This fully funded PhD project at The University of Manchester focuses on uncertainty quantification for multi-physics simulations, a critical challenge in modeling complex systems such as composite materials, carbon sequestration, and electric power grids. Multi-physics systems are characterized by nested components operating at different time and spatial scales, often with non-linear interactions and a large number of elements. Simulating these systems is computationally intensive, and while computer emulation has advanced for individual components, its application to multi-physics scenarios remains underdeveloped. The project aims to advance the theory and practical tools for composing individual computer emulators into hierarchical structures, leveraging concepts from deep Gaussian processes (deep GPs) and linked emulators. The research will bridge the gap between generic model formulation and real-world multi-physics applications, with a particular focus on fusion energy. The ideal candidate will have an MSc in Physics, Computer Science, Statistics, Mathematics, or a related field, and will contribute to methods development in this emerging area. The program is part of the UKRI AI Decisions CDT and is supported by the UK Atomic Energy Authority (UKAEA) as an industry partner. Successful applicants will receive full funding, including home tuition fees and a tax-free stipend at the UKRI rate (£20,780 for 2025/26), with a start date in September 2026. The University of Manchester is committed to equality, diversity, and inclusion, encouraging applicants from all backgrounds and offering flexible study options. Applicants are required to submit transcripts, CV, a supporting statement, and referee details, and are encouraged to contact the project supervisor or the UKRI AI Decisions CDT Team for queries. The project offers an excellent opportunity to develop expertise in AI, machine learning, and statistical modeling for complex multi-physics systems, with direct industry engagement and a supportive research environment.