基于物理信息神经网络的燃烧化学微分方程求解

doi:10.3785/j.issn.1008-973X.2022.10.020

浙江大学学报(工学版)

2022, Vol. 56

Issue (10): 2084-2092 DOI: 10.3785/j.issn.1008-973X.2022.10.020

能源工程、机械工程

基于物理信息神经网络的燃烧化学微分方程求解

王意存1(

),邢江宽1,2,罗坤1,*(

),王海鸥1,樊建人1

1. 浙江大学能源清洁利用国家重点实验室，浙江杭州 310027
2. 京都大学机械工程与科学系，日本京都 6158540

Solving combustion chemical differential equations via physics-informed neural network

Yi-cun WANG1(

),Jiang-kuan XING1,2,Kun LUO1,*(

),Hai-ou WANG1,Jian-ren FAN1

1. State Key Laboratory of Clean Energy Utilization, Zhejiang University, Hangzhou 310027, China
2. Department of Mechanical Engineering and Science, Kyoto University, Kyoto 6158540, Japan

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摘要：

为了有效地将湍流燃烧复杂的物理化学信息嵌入到物理信息神经网络（PINNs），选取湍流燃烧模拟中的2个典型场景案例，即刚性常微分方程ROBER问题及稳态射流火焰混合分数方程求解，探索PINNs在燃烧化学微分方程计算中的应用潜力. 结果表明，对于零维刚性反应系统，利用PINNs模型可以较好地捕捉到系统的演化过程；对于稳态射流火焰，PINNs的预测解与传统的数值解有较好的一致性. 残差点的选取对于燃烧化学领域内的复杂微分方程求解尤为重要，应基于具体的构型详细考虑.

关键词： 物理信息神经网络; 人工神经网络; 燃烧数值模拟; 微分方程; 残差点

Abstract:

Two typical cases including the stiff system of ordinary differential equations ROBER problem and the steady-state mixture fraction equation in jet flame were selected in order to efficiently embed the complex physicochemical information of turbulent combustion into physics-informed neural networks (PINNs). The potential of PINNs in solving combustion chemical differential equations was explored. Results show that the PINNs model can correctly capture the evolution of the zero-dimensional stiff reaction system. PINNs solution accorded well with the conventional numerical solution for steady jet flame. The selection of residual points was particularly important for solving complex differential equations in the field of combustion and chemistry, which should be considered based on the specific configuration in detail.

Key words: physics-informed neural network artificial neural network numerical simulation of combustion differential equation residual point

收稿日期: 2022-03-17 出版日期: 2022-10-25

CLC:

TK 4

基金资助: 国家杰出青年科学基金资助项目（51925603）

通讯作者: 罗坤 E-mail: wangyicun@zju.edu.cn;zjulk@zju.edu.cn

作者简介: 王意存（1996—），男，博士生，从事喷雾燃烧数值模拟及模型研究. orcid.org/0000-0001-7554-5919. E-mail： wangyicun@zju.edu.cn

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引用本文:

王意存,邢江宽,罗坤,王海鸥,樊建人. 基于物理信息神经网络的燃烧化学微分方程求解[J]. 浙江大学学报(工学版), 2022, 56(10): 2084-2092.

Yi-cun WANG,Jiang-kuan XING,Kun LUO,Hai-ou WANG,Jian-ren FAN. Solving combustion chemical differential equations via physics-informed neural network. Journal of ZheJiang University (Engineering Science), 2022, 56(10): 2084-2092.

链接本文:

https://www.zjujournals.com/eng/CN/10.3785/j.issn.1008-973X.2022.10.020 或 https://www.zjujournals.com/eng/CN/Y2022/V56/I10/2084

图 1 PINNs网络拓扑结构示意图

表 1 ROBER问题（Te = 1 s）不同隐藏层配置的训练损失

表 2 顺序的PINNs结构

图 2 动力系统组分的演化过程（Te= 1 s）

图 3 动力系统组分的演化过程（Te= 103 s）

图 4 二维射流扩散火焰算例构型

图 5 混合分数分布云图的对比

图 6 2种求解器在不同位置处的混合分数解对比

图 7 温度分布云图的对比

图 8 残差点分布示意图

表 3 不同采样方式训练所需的时间及损失大小

图 9 不同采样方式的损失值随迭代步数的变化

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