Variable linear transformation improved physics-informed neural networks to solve thin-layer flow problems

规范化(社会学) 人工神经网络 计算机科学 缩放比例 应用数学 变量(数学) 反向 统计物理学 数学 数学优化 人工智能 物理 数学分析 几何学 社会学 人类学
作者
Jiahao Wu,Yuxin Wu,Guihua Zhang,Yang Zhang
出处
期刊:Journal of Computational Physics [Elsevier BV]
卷期号:500: 112761-112761 被引量:10
标识
DOI:10.1016/j.jcp.2024.112761
摘要

Physics-informed neural networks (PINNs) have attracted wide attention due to their ability to seamlessly embed the learning process with physical laws and their considerable success in solving forward and inverse differential equation (DE) problems. While most studies are improving the learning process and network architecture of PINNs, less attention has been paid to the modification of the DE system, which may play an important role in addressing some limitations of PINNs. One of the simplest modifications that can be implemented to all DE systems is the variable linear transformation (VLT). Therefore, in this work, we propose the VLT-PINNs that solve the DE systems of the linear-transformed variables instead of the original ones. To clearly illustrate the importance of prior knowledge in determining the VLT parameters, we choose the thin-layer flow problems as our focus. Ten related cases were tested, including the jet flows, wake flows, mixing layers, boundary layers and Kovasznay flows. Based on the principle of normalization and for a better match of the DE system to the preference of NNs, we identify three principles for determining the VLT parameters: magnitude normalization for dependent variables (principle 1), local normalization for independent variables (principle 2), and appropriate scaling for physics-related parameters in inverse problems (principle 3). The VLT-PINNs with the VLT parameters suggested by the proposed principles show excellent performance over all the test cases, while the results are quite poor with the VLT parameters suggested by traditional linear transformations, such as nondimensionalization and global normalization. Comparison studies also show that only under the constraints of the VLT principles can we obtain satisfactory results. Besides, we find tanh is more appropriate as the activation function than sin for thin-layer flow problems, from both posteriori results and priori analyses with physical intuition. We highlight that our VLT method is an attempt to combine the three advantages of accuracy, universality and simplicity, and hope that it can provide new insights into the better integration of prior knowledge, physical intuition and the nature of NNs. The code for this paper is available on https://github.com/CAME-THU/VLT-PINN.
最长约 10秒,即可获得该文献文件

科研通智能强力驱动
Strongly Powered by AbleSci AI
更新
PDF的下载单位、IP信息已删除 (2025-6-4)

科研通是完全免费的文献互助平台,具备全网最快的应助速度,最高的求助完成率。 对每一个文献求助,科研通都将尽心尽力,给求助人一个满意的交代。
实时播报
可爱的函函应助重要鑫磊采纳,获得10
1秒前
2秒前
Nuckylin发布了新的文献求助10
3秒前
寸光发布了新的文献求助10
4秒前
6秒前
乙醇发布了新的文献求助10
6秒前
6秒前
Gengar发布了新的文献求助10
7秒前
8秒前
Tancl1235完成签到,获得积分10
8秒前
9秒前
10秒前
生医工小博完成签到,获得积分20
10秒前
壮观以松完成签到,获得积分10
11秒前
小马甲应助Espionage采纳,获得10
12秒前
molotov发布了新的文献求助10
13秒前
健忘捕发布了新的文献求助10
14秒前
希文完成签到,获得积分10
14秒前
biozhp发布了新的文献求助10
15秒前
zack完成签到,获得积分10
18秒前
Nee发布了新的文献求助10
18秒前
Ll_l完成签到,获得积分10
20秒前
21秒前
22秒前
搜集达人应助Tancl1235采纳,获得10
22秒前
23秒前
wang发布了新的文献求助10
23秒前
23秒前
orixero应助zack采纳,获得10
26秒前
无奈初雪完成签到,获得积分10
27秒前
Espionage发布了新的文献求助10
28秒前
上官若男应助jsq采纳,获得10
28秒前
28秒前
大个应助踏雪飞鸿采纳,获得10
29秒前
29秒前
郑159753发布了新的文献求助10
29秒前
顺利毕业发布了新的文献求助10
33秒前
wang完成签到,获得积分10
34秒前
34秒前
35秒前
高分求助中
A new approach to the extrapolation of accelerated life test data 1000
Cognitive Neuroscience: The Biology of the Mind 1000
Technical Brochure TB 814: LPIT applications in HV gas insulated switchgear 1000
Immigrant Incorporation in East Asian Democracies 600
Nucleophilic substitution in azasydnone-modified dinitroanisoles 500
不知道标题是什么 500
A Preliminary Study on Correlation Between Independent Components of Facial Thermal Images and Subjective Assessment of Chronic Stress 500
热门求助领域 (近24小时)
化学 材料科学 医学 生物 工程类 有机化学 生物化学 物理 内科学 纳米技术 计算机科学 化学工程 复合材料 遗传学 基因 物理化学 催化作用 冶金 细胞生物学 免疫学
热门帖子
关注 科研通微信公众号,转发送积分 3967419
求助须知:如何正确求助?哪些是违规求助? 3512730
关于积分的说明 11164792
捐赠科研通 3247704
什么是DOI,文献DOI怎么找? 1793978
邀请新用户注册赠送积分活动 874785
科研通“疑难数据库(出版商)”最低求助积分说明 804517