Numerical Algorithms and Analysis for Deterministic and Stochastic Systems

Details:

Complex systems in biology, chemistry, and physics are often modelled using ordinary/partial/stochastic differential equations. It is desirable and highly nontrivial to design and analyse numerical algorithms that preserve the physical properties of the underlying systems.

The aim of the project, co-supervised by Drs Shang and Duong, is to further explore the optimal design of numerical algorithms and their corresponding numerical analysis for a large class of both deterministic and stochastic systems. We will also explore state-of-the-art machine learning techniques to learn the systems, while preserving their properties.

The project will involve rigorous mathematical analysis (providing comprehensive training in numerical analysis and scientific computing) 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. 

Entry requirements: 

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 ODEs/SDEs; 

- excellent programming skills; 

- good communication skills (oral and written). 

Good knowledge of ODEs/SDEs 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 both Dr Xiaocheng Shang (email: x.shang.1@bham.ac.uk) and Dr Hong Duong (email: h.duong@bham.ac.uk). 

Funding Notes:

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); however, late applications may also be considered;

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-phd.aspx

PhD Placements and Supervisor Mobility Grants China-UK: https://www.britishcouncil.cn/en/programmes/education/higher/opportunities/phd