our vision for a set of such unit tests, that can be used as a basis to check interval arithmetic libraries, or that can be incorporated as internal check procedures.…”

Section: Introductionmentioning

confidence: 99%

“…It is then followed by integration testing that tests whether a whole program behaves properly, and thus whether the various functions of the program perform properly together. Relevant tests for this phase of integration testing are benchmarks such as the one given in Reference 3.…”

Section: Introductionmentioning

confidence: 99%

A framework to test interval arithmetic libraries and their IEEE 1788‐2015 compliance

Benet,

Ferranti,

Revol

2023

Concurrency and Computation

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SummaryAs developers of libraries implementing interval arithmetic, we faced the same difficulties when it comes to testing our libraries. What must be tested? How can we devise relevant test cases for unit testing? How can we ensure a high (and possibly 100%) test coverage? Before considering these questions, we briefly recall the main features of interval arithmetic and of the IEEE 1788‐2015 standard for interval arithmetic. After listing the different aspects that, in our opinion, must be tested, we contribute a first step towards offering a test suite for an interval arithmetic library. First we define a format that enables the exchange of test cases, so that they can be read and tried easily. Then we offer a first set of test cases, for a selected set of mathematical functions. Next, we examine how the Julia interval arithmetic library, IntervalArithmetic.jl, actually performs to these tests. As this is an ongoing work, we list extra tests that we deem important to perform.

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A Large Scale Benchmark for the Incompressible Navier-Stokes Equations

Cited by 5 publications

References 0 publications

CFDBench: A Comprehensive Benchmark for Machine Learning Methods in Fluid Dynamics

CFDBench: A Comprehensive Benchmark for Machine Learning Methods in Fluid Dynamics

PDEBENCH: An Extensive Benchmark for Scientific Machine Learning

A framework to test interval arithmetic libraries and their IEEE 1788‐2015 compliance

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