Solving combustion chemical differential equations via physics-informed neural network

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

Journal of ZheJiang University (Engineering Science)

2022, Vol. 56

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

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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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

Received: 17 March 2022 Published: 25 October 2022

CLC:

TK 4

Fund: 国家杰出青年科学基金资助项目（51925603）

Corresponding Authors: Kun LUO E-mail: wangyicun@zju.edu.cn;zjulk@zju.edu.cn

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Cite this article:

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.

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

基于物理信息神经网络的燃烧化学微分方程求解

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

Fig.1 Schematic topology diagram of PINNs

Tab.1 Training loss for different hidden layers for ROBER problem (T_e = 1 s)

Tab.2 Structure of sequential PINNs model

Fig.2 Evolutionary process of species in dynamic system (T_e = 1 s)

Fig.3 Evolutionary process of species in dynamic system (T_e = 10³ s)

Fig.4 Two-dimensional configuration of jet diffusion flame

Fig.5 Comparison of mixture fraction distributions

Fig.6 Comparison of mixture fraction profiles at different locations

Fig.7 Comparison of temperature distributions

Fig.8 Distribution of residual points

Tab.3 Training time and loss value for different sampling approaches

Fig.9 Loss value vs. iterations for different sampling approaches


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