基于物理信息神经网络的传热过程物理场代理模型的构建

doi:10.11949/0438-1157.20201879

化工学报 ›› 2021, Vol. 72 ›› Issue (3): 1496-1503.DOI: 10.11949/0438-1157.20201879

基于物理信息神经网络的传热过程物理场代理模型的构建

陆至彬¹(),瞿景辉²,刘桦²,何畅^2,³(),张冰剑^2,³,陈清林^2,³

^1.中山大学材料科学与工程学院，广东广州 510275
^2.中山大学化学工程与技术学院，广东珠海 519082
^3.广东省石化过程节能工程技术研究中心，广东广州 510275

收稿日期:2020-12-20 修回日期:2020-12-26 出版日期:2021-03-05 发布日期:2021-03-05
通讯作者: 何畅
作者简介:陆至彬（1998—），男，硕士研究生，luzhb6@mail2.sysu.edu.cn
基金资助:
国家自然科学基金项目(51776228);中央高校基本科研业务费专项资金(20lgpy01)

Surrogate modeling for physical fields of heat transfer processes based on physics-informed neural network

LU Zhibin¹(),QU Jinghui²,LIU Hua²,HE Chang^2,³(),ZHANG Bingjian^2,³,CHEN Qinglin^2,³

^1.School of Materials Science and Engineering, Sun Yat-sen University, Guangzhou 510275, Guangdong, China
^2.School of Chemical Engineering and Technology, Sun Yat-sen University, Zhuhai 519082, Guangdong, China
^3.Guangdong Engineering Center for Petrochemical Energy Conservation, Sun Yat-sen University, Guangzhou 510275, Guangdong, China

Received:2020-12-20 Revised:2020-12-26 Online:2021-03-05 Published:2021-03-05
Contact: HE Chang

摘要/Abstract

摘要：

物理信息的神经网络（PINN）通过构建结构化的深度神经网络体系，可以有效地耦合基于物理定律的非线性偏微分方程组（如Navier-Stokes方程），能够在较少量的边界数据条件下解决监督学习问题。但是，PINN训练效果与边界条件的设置方式密切相关。本工作以具有内热源的二维稳态导热方程和平板间二维稳态对流传热方程为案例，基于软边界和硬边界两种设定方法构建PINN。将训练所得到的代理模型预测温度场输出，并将其与软件模拟结果进行验证分析，结果表明硬边界PINN代理模型预测能力较优。

关键词: 神经网络, 物理定律, 非线性偏微分方程组, 边界设置, 代理模型, 传热, 预测

Abstract:

By constructing structured deep neural network architecture, physics-informed neural networks (PINN) can be trained to solve supervised learning tasks with limited amount of boundary data while effectively integrating any given laws of physics described by general nonlinear partial differential equations (i.e., Navier-Stokes equation). However, the effect of PINN training is closely related to how the boundary conditions are set. In this work, two 2-D steady-state heat transfer problems, namely heat conduction model with internal heat source and convection heat transfer equation between plates are taken as examples. Two surrogate models are trained based on PINN by using two setting methods of soft boundary and hard boundary. The trained surrogate models are used to predict the output of temperature fields, which are verified and compared with the simulated data. The comparison results show that the prediction ability of PINN based on hard boundary is superior to the rival.

Key words: neural networks, laws of physics, nonlinear partial differential equations, boundary setting, surrogate model, heat transfer, prediction

中图分类号:

陆至彬, 瞿景辉, 刘桦, 何畅, 张冰剑, 陈清林. 基于物理信息神经网络的传热过程物理场代理模型的构建[J]. 化工学报, 2021, 72(3): 1496-1503.

LU Zhibin, QU Jinghui, LIU Hua, HE Chang, ZHANG Bingjian, CHEN Qinglin. Surrogate modeling for physical fields of heat transfer processes based on physics-informed neural network[J]. CIESC Journal, 2021, 72(3): 1496-1503.

图/表 7

图1 PINN结构示意图

Fig.1 PINN structure diagram

图2 PINN代理模型和COMSOL模拟对温度场的预测结果对比

Fig.2 Comparsion of temperature fields predicted by soft PINN, hard PINN, and COMSOL simulation

图3 软边界PINN温度等值线的预测结果对比

Fig.3 Comparsion of temperature contours predicted by soft PINN

图4 硬边界PINN温度等值线的预测结果对比

Fig.4 Comparsion of temperature contours predicted by hard PINN

图5 平板的几何结构示意图

Fig.5 Geometric diagram of the flat plate

图6 COMSOL模拟温度场与硬边界PINN预测温度场对比

Fig.6 Comparsion of temperature fields predicted by hard PINN and COMSOL simulation

图7 硬边界PINN代理模型（红）与COMSOL模拟（黑）预测温度等值线结果对比

Fig.7 Comparsion of temperature contours predicted by hard PINN (red line) and COMSOL simulation (black line)

