{"type":"ScholarlyArticle","title":"PDENNEval: A Comprehensive Evaluation of Neural Network Methods for Solving PDEs","authors":[{"name":"Ping Wei","slug":"ping-wei","given":"Ping","family":"Wei","affiliation":"School of Computer Science and Engineering , Sun Yat-sen University , Guangzhou , China Guangdong Province"},{"name":"Menghan Liu","slug":"menghan-liu","given":"Menghan","family":"Liu","affiliation":"School of Computer Science and Engineering , Sun Yat-sen University , Guangzhou , China Guangdong Province"},{"name":"Jianhuan Cen","slug":"jianhuan-cen","given":"Jianhuan","family":"Cen","affiliation":"School of Computer Science and Engineering , Sun Yat-sen University , Guangzhou , China Guangdong Province"},{"name":"Ziyang Zhou","slug":"ziyang-zhou","given":"Ziyang","family":"Zhou","affiliation":"Key Laboratory of Computational Science , Guangzhou , China"},{"name":"Liao Chen","slug":"liao-chen","given":"Liao","family":"Chen","affiliation":"Key Laboratory of Computational Science , Guangzhou , China"},{"name":"Qingsong Zou","slug":"qingsong-zou","given":"Qingsong","family":"Zou","affiliation":"School of Computer Science and Engineering , Sun Yat-sen University , Guangzhou , China Guangdong Province"}],"abstract":"The rapid development of neural network (NN) methods for solving partial differential equations (PDEs) has created an urgent need for  evaluation and comparison of these methods. In this study, we propose PDENNEval, a comprehensive and systematic  evaluation of 12 NN methods for PDEs. These methods are classified into function learning type and operator learning type based on their different mathematical foundations. The evaluation is implemented using a diverse dataset comprising 19 distinct PDE problems selected from various scientific fields such as fluid, materials, finance, and electromagnetic. Several evaluation results are reported, aiming to provide guidance for further research in this field. Our code and data are publicly available at https://github.com/zhouzy36/PDENNEval.","doi":"10.24963/ijcai.2024/573","url":"https://ijcai.org/proceedings/2024/573","pdf":"https://ijcai.org/proceedings/2024/0573.pdf","markdown":"https://ijcai.org/proceedings/2024/573.md","bibtex":"https://ijcai.org/proceedings/2024/bibtex/573","volume":{"slug":"2024","title":"Proceedings of the Thirty-Third International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2024","url":"https://ijcai.org/proceedings/2024/","year":2024,"location":"Jeju, Korea","dates":"3-9 August 2024","editors":"Kate Larson","isbn":"978-1-956792-04-1","publisher":"International Joint Conferences on Artificial Intelligence Organization","doi_prefix":"10.24963/ijcai.2024"},"section":"Machine Learning","track":"Main Track","number":573,"pages":{"first":5181,"last":5189},"keywords":["Machine Learning: ML: Applications","Machine Learning: ML: Evaluation","Multidisciplinary Topics and Applications: MTA: Physical sciences"],"videos":[],"references":[{"position":1,"raw":"[Barron, 1994] Andrew R Barron. 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