Neural Networks for Complex Dynamical Systems

Details:

Dynamical systems are often solved/integrated by a suitable numerical discretisation method in such a way that certain properties of the underlying systems will be preserved. However, it is highly nontrivial to design such a method for complex systems in biology, chemistry, and physics, particularly in high dimensions.

The aim of the project is to further explore the state-of-the-art development in applying neural networks to approximate the solutions of the dynamical systems, while preserving their properties. We will also aim to understand how exactly those advanced machine learning techniques work so well and explore how mathematics could play a significant role in further exploring their potential in real applications.

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 dynamical systems; 

- excellent programming skills; 

- good communication skills (oral and written). 

Good knowledge of dynamical systems 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: x.shang.1@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/funding/postgraduate/china-scholarship-council-university-of-birmingham-phd-scholarships.aspx

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