Verification of Neuro-Cyber-Physical Systems University of Southampton in United Kingdom

This fully funded PhD project at the University of Southampton focuses on the formal verification of neuro-symbolic cyber-physical systems, including drones, medical devices, and robots. The research addresses the challenge of integrating neural components—trained for optimal performance and safety—with symbolic models of cyber and physical behaviors. These models are verified using interactive theorem provers and advanced mathematical libraries to reason about both discrete and continuous dynamics. The project aims to develop a compositional methodology for constructing integrated proofs within the Vehicle framework, which provides a functional, domain-specific language for specifying, training, and verifying neural components of cyber-physical systems.

Students with interests in formal logic (quantitative, differential, linear logic), types and programming languages (functional DSLs, dependent types), and theorem proving and verification (including solvers, interactive theorem provers like Rocq or LEAN, and neural network verifiers) will find this project particularly suitable. The research environment offers access to a large network of international collaborators, as well as opportunities to attend relevant meetings, seminars, and conferences.

Entry requirements include a UK 2:1 honours degree or its international equivalent in mathematics, engineering, or computer science. Essential skills include experience in logic, functional programming languages, or formal verification, with knowledge of and interest in machine learning considered desirable. The project is fully funded through an Industrial CASE (Cooperative Awards in Science and Technology) studentship, covering tuition fees and providing an annual stipend for up to four years.

Applicants should prepare a research proposal, CV, two academic references, degree transcripts and certificates, and evidence of English language qualification if applicable. The University of Southampton is committed to equality, diversity, and inclusivity, offering flexible working patterns, generous maternity policy, onsite childcare, and a range of benefits to support well-being and work-life balance. The School of Electronics and Computer Science holds an Athena SWAN award and the institution has received the Platinum EcoAward for sustainability.

For further information or an initial conversation, contact Dr E Komendantskaya at [email protected]. General queries can be directed to [email protected]. Apply online by searching for the PhD Computer Science (7089) programme and following the specified application steps.