[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-119081-en":3,"doc-seo-119081-105":30,"detail-sidebar-cat-0-en-105":91},{"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},119081,5909877438554,"Maeve","https://ap-avatar.wpscdn.com/avatar/5600025385ad2bf12a7?_k=1778553567797529272",8,"Research & Report","Formal Verification of Dynamical Models via Neural Synthesis","Dynamical models provide a mathematical basis for representing, understanding, and analysing complex systems across science and engineering. Nonlinearity and complexity often preclude analytical solutions, making verification for safety-critical applications challenging or intractable. This thesis investigates two verification strategies for continuous-time nonlinear dynamical models: abstraction that disregards nonlinearity and indirect certificate-based methods that treat it through certificates. It proposes neural abstractions and neural network certificates, and uses formal synthesis with counterexample-guided inductive synthesis and satisfiability modulo theories to guarantee correctness.","Formal Verification of Dynamical Models via Neural Synthesis  \nAlec Edwards Worcester College  \nUniversity of Oxford  \nA thesis submitted for the degree of Doctor of Philosophy in Computer Science  \n“To light a candle  \nis to cast a shadow...”  \n—Ursula K. Le Guin  \nAcknowledgements  \nThis thesis details the research I conducted during my PhD. This journey has been fraught with obstacles both external and self-imposed which could not have been overcome alone. Here, I hope to acknowledge the support I have received from others that has enabled this work to be completed.  \nFirst of all, I am grateful to my supervisor, Alessandro Abate, for his supervision and guidance throughout the course of my PhD. His patience, understanding, and uncompromising support have been a cherished and immutable luxury.  \nThroughout my PhD I have been fortunate enough to work with many different collaborators, to all of whom I am grateful for their impact on me and my research. In particular, Andrea Peruffo has been a better mentor and friend than I could ask for or deserve, and I’m grateful for our collaborations together so far. Daniele Ahmed’s kindness and patience early on in my PhD, and in particular his feedback on good programming practice, has both improved my own ability and the quality of my research. I am thankful to Mirco Giacobbe for many discussions in which ideas could grow. Other collaborators, including Sergiy Bogomolov, Virginie Debauche, Raphael Jungers, Kostiantyn Potomkin, Hashan Punchihewa, Diptarko Roy, Sadegh Soudjani and Paolo Zuliani, have all been a pleasure to work with.  \nDuring my PhD I have been a member of the EPSRC CDT in Autonomous Intelligent Machines and Systems (AIMS, EP/S024050/1), which has been a privilege tobe a part of. Its student members have been kind, encouraging friends and colleagues  \nwho I have learned a lot from and had a lot of fun with. I am grateful to the CDT’s staff, in particular to its administrator Wendy Poole who has been a constant source of support.  \nI would like to thank my examiners, Rupak Majumdar and Kostas Margellos, for their time and effort in reviewing my thesis. I hope I have addressed their comments and suggestions to their satisfaction, and this work is enhanced by their feedback. I am thankful to my internal assessors: James Worrell, Konstantinos Gatsis and Christoph Haase, who have provided constructive feedback and guidance at significant milestones in my PhD. I would like to thank my college advisor and tutor, Antonis Papachristodoulou, who also first gave me the confidence to pursue a research degree.  \nThank you to my parents, Sandra and Clive, for their unyielding devotion to my education and my happiness.  \nAnd finally thank you to Becca, who is my light, my rock, and my joy.  \nAbstract  \nDynamical models are a mathematical tool for representing, understanding, and analysing complex systems that are ubiquitous across science and engineering. Complexity and nonlinearity in these systems result in a lack of analytical solutions and challenging, or even intractable, analysis in view of safety-critical applications. Effective methodologies for the verification of behaviours of dynamical models are therefore of great importance, and their effectiveness is often determined by their ability to handle nonlinearity. This thesis studies two alternative approaches to verifying continuous-time nonlinear dynamical models: abstraction, which directly disregards nonlinearity, and indirect certificate-based approaches, which indirectly handle nonlinearity. The strength of neural networks as universal approximators has seen widespread interest from the formal verification community. Commonly, this is in the context of verifying machine learning models themselves. Conversely, this thesis explores the use of neural networks as a tool for verification, in particular for dynamical models. In particular, we introduce a novel approach for abstracting nonlinear dynamical models via neural netw","cbCaiuo70J1xfHec","https://ap.wps.com/l/cbCaiuo70J1xfHec","pdf",1297366,1,178,"English","en",105,"# 1 Introduction\n## 1.1 Motivation and Research Questions\n## 1.2 Overview of Thesis\n## 1.2.1 Publications and Contributions\n# 2 Preliminaries\n## 2.1 General Notation\n## 2.2 Hybrid Systems Modelling\n## 2.2.1 Dynamical Models\n## 2.2.2 Hybrid Automata\n## 2.3 Counter-example Guided Inductive Synthesis\n## 2.4 Neural Networks\n## 2.5 Satisfiability Modulo Theories\n# 3 Formal Neural Abstractions of Dynamical Models\n## 3.1 Introduction\n## 3.1.1 Contributions\n## 3.1.2 Outline","[{\"question\":\"What problem does the thesis address in verifying dynamical models?\",\"answer\":\"It targets the difficulty of verifying continuous-time nonlinear dynamical models for safety-critical applications, where nonlinearity and complexity make analysis hard or intractable.\"},{\"question\":\"What two main approaches does the thesis study for verification?\",\"answer\":\"The thesis compares abstraction methods that directly disregard nonlinearity and indirect certificate-based approaches that handle nonlinearity through neural-network certificates.\"},{\"question\":\"How are formal correctness guarantees achieved in the proposed framework?\",\"answer\":\"It uses counterexample-guided inductive synthesis (CEGIS), employing neural networks as approximators together with satisfiability modulo theories solvers to construct networks that satisfy required properties.\"}]","Formal Verification of Dynamical Models via Neural Synthesis | 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problem does the thesis address in verifying dynamical models?","Question",{"text":75,"@type":76},"It targets the difficulty of verifying continuous-time nonlinear dynamical models for safety-critical applications, where nonlinearity and complexity make analysis hard or intractable.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"What two main approaches does the thesis study for verification?",{"text":80,"@type":76},"The thesis compares abstraction methods that directly disregard nonlinearity and indirect certificate-based approaches that handle nonlinearity through neural-network certificates.",{"name":82,"@type":73,"acceptedAnswer":83},"How are formal correctness guarantees achieved in the proposed framework?",{"text":84,"@type":76},"It uses counterexample-guided inductive synthesis (CEGIS), employing neural networks as approximators together with satisfiability modulo theories solvers to construct networks that satisfy required 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