{"title":"图形神经反应扩散模型","authors":"Moshe Eliasof, Eldad Haber, Eran Treister","doi":"10.1137/23m1576700","DOIUrl":null,"url":null,"abstract":"SIAM Journal on Scientific Computing, Volume 46, Issue 4, Page C399-C420, August 2024. <br/> Abstract. The integration of graph neural networks (GNNs) and neural ordinary and partial differential equations has been extensively studied in recent years. GNN architectures powered by neural differential equations allow us to reason about their behavior, and develop GNNs with desired properties such as controlled smoothing or energy conservation. In this paper we take inspiration from Turing instabilities in a reaction diffusion (RD) system of partial differential equations, and propose a novel family of GNNs based on neural RD systems, called RDGNN. We show that our RDGNN is powerful for the modeling of various data types, from homophilic, to heterophilic, and spatiotemporal datasets. We discuss the theoretical properties of our RDGNN, its implementation, and show that it improves or offers competitive performance to state-of-the-art methods.","PeriodicalId":49526,"journal":{"name":"SIAM Journal on Scientific Computing","volume":"75 1","pages":""},"PeriodicalIF":3.0000,"publicationDate":"2024-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Graph Neural Reaction Diffusion Models\",\"authors\":\"Moshe Eliasof, Eldad Haber, Eran Treister\",\"doi\":\"10.1137/23m1576700\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"SIAM Journal on Scientific Computing, Volume 46, Issue 4, Page C399-C420, August 2024. <br/> Abstract. The integration of graph neural networks (GNNs) and neural ordinary and partial differential equations has been extensively studied in recent years. GNN architectures powered by neural differential equations allow us to reason about their behavior, and develop GNNs with desired properties such as controlled smoothing or energy conservation. In this paper we take inspiration from Turing instabilities in a reaction diffusion (RD) system of partial differential equations, and propose a novel family of GNNs based on neural RD systems, called RDGNN. We show that our RDGNN is powerful for the modeling of various data types, from homophilic, to heterophilic, and spatiotemporal datasets. We discuss the theoretical properties of our RDGNN, its implementation, and show that it improves or offers competitive performance to state-of-the-art methods.\",\"PeriodicalId\":49526,\"journal\":{\"name\":\"SIAM Journal on Scientific Computing\",\"volume\":\"75 1\",\"pages\":\"\"},\"PeriodicalIF\":3.0000,\"publicationDate\":\"2024-08-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"SIAM Journal on Scientific Computing\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1137/23m1576700\",\"RegionNum\":2,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"SIAM Journal on Scientific Computing","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1137/23m1576700","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
SIAM Journal on Scientific Computing, Volume 46, Issue 4, Page C399-C420, August 2024. Abstract. The integration of graph neural networks (GNNs) and neural ordinary and partial differential equations has been extensively studied in recent years. GNN architectures powered by neural differential equations allow us to reason about their behavior, and develop GNNs with desired properties such as controlled smoothing or energy conservation. In this paper we take inspiration from Turing instabilities in a reaction diffusion (RD) system of partial differential equations, and propose a novel family of GNNs based on neural RD systems, called RDGNN. We show that our RDGNN is powerful for the modeling of various data types, from homophilic, to heterophilic, and spatiotemporal datasets. We discuss the theoretical properties of our RDGNN, its implementation, and show that it improves or offers competitive performance to state-of-the-art methods.
期刊介绍：
The purpose of SIAM Journal on Scientific Computing (SISC) is to advance computational methods for solving scientific and engineering problems.
SISC papers are classified into three categories:
1. Methods and Algorithms for Scientific Computing: Papers in this category may include theoretical analysis, provided that the relevance to applications in science and engineering is demonstrated. They should contain meaningful computational results and theoretical results or strong heuristics supporting the performance of new algorithms.
2. Computational Methods in Science and Engineering: Papers in this section will typically describe novel methodologies for solving a specific problem in computational science or engineering. They should contain enough information about the application to orient other computational scientists but should omit details of interest mainly to the applications specialist.
3. Software and High-Performance Computing: Papers in this category should concern the novel design and development of computational methods and high-quality software, parallel algorithms, high-performance computing issues, new architectures, data analysis, or visualization. The primary focus should be on computational methods that have potentially large impact for an important class of scientific or engineering problems.
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