Fast and Robust Surrogate Modelling for Risk-Critical Engineering Systems

Project summary

Simulations that deliver in seconds, without losing rigour.

Critical engineering systems are increasingly reliant on complex digital twins and simulations to guide safety decisions. However, these simulations can be slow and data-hungry. What if we could replace them with fast, uncertainty-aware surrogates that deliver results in seconds without compromising rigour?

This EngD project will develop novel robust surrogate modelling techniques that allow rapid uncertainty quantification and risk analysis across complex, high-dimensional systems. The student will work on methods that preserve physical insight and mathematical rigour even when data are scarce, incomplete, or expensive to obtain.

Key innovations will include the exploration of physics-informed neural networks and Interval Predictor Models trained under uncertainty. These tools will be benchmarked against real industrial scenarios such as thermal-fluid simulations, fatigue life and reliability assessments, or decision support tools. Potential applications within Rolls-Royce include digital twins of propulsion systems or certification of components under variable operating conditions.

The student will gain expertise in applied mathematics, machine learning, and computational engineering. Industry secondments, starting in Year 2, will ensure methods are aligned to practical needs and tested on real systems. By improving both speed and trustworthiness of engineering simulations, this project supports the UK's net-zero and defence capability goals and prepares the ground for AI-assisted certification in future platforms.

Aims and objectives

Aim: design, validate, and deploy robust surrogate models capable of delivering rapid and reliable predictions in uncertain, high-stakes engineering environments.

Objectives:

1. Develop robust surrogate model architectures. Implement and compare surrogate modelling approaches (Imprecise Gaussian Processes, Interval Predictor Models, Physics-Informed Neural Networks). Design architectures that prioritise transparency, error bounds and interpretability.
2. Integrate uncertainty quantification from sparse or imperfect data. Investigate how epistemic and aleatory uncertainties can be modelled with minimal data. Use probabilistic bounds and interval analysis to preserve conservatism without excessive over-approximation.
3. Accelerate risk-critical simulations. Replace expensive high-fidelity simulations (thermal-fluid, structural fatigue, multiphase flow) with validated surrogates. Benchmark performance on fidelity, runtime and safety margin preservation.
4. Integrate robust surrogates into digital twins. Embed surrogates in digital twin pipelines and scenario stress-testing environments.
5. Industrial case study. Co-develop use cases (fatigue risk estimation, fluid flow control, onboard diagnostics) with the industrial partner. Participate in secondments to gain feedback from engineers and simulation experts.
6. Contribute to open-source infrastructure and academic dissemination. Develop reusable, documented codebases with well-defined uncertainty propagation and validation modules. Target top-tier journals and present findings at academic and practitioner conferences.

Alignment to STAND-UP impact targets