Accelerating Atmospheric Simulations with High-Order Methods

Don't miss out on this exciting opportunity to advance weather forecasting with next-generation numerical methods!<br /> <br /> Currently, numerical weather and climate models rely on multi-scale finite-difference methods to solve the complex equations governing atmospheric motion. This approach requires a trade-off between accuracy and performance, and it often struggles with the finer resolutions that are necessary to capture highly localised weather phenomena. This project aims to explore a novel approach that leverages mixed precision to develop a new generation of weather models.<br /> <br /> The impact of this research extends beyond improving weather forecasts. For example, high-fidelity atmospheric simulations are used in climate modelling, as they allow us to understand and predict with greater accuracy the effects of climate change. The equations underlying atmospheric simulations govern many other phenomena, and the methods we will be developing will also improve air-quality forecasting, dispersion models for atmospheric pollutants, and wind energy predictions.<br /> <br /> In this project, you will have an opportunity to collaborate with Environment and Climate Change Canada (ECCC) to develop the next generation of numerical weather and climate models.

<p style="margin-bottom:11px">The project looks at the future of numerical weather prediction, focusing on developing numerical methods for fluid dynamics and implementing them so that they can run efficiently on supercomputers. You are encouraged to pursue the combination of topics that best aligns with your background and aspirations. In either focus area, you will gain valuable expertise and you will contribute to the development of novel numerical weather prediction models.</p> <h2 style="line-height: 100%; margin-bottom: 0in;">Fluid dynamics and numerical methods for partial differential equations</h2> <p>The equations describing atmospheric motion, such as the Euler equation or the shallow water equation, can be partitioned into two distinct parts: a stiff linear term, which governs fast atmospheric processes, and a nonlinear term, that captures large-scale dynamics. By treating these two terms individually, the project aims to derive more efficient numerical models for numerical weather prediction.</p> <p>The traditional time integration schemes (explicit and implicit) approaches used in numerical weather prediction models can easily become computationally expensive, especially when aiming for high resolution. Exponential integrators offer a way to solve the nonlinear term with higher-order accuracy compared to finite differences. In this way, one can capture finer details in atmospheric processes, leading to potentially more precise weather forecasts.</p> <p>Weather simulations involve complex computations on massive amounts of data. To handle these computations more efficiently, this project investigates the use of mixed precision, whereby different levels of precision are used so to ensure faster execution time without sacrificing any accuracy. The goal is to use the faster – but less accurate – low precision for most of the computation, and then refine the initial solution by performing a small portion of the computation in higher precision. This balancing act ensures accuracy where it matters, while keeping the runtime as low as possible.</p> <h2>High-performance computing and efficient implementations</h2> <p>Modern numerical weather forecasting models rely heavily on parallelism to handle the vast amount of data and numer of operations involved. While exponential integrators offer high accuracy, their parallelization can be challenging. The project will focus on developing strategies for efficiently parallelizing these methods within the context of numerical weather prediction models. This will involve exploring communication patterns and synchronization techniques that optimize performance on parallel architectures, to obtain scalable implementations.</p> <p>Another challenge of modern system is represented by their heterogeneity. Supercomputers more and more often include specialized accelerators, such as GPUs and NPUs, which excel at very specific tasks, but require software adaptations to be used effectively. This project will investigate how to leverage these accelerators to implement the mixed-precision approach efficiently. By offloading specific portions of the computation to accelerators, we can achieve a significant boost in efficiency while maintaining the required accuracy.</p> <p>A third issue is caused by the massive scale of modern supercomputers. With several million cores, frequent communication between processors can quickly become the bottleneck of a large computation. The project explores low-synchronization methods that try to minimize communication overhead. These methods allow processors to work more independently, significantly accelerating simulations on large-scale HPC systems. This will be crucial for handling the massive amount of data involved in high-resolution atmospheric simulations.</p> <h2>Skills and career prospects</h2> <p>Depending on the focus area and the specific topic you choose, you will develop a number of field-specific skills.</p> <p>By developing numerical methods, you will gain an in-depth understanding of the partial differential equations governing atmospheric dynamics, and you will develop expertise in advanced numerical methods to solve them.</p> <p>By implementing these methods and deploying them on supercomputers, you will become proficient in utilising high-performance computing resources and software environments, you will acquire the ability to develop parallel algorithms for scientific computing, and you will develop an in-depth knowledge of accelerators architectures.</p> <p>You will also develop a number of transferable skills which will serve you well in a variety of roles, regardless of the career path you choose. For example, you will enhance your ability to understand and solve complex problems, you will develop a research-oriented mindset that will enable you to propose innovative solutions that go beyond traditional approaches, and you will improve your ability to communicate with others efficiently and effectively. You will also learn how to plan a long and complex project, how to keep it on track, how to deal with unexpected and to manage your time effectively to complete it.</p>

<p>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 <em><strong>PHD Computer Science FT</strong></em>, in the research information section that the research degree you wish to be considered for is <em><strong>Accelerating Atmospheric Simulations with High-Order Methods</strong></em> as well as <a href="https://eps.leeds.ac.uk/computing/staff/14034/massimiliano-fasi">Massimiliano Fasi </a>as your proposed supervisor and <em><strong>in the finance section, please state clearly 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>Applications will be considered on an ongoing basis.  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>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> <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>

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.

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.

<p style="margin-bottom:11px"><strong>Self-Funded or externally sponsored students are welcome to apply.</strong></p> <p>UK – The <a href="https://phd.leeds.ac.uk/funding/209-leeds-doctoral-scholarships-2022">Leeds Doctoral Scholarships</a> <strong>(now closed for October 2025 entry)</strong> and <a href="https://phd.leeds.ac.uk/funding/234-leeds-opportunity-research-scholarship-2022">Leeds Opportunity Research Scholarship</a> <strong>(now closed for October 2025 entry)</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>Non-UK – 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>(now closed for october 2025 entry)</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 (£340 in Session 2025/26), 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>For further information about this project, please contact Massimiliano Fasi at <a href="mailto:m.fasi@leeds.ac.uk?subject=%5BPhD%20contact%5D%20Computer%20arithmetic%20for%20the%20next%20generation%20of%20integrated%20circuits">M.Fasi@leeds.ac.uk</a>.</p> <p>For further information about your application, please contact the Postgraduate Research Admissions team at <a href="mailto:phd@engineering.leeds.ac.uk">phd@engineering.leeds.ac.uk</a>.</p>