Mixed precision, approximate computing, and data compression for computational fluid dynamics

Computer hardware is changing noticeably at the fundamental, computer arithmetic level in the last decade. Graphical processing units (GPUs) and some CPUs increasingly started introducing 16- and 8-bit hardware for computing mathematical operations, which work in parallel with classical 32- and 64-bit units. These low precision units are very efficient and to utilize them we need the software to be able to mix precisions. However, they are not always compliant with the IEEE 754 standard which has been around for almost 40 years, and that brings certain challenges at the fundamental level. <br /> <br /> Approximate computing refers to the techniques such as loop perforation, under designed arithmetic operators, or reduced voltage memory. These aim to identify parts of algorithms that can be safely skipped in order to speed up the application. The error that is introduced should be controlled and the application should be able to tolerate it. Data compression techniques similarly aim to reduce the memory footprint of the application, which can bring benefits in algorithms that spend most of the time in memory operations. In this project you will investigate these fundamental techniques in the context of computational fluid dynamics, broadly defined. First of all, you will study the latest results of applying the methods in scientific computing in general. Then you will build on that and you will use your knowledge of CFD algorithms to identify areas where these techniques can bring benefits. <br /> <br /> Finally, you will implement proof-of-concept experiments on custom precision simulators in C, MATLAB or Julia as well as explore running on the latest hardware such as NVIDIA A100, the H100, the AMD MI250X or the ARM A64FX devices.

<p class="MsoNoSpacing">Outcomes:</p> <p>As the project proposed is defined in a very general way, we expect a potential postgraduate researcher to drive the direction of it depending on the initial findings from the literature review. Therefore, any specific outcomes strongly depend on that. In general, we expect the following outcomes.</p> <p>Advances of algorithms and software in CFD. The project has potential in bringing new software artefacts as well as contributions to current software in the field of CFD or the related numerical libraries that are used in CFD. The new software might include for example mixed precision version of some already existent software that is run in high precision entirely.</p> <p>Contributions to fundamental topics of computer arithmetic, data compression, and approximate computing. These contributions can potentially be published separately in respective journals or conferences in addition to any publications that the postgraduate researcher will prepare in the CFD journals and conferences.</p> <p>Experiments on the latest hardware. We will be aiming to study mixed precision and other techniques not only in simulation, but also run on the actual hardware. This will inevitably generate results about the numerical behaviours of the latest hardware devices.</p>

<p style="margin-bottom:11px">Formal applications for research degree study should be made online through the <a href="https://www.leeds.ac.uk/research-applying/doc/applying-research-degrees">University's website</a>. Please state clearly in the Planned Course of Study section that you are applying for <strong><em>PHD Computer Science FT,</em></strong> in the research information section that the research degree you wish to be considered for is <em><strong>Mixed precision, approximate computing, and data compression for computational fluid dynamics</strong></em> as well as <a href="https://eps.leeds.ac.uk/computing/staff/12197/dr-mantas-mikaitis">Dr Mantas Mikaitis</a> as your proposed supervisor and in the finance section, please state clearly <em><strong>the funding that you are applying for, if you are self-funding or externally sponsored</strong></em>.</p> <p>If English is not your first language, you must provide evidence that you meet the University's minimum English language requirements (below).</p> <p><em>As an international research-intensive university, we welcome students from all walks of life and from across the world. We foster an inclusive environment where all can flourish and prosper, and we are proud of our strong commitment to student education. Across all Faculties we are dedicated to diversifying our community and we welcome the unique contributions that individuals can bring, and particularly encourage applications from, but not limited to Black, Asian, people who belong to a minority ethnic community, people who identify as LGBT+ and people with disabilities. Applicants will always be selected based on merit and ability.</em></p> <p>Applications will be considered after the closing date.  Potential applicants are strongly encouraged to contact the supervisors for an informal discussion before making a formal application.  We also advise that you apply at the earliest opportunity as the application and selection process may close early, should we receive a sufficient number of applications or that a suitable candidate is appointed.</p> <p style="margin-bottom:11px"><strong>Please note that you must provide the following documents in support of your application by the closing date of Monday 6 January 2025 if applying for the China Scholarship Council-University of Leeds Scholarship, Monday 3 February 2025 if applying for Leeds Doctoral Scholarship or Tuesday 1 April 2025 for Leeds Opportunity Research Scholarship.</strong></p> <p>If you are applying with external sponsorship or you are funding your own study, please ensure you provide your supporting documents at the point you submit your application:</p> <ul> <li>Full Transcripts of all degree study or if in final year of study, full transcripts to date</li> <li>Personal Statement outlining your interest in the project</li> <li>CV</li> </ul>