参考文献 31

1	LeCun Y, Bengio Y, Hinton G. Deep learning[J]. Nature, 2015, 521(7553): 436-444.
2	Tripathy R K, Bilionis I. Deep UQ: learning deep neural network surrogate models for high dimensional uncertainty quantification[J]. Journal of Computational Physics, 2018, 375: 565-588.
3	Zhu Y, Zabaras N. Bayesian deep convolutional encoder-decoder networks for surrogate modeling and uncertainty quantification[J]. Journal of Computational Physics, 2018, 366: 415-447.
4	Mo S, Zabaras N, Shi X, et al. Deep autoregressive neural networks for high‐dimensional inverse problems in groundwater contaminant source identification[J]. Water Resources Research, 2019, 55(5): 3856-3881.
5	Rudy S H, Brunton S L, Proctor J L, et al. Data-driven discovery of partial differential equations[J]. Science Advances, 2017, 3(4): e1602614.
6	Raissi M, Karniadakis G E. Hidden physics models: machine learning of nonlinear partial differential equations[J]. Journal of Computational Physics, 2018, 357: 125-141.
7	Raissi M, Perdikaris P, Karniadakis G E. Physics-informed neural networks: a deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations[J]. Journal of Computational Physics, 2019, 378: 686-707.
8	He K, Zhang X, Ren S, et al. Deep residual learning for image recognition[C]//Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition. Las Vegas, USA, 2016.
9	Huang G, Liu Z, van der Maaten L, et al. Densely connected convolutional networks[C]//Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition. Honolulu, HI, USA, 2017.
10	Raissi M, Wang Z, Triantafyllou M S, et al. Deep learning of vortex-induced vibrations[J]. Journal of Fluid Mechanics, 2019, 861: 119-137.
11	Raissi M, Yazdani A, Karniadakis G E. Hidden fluid mechanics: learning velocity and pressure fields from flow visualizations[J]. Science, 2020, 367(6481): 1026-1030.
12	Mao Z, Jagtap A D, Karniadakis G E. Physics-informed neural networks for high-speed flows[J]. Computer Methods in Applied Mechanics and Engineering, 2020, 360: 112789.
13	Meng X, Li Z, Zhang D, et al. PPINN: parareal physics-informed neural network for time-dependent PDEs[J]. Computer Methods in Applied Mechanics and Engineering, 2020, 370: 113250.
14	Jagtap A D, Kharazmi E, Karniadakis G E. Conservative physics-informed neural networks on discrete domains for conservation laws: applications to forward and inverse problems[J]. Computer Methods in Applied Mechanics and Engineering, 2020, 365: 113028.
15	Wang J X, Wu J L, Xiao H. Physics-informed machine learning approach for reconstructing Reynolds stress modeling discrepancies based on DNS data[J]. Physical Review Fluids, 2017, 2(3): 034603.
16	Tartakovsky A M, Marrero C O, Perdikaris P, et al. Physics‐informed deep neural networks for learning parameters and constitutive relationships in subsurface flow problems[J]. Water Resources Research, 2020, 56(5): e2019WR026731.
17	Purja Pun G P, Batra R, Ramprasad R, et al. Physically informed artificial neural networks for atomistic modeling of materials[J]. Nature Communications, 2019, 10: 2339.
18	He Q Z, Barajas-Solano D, Tartakovsky G, et al. Physics-informed neural networks for multiphysics data assimilation with application to subsurface transport[J]. Advances in Water Resources, 2020, 141: 103610.
19	Yang Y, Perdikaris P. Adversarial uncertainty quantification in physics-informed neural networks[J]. Journal of Computational Physics, 2019, 394: 136-152.
20	Zhang D, Lu L, Guo L, et al. Quantifying total uncertainty in physics-informed neural networks for solving forward and inverse stochastic problems[J]. Journal of Computational Physics, 2019, 397: 108850.
21	Geneva N, Zabaras N. Modeling the dynamics of PDE systems with physics-constrained deep auto-regressive networks[J]. Journal of Computational Physics, 2020, 403: 109056.
22	Sun L, Gao H, Pan S, et al. Surrogate modeling for fluid flows based on physics-constrained deep learning without simulation data[J]. Computer Methods in Applied Mechanics and Engineering, 2020, 361: 112732.
23	Gao H, Sun L, Wang J X. PhyGeoNet: physics-informed geometry-adaptive convolutional neural networks for solving parameterized steady-state PDEs on irregular domain[J]. Journal of Computational Physics, 2021, 428: 110079.
24	Zhu Y, Zabaras N, Koutsourelakis P S, et al. Physics-constrained deep learning for high-dimensional surrogate modeling and uncertainty quantification without labeled data[J]. Journal of Computational Physics, 2019, 394: 56-81.
25	Karumuri S, Tripathy R, Bilionis I, et al. Simulator-free solution of high-dimensional stochastic elliptic partial differential equations using deep neural networks[J]. Journal of Computational Physics, 2020, 404: 109120.
26	Baydin A G, Pearlmutter B A, Radul A A, et al. Automatic differentiation in machine learning: a survey[J]. Journal of Machine Learning Research, 2018, 18(153): 1-43.
27	Kingma D P, Ba J. Adam: a method for stochastic optimization[J]. arXiv preprint arXiv: 1412.6980, 2014. .
28	Zhang R, Liu Y, Sun H. Physics-guided convolutional neural network (PhyCNN) for data-driven seismic response modeling[J]. Engineering Structures, 2020, 215: 110704.
29	Jagtap A D, Kawaguchi K, Karniadakis G E. Adaptive activation functions accelerate convergence in deep and physics-informed neural networks[J]. Journal of Computational Physics, 2020, 404: 109136.
30	Nabian M A, Meidani H. Physics-driven regularization of deep neural networks for enhanced engineering design and analysis [J]. Journal of Computing and Information Science in Engineering, 2020, 20(1): 011006.
31	Berg J, Nyström K. A unified deep artificial neural network approach to partial differential equations in complex geometries[J]. Neurocomputing, 2018, 317: 28-41.

