[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-119278-en":3,"doc-seo-119278-105":30,"detail-sidebar-cat-0-en-105":95},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":4,"is_deleted":4,"is_public":20,"is_downloadable":20,"audit_status":20,"page_count":21,"language":22,"language_code":23,"site_id":24,"html_lang":23,"table_of_contents":25,"faqs":26,"seo_title":27,"seo_description":14,"update_tm":28,"read_time":29},119278,7971461740909,"Levi","https://ap-avatar.wpscdn.com/davatar_155a257f0dc6eb9ab79c44ca47cae57d",8,"Research & Report","Modelling Temporal Networks with Scientific Machine Learning","Temporal networks arise in many domains, from symptom prediction and epidemiology to social and protein interactions. This thesis develops a flexible modelling framework for temporal network progression, combining truncated singular value decomposition, scientific machine learning via neural network differential equations, and symbolic regression to obtain interpretable dynamics. The approach is demonstrated on multiple small temporal networks, showing its ability to capture progression and support forward prediction. A Julia package is also provided to streamline temporal-network workflows and future research adoption.","School of Mathematics and Statistics University of Canterbury  \nChristchurch, New Zealand  \nModelling Temporal Networks with Scientific Machine Learning  \nSubmitted in partial fulfilment of the requirements for  \nThe Degree of Master of Mathematical Sciences in Computational and Applied Mathematics  \nby  \nConnor Smith  \n2023  \nAbstract  \nTemporal networks appear in applications ranging from symptom prediction to social networks to epidemiology. This thesis proposes a flexible framework for modelling temporal network progression which utilises a combination of singular value decomposition, scientific machine learning, and symbolic regression. We demonstrate the usefulness of the framework for modelling the progression of a variety of small temporal networks. Additionally, we present a Julia programming package for streamlining work with temporal networks. This thesis demonstrates our framework as a proof of concept, and we are confident that with further research, this framework will be a useful tool for modelling temporal networks in many fields.  \nAcknowledgments  \nI’d like to thank my parents for teaching me to be curious, to enjoy my life at university, and to always strive to grow and learn. Without their love and support, I would not have made it to the point I am today.  \nI’d like to thank my supervisors, Giulio and Miguel, who dedicated their time to help me overcome the countless challenges I faced over the course of this Thesis. Thanks to them, I am a better writer and researcher than I was when I started.  \nThanks to my office mates, who kept morale high by convincing me that everyday was a good day for a pie. Without them, I would likely have given up a longtime ago.  \nThanks to Trinity, whose love, support, and encouragement has been unwavering since day one.  \nContents  \nChapter 1 . Introduction 5  \nChapter 2 . Literature Review 8  \n2.1. Temporal Networks 8  \n2.2. UDEs and NNDEs 11  \n2.3. Symbolic Regression 15  \nChapter 3 . Methodology 18  \n3.1. Singular Value Decomposition and Random Dot Product Graphs 20  \n3.2. Neural Network Differential Equation 22  \n3.3. Symbolic Regression 23  \n3.4. Reconstructing the Temporal Network 24  \nChapter 4 . Data 26  \n4.1. Two Community System 26  \n4.2. Long Tail System 29  \n4.3. Three community System 30  \nChapter 5 . Results and Discussion 32  \n5.1. Embedding Prediction 32  \n5.2. Further Exploration 34  \n5.3. Summary 38  \nChapter 6 . Code 40  \n6.1. Summary 40  \n6.2. Statement of Need 40  \n6.3. Package Methods 41  \n6.4. Future Work 42  \nChapter 7 . Conclusion 43  \nBibliography 44  \nCHAPTER 1  \nIntroduction  \nTemporal networks are networks whose nodes and edges change in time. We aim, in this thesis, to describe the changing temporal network using mathematical language; that is to construct a model for the temporal network. Temporal network modelling is an important task in many real world applications; these include symptom interactions for mental health [27 , 24], epidemiology [19], and protein interactions [43 , 13] .  \nTemporal networks are constructed with nodes and edges. The state of a given node can be described by the set of edges connecting to it. As these edges change in time, so too does the state of the node. Hence, we can see temporal networks as a system of nodes whose states vary in time, a dynamical system.  \nIn the common representation of networks as binary-valued adjacency matrices (matrices where the observation or lack thereof, of an edge is represented as a 1 or 0 respectively) the events recorded in a temporal sequence of networks correspond to the appearance or the disappearance of links.  \nDifferential equations are particularly useful for modelling systems where the state of one variable can effect the trajectories of other variables. We observe this behavior in temporal networks; nodes’ connections within the network can influence the appearance of edges between other nodes, for example the phenomenon observed in [7 , 10], where a node is more likely to","cbCaiue3eSbQXexy","https://ap.wps.com/l/cbCaiue3eSbQXexy","pdf",495696,1,51,"English","en",105,"# Chapter 1. Introduction\n## Temporal networks and modelling motivation\n## Differential equations and discreteness challenge\n## Singular value decomposition and embedding\n## Neural Network Differential Equations and symbolic regression\n# Chapter 2. Literature Review\n## Temporal Networks\n## UDEs and NNDEs\n## Symbolic Regression\n# Chapter 3. Methodology\n## Singular Value Decomposition and Random Dot Product Graphs\n## Neural Network Differential Equation\n## Symbolic Regression\n## Reconstructing the Temporal Network\n# Chapter 4. Data\n## Two Community System\n## Long Tail System\n## Three community System\n# Chapter 5. Results and Discussion\n## Embedding Prediction\n## Further Exploration\n## Summary\n# Chapter 6. Code\n## Summary\n## Statement of Need\n## Package Methods\n## Future Work\n# Chapter 7. Conclusion","[{\"question\":\"What problem does the thesis address?\",\"answer\":\"The thesis focuses on modelling how temporal networks evolve over time, using mathematical models to describe progression from observed network states.\"},{\"question\":\"How does the framework turn discrete temporal events into a tractable modelling task?\",\"answer\":\"It embeds temporal networks into a continuous low-dimensional space using truncated singular value decomposition (Random Dot Product Graphs), then models continuous change in that embedding space.\"},{\"question\":\"What roles do neural network differential equations and symbolic regression play?\",\"answer\":\"Neural Network Differential Equations approximate the time evolution of the embedding dynamics, while symbolic regression searches for interpretable functional forms for those learned dynamics.\"},{\"question\":\"What tools or outputs are provided beyond the modelling results?\",\"answer\":\"The thesis includes a Julia programming package designed to streamline work with temporal networks, supporting practical application of the proposed framework.\"}]","Modelling Temporal Networks with Scientific Machine Learning | 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