Real-world engineering systems are inevitably affected by various uncertain or random factors, and these random factors can cause some probabilistic events with serious consequences, e.g., system failures. From a practical perspective, it is of essential importance to estimate the probability of such critical events and analyse the reliability of the system. On the other hand, many real-world systems are governed by large-scale Partial Differential Equation (PDE) models that are computationally expensive, and to accurately characterise the reliability of the system, the PDE model may need to be solved for a large number of times. As a result, the total computational cost becomes prohibitively high and novel methods must be developed to address this computational challenge.
The primary goal of this project is to develop fast algorithms that are specifically designed for the PDE-based reliability analysis problems and employ the state-of-the-art machine learning techniques for cost-efficient implementation.
The project will provide highly interdisciplinary training in machine learning, scientific computing, uncertainty quantification, and engineering applications, thus equipping the student with sought after skills for working in either industry or academia.
Person specification and entry requirements:
We are looking for an enthusiastic and highly-motivated graduate with
- a 1st class degree in Mathematics or a closely related discipline with strong mathematical component (Master’s level or equivalent);
- a solid background in scientific computing and numerical solution of PDEs;
- excellent programming skills;
- good communication skills (oral and written).
Good knowledge of probability theory, statistics as well as basic understanding of machine learning techniques and experience with the associated software will be advantageous.
The application procedure and the deadlines for scholarship applications are advertised at https://www.birmingham.ac.uk/schools/mathematics/phd/phd-programme.aspx.
Informal inquiries should be directed to Prof Jinglai Li and Dr Alex Bespalov by e-mail: firstname.lastname@example.org, email@example.com