[1]	晁京伟, 许嘉兴, 李廷贤. 基于无管束蒸发换热强化策略的吸附热池的供热性能研究[J]. 化工学报, 2023, 74(S1): 302-310.
[2]	程成, 段钟弟, 孙浩然, 胡海涛, 薛鸿祥. 表面微结构对析晶沉积特性影响的格子Boltzmann模拟[J]. 化工学报, 2023, 74(S1): 74-86.
[3]	张双星, 刘舫辰, 张义飞, 杜文静. R-134a脉动热管相变蓄放热实验研究[J]. 化工学报, 2023, 74(S1): 165-171.
[4]	张义飞, 刘舫辰, 张双星, 杜文静. 超临界二氧化碳用印刷电路板式换热器性能分析[J]. 化工学报, 2023, 74(S1): 183-190.
[5]	陈爱强, 代艳奇, 刘悦, 刘斌, 吴翰铭. 基板温度对HFE7100液滴蒸发过程的影响研究[J]. 化工学报, 2023, 74(S1): 191-197.
[6]	刘明栖, 吴延鹏. 导光管直径和长度对传热影响的模拟分析[J]. 化工学报, 2023, 74(S1): 206-212.
[7]	王志国, 薛孟, 董芋双, 张田震, 秦晓凯, 韩强. 基于裂隙粗糙性表征方法的地热岩体热流耦合数值模拟与分析[J]. 化工学报, 2023, 74(S1): 223-234.
[8]	齐聪, 丁子, 余杰, 汤茂清, 梁林. 基于选择吸收纳米薄膜的太阳能温差发电特性研究[J]. 化工学报, 2023, 74(9): 3921-3930.
[9]	李艺彤, 郭航, 陈浩, 叶芳. 催化剂非均匀分布的质子交换膜燃料电池操作条件研究[J]. 化工学报, 2023, 74(9): 3831-3840.
[10]	温凯杰, 郭力, 夏诏杰, 陈建华. 一种耦合CFD与深度学习的气固快速模拟方法[J]. 化工学报, 2023, 74(9): 3775-3785.
[11]	王玉兵, 李杰, 詹宏波, 朱光亚, 张大林. R134a在菱形离散肋微小通道内的流动沸腾换热实验研究[J]. 化工学报, 2023, 74(9): 3797-3806.
[12]	李科, 文键, 忻碧平. 耦合蒸气冷却屏的真空多层绝热结构对液氢储罐自增压过程的影响机制研究[J]. 化工学报, 2023, 74(9): 3786-3796.
[13]	陈天华, 刘兆轩, 韩群, 张程宾, 李文明. 喷雾冷却换热强化研究进展及影响因素[J]. 化工学报, 2023, 74(8): 3149-3170.
[14]	诸程瑛, 王振雷. 基于改进深度强化学习的乙烯裂解炉操作优化[J]. 化工学报, 2023, 74(8): 3429-3437.
[15]	闫琳琦, 王振雷. 基于STA-BiLSTM-LightGBM组合模型的多步预测软测量建模[J]. 化工学报, 2023, 74(8): 3407-3418.

基于物理信息神经网络的传热过程物理场代理模型的构建

Surrogate modeling for physical fields of heat transfer processes based on physics-informed neural network

RichHTML

PDF (PC)

可视化

摘要/Abstract

引用本文

使用本文

图/表 7

参考文献 31

相关文章 15

编辑推荐

Metrics

本文评价