Stochastic differential equations (SDEs) are widely used in science and engineering in order to model systems where random effects play a significant role. They arise in many application areas, including molecular dynamics and Bayesian sampling techniques used in emerging machine learning applications. However, the design of efficient and accurate numerical algorithms for such problems is highly nontrivial, since they are often in high dimensional spaces (or large-scale datasets in data science applications). This is a challenging but active field of research.
The aim of this project is to further explore the optimal design of numerical algorithms in challenging settings as well as in large-scale machine learning applications. Moreover, it would be very interesting to explore whether or not there exists a general framework to construct numerical algorithms with desired properties.
The project will involve rigorous mathematical analysis (providing comprehensive training in numerical analysis, scientific computing, and Bayesian sampling techniques) and implementation of the developed algorithms as well as extensive numerical experimentation, thus equipping the student with highly desirable skills for working in either industry or academia.
We are looking for an enthusiastic and highly-motivated graduate with
- a first class degree in Mathematics or a closely related discipline with strong mathematical component (Master’s level or equivalent);
- a solid background in numerical methods/analysis of SDEs;
- excellent programming skills;
- good communication skills (oral and written).
Good knowledge of molecular dynamics, statistical mechanics as well as basic understanding of machine learning techniques and 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.aspx
Informal inquiries should be directed to Dr Xiaocheng Shang (email: firstname.lastname@example.org).
For UK and EU candidates:
Funding may be available through a college or EPSRC scholarship in competition with all other PhD applications;
The scholarship will cover tuition fees, training support, and a stipend at standard rates for 3-3.5 years;
Early applications are strongly recommended; deadline for scholarship applications is midday UK time on 31st January (annually);
Strong candidates are encouraged to make an informal inquiry.
For non-UK/non-EU candidates:
Strong self-funded applicants will be considered;
Exceptionally strong candidates in this category may be awarded a tuition fee waiver (for up to 3 years) in competition with all other PhD applications.
For Chinese candidates:
The China Scholarship Council (CSC) Scholarship: https://www.csc.edu.cn/chuguo
China Scholarship Council (CSC) PhD Scholarships Programme at the University of Birmingham: https://www.birmingham.ac.uk/postgraduate/funding/china-scholarship-council-%E2%80%93-university-of-birmingham-phd-scholarships.aspx
PhD Placements and Supervisor Mobility Grants China-UK: https://www.britishcouncil.cn/en/programmes/education/higher/opportunities/phd