Model order reduction for the 1D Boltzmann-BGK equation: identifying intrinsic variables using neural networks

IF 2.3 4区 工程技术 Q2 INSTRUMENTS & INSTRUMENTATION Microfluidics and Nanofluidics Pub Date : 2024-02-28 DOI:10.1007/s10404-024-02711-5
Julian Koellermeier, Philipp Krah, Julius Reiss, Zachary Schellin
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Abstract

Kinetic equations are crucial for modeling non-equilibrium phenomena, but their computational complexity is a challenge. This paper presents a data-driven approach using reduced order models (ROM) to efficiently model non-equilibrium flows in kinetic equations by comparing two ROM approaches: proper orthogonal decomposition (POD) and autoencoder neural networks (AE). While AE initially demonstrate higher accuracy, POD’s precision improves as more modes are considered. Notably, our work recognizes that the classical POD model order reduction approach, although capable of accurately representing the non-linear solution manifold of the kinetic equation, may not provide a parsimonious model of the data due to the inherently non-linear nature of the data manifold. We demonstrate how AEs are used in finding the intrinsic dimension of a system and to allow correlating the intrinsic quantities with macroscopic quantities that have a physical interpretation.

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减少一维波兹曼-BGK方程的模型阶次:利用神经网络识别内在变量
摘要 动力方程是模拟非平衡现象的关键,但其计算复杂性是一项挑战。本文通过比较两种 ROM 方法:适当正交分解(POD)和自动编码器神经网络(AE),提出了一种数据驱动的方法,即使用减阶模型(ROM)对动力学方程中的非平衡流动进行有效建模。AE 最初表现出更高的精度,而 POD 的精度则随着考虑的模式增多而提高。值得注意的是,我们的工作认识到,经典的 POD 模型阶次缩减方法虽然能够准确表示动力学方程的非线性解流形,但由于数据流形本身的非线性性质,它可能无法提供一个简洁的数据模型。我们展示了如何利用 AE 来发现系统的内在维度,并将内在量与具有物理解释的宏观量联系起来。
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来源期刊
Microfluidics and Nanofluidics
Microfluidics and Nanofluidics 工程技术-纳米科技
CiteScore
4.80
自引率
3.60%
发文量
97
审稿时长
2 months
期刊介绍: Microfluidics and Nanofluidics is an international peer-reviewed journal that aims to publish papers in all aspects of microfluidics, nanofluidics and lab-on-a-chip science and technology. The objectives of the journal are to (1) provide an overview of the current state of the research and development in microfluidics, nanofluidics and lab-on-a-chip devices, (2) improve the fundamental understanding of microfluidic and nanofluidic phenomena, and (3) discuss applications of microfluidics, nanofluidics and lab-on-a-chip devices. Topics covered in this journal include: 1.000 Fundamental principles of micro- and nanoscale phenomena like, flow, mass transport and reactions 3.000 Theoretical models and numerical simulation with experimental and/or analytical proof 4.000 Novel measurement & characterization technologies 5.000 Devices (actuators and sensors) 6.000 New unit-operations for dedicated microfluidic platforms 7.000 Lab-on-a-Chip applications 8.000 Microfabrication technologies and materials Please note, Microfluidics and Nanofluidics does not publish manuscripts studying pure microscale heat transfer since there are many journals that cover this field of research (Journal of Heat Transfer, Journal of Heat and Mass Transfer, Journal of Heat and Fluid Flow, etc.).
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