{"title":"On the choice of physical constraints in artificial neural networks for predicting flow fields","authors":"","doi":"10.1016/j.future.2024.07.009","DOIUrl":null,"url":null,"abstract":"<div><p>The application of Artificial Neural Networks (ANNs) has been extensively investigated for fluid dynamic problems. A specific form of ANNs are Physics-Informed Neural Networks (PINNs). They incorporate physical laws in the training and have increasingly been explored in the last few years. In this work, the prediction accuracy of PINNs is compared with that of conventional Deep Neural Networks (DNNs). The accuracy of a DNN depends on the amount of data provided for training. The change in prediction accuracy of PINNs and DNNs is assessed using a varying amount of training data. To ensure the correctness of the training data, they are obtained from analytical and numerical solutions of classical problems in fluid mechanics. The objective of this work is to quantify the fraction of training data relative to the maximum number of data points available in the computational domain, such that the accuracy gained with PINNs justifies the increased computational cost. Furthermore, the effects of the location of sampling points in the computational domain and noise in training data are analyzed. In the considered problems, it is found that PINNs outperform DNNs when the sampling points are positioned in the Regions of Interest. PINNs for predicting potential flow around a Rankine oval have shown a better robustness against noise in training data compared to DNNs. Both models show higher prediction accuracy when sampling points are randomly positioned in the flow domain as compared to a prescribed distribution of sampling points. The findings reveal new insights on the strategies to massively improve the prediction capabilities of PINNs with respect to DNNs.</p></div>","PeriodicalId":55132,"journal":{"name":"Future Generation Computer Systems-The International Journal of Escience","volume":null,"pages":null},"PeriodicalIF":6.2000,"publicationDate":"2024-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0167739X24003728/pdfft?md5=06cd01a8ffd48b55efbf83d9e5e961dc&pid=1-s2.0-S0167739X24003728-main.pdf","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Future Generation Computer Systems-The International Journal of Escience","FirstCategoryId":"94","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0167739X24003728","RegionNum":2,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"COMPUTER SCIENCE, THEORY & METHODS","Score":null,"Total":0}
引用次数: 0
Abstract
The application of Artificial Neural Networks (ANNs) has been extensively investigated for fluid dynamic problems. A specific form of ANNs are Physics-Informed Neural Networks (PINNs). They incorporate physical laws in the training and have increasingly been explored in the last few years. In this work, the prediction accuracy of PINNs is compared with that of conventional Deep Neural Networks (DNNs). The accuracy of a DNN depends on the amount of data provided for training. The change in prediction accuracy of PINNs and DNNs is assessed using a varying amount of training data. To ensure the correctness of the training data, they are obtained from analytical and numerical solutions of classical problems in fluid mechanics. The objective of this work is to quantify the fraction of training data relative to the maximum number of data points available in the computational domain, such that the accuracy gained with PINNs justifies the increased computational cost. Furthermore, the effects of the location of sampling points in the computational domain and noise in training data are analyzed. In the considered problems, it is found that PINNs outperform DNNs when the sampling points are positioned in the Regions of Interest. PINNs for predicting potential flow around a Rankine oval have shown a better robustness against noise in training data compared to DNNs. Both models show higher prediction accuracy when sampling points are randomly positioned in the flow domain as compared to a prescribed distribution of sampling points. The findings reveal new insights on the strategies to massively improve the prediction capabilities of PINNs with respect to DNNs.
期刊介绍:
Computing infrastructures and systems are constantly evolving, resulting in increasingly complex and collaborative scientific applications. To cope with these advancements, there is a growing need for collaborative tools that can effectively map, control, and execute these applications.
Furthermore, with the explosion of Big Data, there is a requirement for innovative methods and infrastructures to collect, analyze, and derive meaningful insights from the vast amount of data generated. This necessitates the integration of computational and storage capabilities, databases, sensors, and human collaboration.
Future Generation Computer Systems aims to pioneer advancements in distributed systems, collaborative environments, high-performance computing, and Big Data analytics. It strives to stay at the forefront of developments in grids, clouds, and the Internet of Things (IoT) to effectively address the challenges posed by these wide-area, fully distributed sensing and computing systems.