Error estimates for deep learning methods in fluid dynamics

Biswas A.; Tian J.; Ulusoy S.

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Error estimates for deep learning methods in fluid dynamics

机译：流体动力学中深度学习方法的误差估计

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摘要

In this study, we provide error estimates and stability analysis of deep learning techniques for certain partial differential equations including the incompressible Navier-Stokes equations. In particular, we obtain explicit error estimates (in suitable norms) for the solution computed by optimizing a loss function in a Deep Neural Network approximation of the solution, with a fixed complexity.

机译：在这项研究中，我们为某些偏微分方程（包括不可压缩的纳维-斯托克斯方程）提供了深度学习技术的误差估计和稳定性分析。特别是，我们通过优化深度神经网络近似解中的损失函数来计算解，获得显式误差估计（在合适的范数中），具有固定的复杂度。

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《Numerische Mathematik》 |2022年第3期|753-777|共25页
作者
Biswas A.; Tian J.; Ulusoy S.;
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作者单位

Towson Univ;

Amer Univ Ras Al Khaimah;

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原文格式 PDF
正文语种英语
中图分类数值分析;
关键词
35Q35; 35Q30; 65M70; NAVIER-STOKES EQUATIONS; UNIVERSAL APPROXIMATION; DERIVATIVES; ORDER;

机译：35Q35;35Q30;65米70;纳维-斯托克斯方程;通用近似;衍生品;次序;

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机译：THE DISCOVERY OF DYNAMICS VIA LINEAR MULTISTEP METHODS AND DEEP LEARNING: ERROR ESTIMATION
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4. 过程工业中一种简易实用的过失误差识别与校正方法（A Simple and Practical Method for Detection of Gross Error in Process Industries） [C] . Chinese Control Conference vol.2; 20040810-13; Wuxi(CN) . 2004

机译：过程工业中一种简易实用的过失误差识别与校正方法（A Simple and Practical Method for Detection of Gross Error in Process Industries）
5. Learning Task-Oriented Dialog with Neural Network Methods =基于神经网络的任务型对话学习 [D] . Liu, Bing. 2018

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6. Prediction Model of Aryl Hydrocarbon Receptor Activation by a Novel QSAR Approach DeepSnap–Deep Learning [O] . Yasunari Matsuzaka, Takuomi Hosaka, Anna Ogaito, 2020

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7. Finite Element Method of Incompressible Viscous Fluid Flow by Means of Perturbation Method (有限要素法の数学的基礎理論) [O] . KAWAHARA MUTSUTO 1975

机译：Finite Element Method of Incompressible Viscous Fluid Flow by Means of Perturbation Method (有限要素法の数学的基础理论)

Error estimates for deep learning methods in fluid dynamics

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