Applicants to this research degree programme must hold a minimum of First Class Honours Bachelor Degree (or equivalent) in an appropriate discipline. If an Upper Second Class British Bachelors Honours degree (or equivalent) is held, a Masters Degree with Distinction in Computer Science or Applied Mathematics is also required. 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.

The minimum English language entry requirement for research postgraduate research study is an IELTS of 6.5 overall with at least 6.5 in writing and at least 6.0 in reading, 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. Some schools and faculties have a higher requirement.

<p style="margin-bottom:11px"><strong>Self-Funded or externally sponsored students are welcome to apply.</strong></p> <p><strong>UK</strong> – The <a href="http://phd.leeds.ac.uk/funding/138-leeds-doctoral-scholarship-2025-faculty-of-engineering-and-physical-sciences#:~:text=Key%20facts&text=One%20Leeds%20Doctoral%20Scholarship%20is,rata%20for%20part%2Dtime%20study.">Leeds Doctoral Scholarship</a> <strong>(closing date: Monday 3 February 2025) </strong>and <a href="https://phd.leeds.ac.uk/funding/234-leeds-opportunity-research-scholarship-2022">Leeds Opportunity Research Scholarship</a> <strong>(closing date: Tuesday 1 April 2025)</strong> are available to UK applicants.  <a href="https://phd.leeds.ac.uk/funding/60-alumni-bursary">Alumni Bursary</a> is available to graduates of the University of Leeds.</p> <p><strong>Non-UK</strong> – The <a href="https://phd.leeds.ac.uk/funding/48-china-scholarship-council-university-of-leeds-scholarships-2021">China Scholarship Council - University of Leeds Scholarship</a> is available to nationals of China <strong>(closing date: Monday 6 January 2025)</strong>. The <a href="https://phd.leeds.ac.uk/funding/73-leeds-marshall-scholarship">Leeds Marshall Scholarship</a> is available to support US citizens. <a href="https://phd.leeds.ac.uk/funding/60-alumni-bursary">Alumni Bursary</a> is available to graduates of the University of Leeds.</p> <p>You will be responsible for paying the overtime fee in full in your writing up/overtime year (£320 in Session 2024/25), but the scholarship maintenance allowance will continue to be paid for up to 6 months in the final year of award.</p> <p><strong>Important:</strong> Please note that that the award does <em><strong>not </strong></em>cover the costs associated with moving to the UK.  All such costs (<a href="https://www.leeds.ac.uk/international-visas-immigration/doc/applying-student-visa">visa, Immigration Health Surcharge</a>, flights etc) would have to be met by yourself, or you will need to find an alternative funding source. </p> <p>Please refer to the <a href="https://www.ukcisa.org.uk/">UKCISA</a> website for information regarding Fee Status for Non-UK Nationals.</p>

<p style="margin-bottom:11px">For further information about this project, please contact Dr Mantas Mikaitis by email to <a href="mailto:M.Mikaitis@leeds.ac.uk">M.Mikaitis@leeds.ac.uk</a></p> <p>For further information about your application, please contact PGR Admissions by email to <a href="mailto:phd@engineering.leeds.ac.uk">phd@engineering.leeds.ac.uk</a></p>