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Variational Bayesian methods for fast solution of electrical tomography problems

PGR-P-694

Key facts

Type of research degree
PhD
Application deadline
Friday 17 April 2020
Project start date
Thursday 1 October 2020
Country eligibility
UK and EU
Funding
Competition funded
Source of funding
Research council
Supervisors
Dr Robert Aykroyd and Professor Mi Wang
Additional supervisors
Professor Daniel Lesnic
Schools
School of Chemical and Process Engineering, School of Mathematics
Research groups/institutes
Modern applied statistics, Process tomography, Statistics
<h2 class="heading hide-accessible">Summary</h2>

The Bayesian modelling approach provides a natural framework within which many applied science problems can be considered. The resulting posterior distribution, derived from data likelihood and prior knowledge, is then the basis for inference. In many problems, however, it is not practical to work directly with the posterior distribution, as it is too complicated or complex, and hence it is popular to use Markov chain Monte Carlo (MCMC) methods.

<h2 class="heading hide-accessible">Full description</h2>

<p>Such approaches are still computational expensive, as they often require the solution of a system of partial differential equations (PDEs), and so are impractical when rapid solution is needed. The method of fundamental solutions (MFS), however, provides a fast and easily programmed approach to the solution of the PDEs and the use of variational Bayesian (VB) algorithms, based on suitable conditional independence approximations, are&nbsp;orders of magnitude faster&nbsp;with little reduction in accuracy compared to sampling based MCMC algorithms. There has been little research examining the use of VB methods for inverse problem but if successful they have the potential to create a dramatic impact. For example, for industrial electrical tomography existing methods work well for static problems which can be analysed &ldquo;off-line&rdquo;&nbsp;or on-line but&nbsp;too slow for dynamic monitoring problems,&nbsp;e.g. phase velocity measurement or flow regime recognition in multiphase pipeline flows. This means that&nbsp;their usefulness in&nbsp;&ldquo;real-time&rdquo; applications are&nbsp;dramatically limited. This project will consider Bayesian models and MFS methods for a range of electrical tomography examples in process and chemical engineering. The project will begin by exploring the basic ideas of Bayesian methods and learning about industrial electrical tomography before moving on to study computational methods. The project supervisors have significant practical experience in these areas and have access&nbsp;to&nbsp;real datasets covering a wide variety f&nbsp;engineering&nbsp;applications and, hence modelling alternatives.</p>

<h2 class="heading">How to apply</h2>

<p>Formal applications for research degree study should be made online through the&nbsp;<a href="https://eps.leeds.ac.uk/maths-research-degrees/doc/apply">University&#39;s website</a>. Please state clearly in the research information section&nbsp;that the research degree you wish to be considered for is &ldquo;Variational Bayesian methods for fast solution of electrical tomography problems&rdquo; as well as <a href="https://eps.leeds.ac.uk/maths/staff/4002/dr-robert-g-aykroyd">Dr Robert G Aykroyd</a> as your proposed supervisor.</p> <p>If English is not your first language, you must provide evidence that you meet the University&#39;s minimum English language requirements (below).</p> <p><em>We welcome applications from all suitably-qualified candidates, but UK black and minority ethnic (BME) researchers are currently under-represented in our Postgraduate Research community, and we would therefore particularly encourage applications from UK BME candidates. All scholarships will be awarded on the basis of merit.</em></p>

<h2 class="heading heading--sm">Entry requirements</h2>

Applicants to research degree programmes should normally have at least a first class or an upper second class British Bachelors Honours degree (or equivalent) in an appropriate discipline. The criteria for entry for some research degrees may be higher, for example, several faculties, also require a Masters degree. Applicants are advised to check with the relevant School prior to making an application. Applicants who are uncertain about the requirements for a particular research degree are advised to contact the School or Graduate School prior to making an application.

<h2 class="heading heading--sm">English language requirements</h2>

The minimum English language entry requirement for research postgraduate research study is an IELTS of 6.0 overall with at least 5.5 in each component (reading, writing, listening and speaking) or equivalent. The test must be dated within two years of the start date of the course in order to be valid.

<h2 class="heading">Funding on offer</h2>

<p><strong>UK/EU</strong>&nbsp;&ndash;&nbsp;Engineering &amp; Physical Sciences Research Council Studentship&nbsp;for 3.5 years. A full standard studentship consists of academic fees (&pound;4,600 in Session 2020/21), together with a maintenance grant (&pound;15,009 in Session 2019/20) paid at standard Research Council rates. UK applicants will be eligible for a full award paying tuition fees and maintenance. European Union applicants will be eligible for an award paying tuition fees only, except in exceptional circumstances, or where residency has been established for more than 3 years prior to the start of the course.&nbsp;&nbsp;Funding is awarded on a competitive basis.</p>

<h2 class="heading">Contact details</h2>

<p>For enquiries about the application procedure,&nbsp;contact Doctoral College Admissions,<br /> e:&nbsp;<a href="mailto:maps.pgr.admissions@leeds.ac.uk">maps.pgr.admissions@leeds.ac.uk</a>, t:&nbsp;+44 (0)113 343 5057</p> <p>For questions about the research project, contact Dr Robert G Aykroyd,<br /> e: <a href="mailto:r.g.aykroyd@leeds.ac.uk">r.g.aykroyd@leeds.ac.uk</a></p>


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