Using AI to predict coronal-loop kink instabilities by designing physics-informed neural networks (Ref: NUDATA24/EE/MPEE/BOTHA)

   Faculty of Engineering and Environment

This project is no longer listed on and may not be available.

Click here to search for PhD studentship opportunities
  Dr Gert Botha  No more applications being accepted  Competition Funded PhD Project (Students Worldwide)

About the Project

Overview of the CDT

This project is being offered as part of the STFC Centre for Doctoral Training in Data Intensive Science, called NUdata, which is a collaboration between Northumbria and Newcastle Universities, STFC, and a portfolio of over 40 industrial partners, including SMEs, large/multinational companies, Government and not-for profit organisations, and international humanitarian organisations. Please visit for full information.

Project Description

The solar atmosphere is a highly structured medium consisting of hot plasma and magnetic fields. These fields form open structures and closed loops. Instabilities inherent to the magnetic field topology cause flares and coronal mass ejections that drive extreme space weather events. To predict them is essential for accurate space weather forecasting.

The kink instability in coronal loops has been studied solving the magnetohydrodynamic (MHD) equations in large numerical simulations. Various magnetic formulations can be used to describe a cylindrical loop structure that goes kink unstable. By exploring initial values and boundary conditions, one can determine universal stability thresholds for cylindrical loops and describe their detailed physical evolution.

Neural networks provide an alternative approach to studying the kink instability in cylindrical coronal loops. Rather than directly solving the MHD equations, one can use their formulation to constrain the decision algorithms between the various layers of the neural network. The validity of the final output can be judged by comparing it directly to the final result from a numerical simulation.

In this PhD project you will be responsible for the development and production of three-dimensional MHD simulations describing the onset the kink instability in cylindrical coronal loops. You will be using an existing numerical code (Lare3D) that will be initialised with different magnetic field configurations. In parallel to this you will be designing a physics-informed neural network by incorporating the MHD equations and theory into a neural-network architecture. You will measure the success of this approach by comparing the output from the neural network directly with the numerical solutions.

Academic Enquiries

This project is supervised by Dr Gert Botha. For informal queries, please contact Dr Botha at [Email Address Removed] all other enquiries relating to eligibility or application process please contact Admissions at [Email Address Removed].  

Recruitment Event

You will join a strong and supportive research team. To help better understand the aims of the CDT and to meet the PhD supervisors, we are hosting a day-long event on campus on Monday 15th January 2024. At that event, there will be an opportunity to discuss your research ideas, meet potential PhD supervisors, as well as hear from speakers from a variety of backgrounds (academia, industry, government, charity) discussing both STFC and data science as well as their personal paths and backgrounds. Click here for details.

Eligibility Requirements:

  • Academic excellence i.e. 2:1 (or equivalent GPA from non-UK universities with preference for 1st class honours); or a Masters (preference for Merit or above); or APEL evidence of substantial practitioner achievement.
  • Appropriate IELTS score, if required.
  • Applicants cannot apply if they are already a PhD holder or if currently engaged in Doctoral study at Northumbria or elsewhere.

To be classed as a Home student, candidates must:

  • Be a UK National (meeting residency requirements), or
  • have settled status, or
  • have pre-settled status (meeting residency requirements), or
  • have indefinite leave to remain or enter.

If a candidate does not meet the criteria above, they would be classed as an International student. 

Applicants will need to be in the UK and fully enrolled before stipend payments can commence and be aware of the following additional costs that may be incurred, as these are not covered by the studentship.

  • Immigration Health Surcharge
  • If you need to apply for a Student Visa to enter the UK, please refer to It is important that you read this information carefully as it is your responsibility to ensure that you hold the correct funds required for your visa application, otherwise your visa may be refused.
  • Costs associated with English Language requirements which may be required for students not having completed a first degree in English, will not be paid by the University.

For further details on how to apply see  

You must include the relevant advert reference/studentship code (e.g. NUDATA24/…) in your application.

If you are interested in more than one of the Northumbria-hosted NUdata research projects, then you can say this in the cover letter of your application and you can rank all the projects you are interested in (e.g. first choice, second choice, third choice). You are strongly encouraged to do this, since some projects are more popular than others. You only need to submit one application even if you are interested in multiple projects (we recommend you submit your application to your first choice).

Deadline for applications : 31st January 2024

Start date of course :  23rd September 2024

Northumbria University is committed to creating an inclusive culture where we take pride in, and value, the diversity of our postgraduate research students. We encourage and welcome applications from all members of the community. The University holds a bronze Athena Swan award in recognition of our commitment to advancing gender equality, we are a Disability Confident Leader, a member of the Race Equality Charter and are participating in the Stonewall Diversity Champion Programme. We also hold the HR Excellence in Research award for implementing the concordat supporting the career Development of Researchers and are members of the Euraxess initiative to deliver information and support to professional researchers.

Computer Science (8) Mathematics (25) Physics (29)

Funding Notes

The 4-year studentship is available to Home and international (including EU) students and includes a full stipend at UKRI rates (for 2023/24 full-time study this was £18,622 per year) and full tuition fees. Studentships are also available for applicants who wish to study on a part-time basis in combination with work or personal responsibilities.


Botha et al., Thermal conduction effects on the kink instability in coronal loops, A&A, (2011), 525, A96, doi:10.1051/0004-6361/201015534
Hood et al., Coronal heating by magnetic reconnection in loops with zero net current, A&A, (2009), 506, 913, doi:10.1051/0004-6361/200912285
Raissi et al., Hidden fluid mechanics: Learning velocity and pressure fields from flow visualizations, Science, (2020), 367, 1026, doi:10.1126/science.aaw4741
Zhua et al., Physics-constrained deep learning for high-dimensional surrogate modeling and uncertainty quantification without labeled data, J Comp Physics, (2019), 394, 56, doi:10.1016/
Arber et al., A staggered grid, Lagrangian–Eulerian remap code for 3-D MHD simulations, J Comp Physics, (2001) 171, 151, doi:10.1006/jcph.2001.6780

How good is research at Northumbria University in Geography and Environmental Studies?

Research output data provided by the Research Excellence Framework (REF)

Click here to see the results for all UK universities

Where will I study?

Search Suggestions
Search suggestions

Based on your current searches we recommend the following search filters.