PhD Studentship: Physics Informed Neural Networks to solve the Boltzmann Transport Equation

University of Exeter

Project Title: Physics Informed Neural Networks to solve the Boltzmann Transport Equation

Project Description:

Plasma physics presents a number of physical challenges. In some regimes the physics is best described by the Boltzmann equation. This models the gas in a 6 dimensional space of spatial coordinates and velocity components; the evolution of the state of the plasma corresponds to the transport of the particles in this 6-d space. The plasma can be collisionless, or collisions can be represented by an additional term in the equation. The solution of this is challenging due to the high dimensionality of the phase space, and standard techniques such as finite difference methods quickly explode in memory and computational cost.

Machine Learning techniques are making significant impacts in all areas of physical modelling. In applying a Neural Network to a physics problem, the objective is for the NN to “learn” the behaviour of the system. In “Physics Informed Neural Networks” (PINNs), the structure of the ODE or PDE to be solved is built into the NN. This can be highly advantageous for high dimensional systems. The objective of the project is to apply PINN to solve the Boltzmann equation and extend this to complex domains; after training the NN could provide almost instantaneous solution to this very challenging equation.

This award provides annual funding to cover Home tuition fees and a tax-free stipend.  For students who pay Home tuition fees the award will cover the tuition fees in full, plus at least £17,668 per year tax-free stipend. Students who pay international tuition fees are eligible to apply, but should note that the award will only provide payment for part of the international tuition fee and no stipend.   

The studentship will be awarded on the basis of merit for 3.5 years of full-time study to commence on 25 September 2023.

International applicants need to be aware that you will have to cover the cost of your student visa, healthcare surcharge and other costs of moving to the UK to do a PhD.

The conditions for eligibility of home fees status are complex and you will need to seek advice if you have moved to or from the UK (or Republic of Ireland) within the past 3 years or have applied for settled status under the EU Settlement Scheme.

Entry requirements

Applicants for this studentship must have obtained, or be about to obtain, a First or Upper Second Class UK Honours degree, or the equivalent qualifications gained outside the UK, in an appropriate area of science or technology, eg Engineering, Physics, or Mathematics.
If English is not your first language you will need to meet the required level (Profile A/B/C)  as per our guidance at

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