Deep Learning and Partial Differential Equations

Automated Finite Element Mesh Generation<br /> <br /> Artificial Intelligence/Machine Learning/Deep Learning, Fluid Dynamics<br /> <br /> Finite Element Methods (FEM) have been ubiquitously used in solving Partial Differential Equations (PDE) in an extremely wide range of fields in computer science and engineering, ranging from critical domains such as construction, material, fluid dynamics, to entertainments/education such as visual effects, computer graphics &amp; animation and virtual reality. One key fundamental aspect to such research is a well-balanced trade-off between accuracy and speed, and a significant proportion of the effort has been devoted to generating high-quality and adaptive FEM meshes.<br /> <br /> In the era of machine learning and deep learning, scientists have been actively exploring data-driven methods such as deep neural networks to help directly solve PDEs. However, we argue that there is a different route to this problem. We can combine traditional numerical solvers with smartly generated FEM meshes via deep learning. This way, we aim to both accelerate the speed and safeguard the accuracy. This route eliminates the worst-case scenarios where deep learning models can generate wrong predictions due to limited training data or the lack of model generalizability when used to predict the solutions directly.<br /> <br /> The team has published a series of papers in deep learning-based FEM mesh generation including MeshingNet: A New Mesh Generation Method Based on Deep Learning and MeshingNet3D: Efficient Generation of Adapted Tetrahedral Meshes for Computational Mechanics. Given it is the inception of such research, we invite promising PhD candidates to work with us for further theoretical explorations and wider applications.<br />

<p>The supervision team has expertise in computer graphics, computer vision, machine learning, visualization, virtual reality with regularly published research papers at the very top venues in related fields. The <a href="http://vcg.leeds.ac.uk">Visual and Computer Graphics Research Group </a>is also well supported in terms of research equipment including studio-level motion capture systems, eye-tracking devices, deep learning servers and virtual reality kits, to which the candidate will have access.</p>

<p>Formal applications for research degree study should be made online through the&nbsp;<a href="https://www.leeds.ac.uk/research-applying/doc/applying-research-degrees">University&#39;s website</a>. Please state clearly in the Planned Course of Study section that you are applying for <em><strong>PHD Computing FT</strong></em> and in the research information section&nbsp;that the research degree you wish to be considered for is <em><strong>Deep Learning and Partial Differential Equations</strong></em> as well as&nbsp;<a href="https://eps.leeds.ac.uk/computing/staff/868/dr-he-wang">Dr He Wang</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>&nbsp;</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 in the School of Computing is IELTS - overall score of 6.5 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><strong>Self-Funded or externally sponsored students are welcome to apply.</strong></p> <p><strong>UK</strong>&nbsp;(or home fee) &ndash;&nbsp;The&nbsp;<a href="https://phd.leeds.ac.uk/funding/209-leeds-doctoral-scholarships-2022">Leeds Doctoral Scholarships</a>, <a href="https://phd.leeds.ac.uk/funding/53-school-of-computing-scholarship">School of Computing Scholarship&nbsp;</a>, <a href="https://phd.leeds.ac.uk/funding/198-akroyd-and-brown-scholarship-2022">Akroyd &amp; Brown</a>, <a href="https://phd.leeds.ac.uk/funding/199-frank-parkinson-scholarship-2022">Frank Parkinson</a> and <a href="https://phd.leeds.ac.uk/funding/204-boothman-reynolds-and-smithells-scholarship-2022">Boothman, Reynolds &amp; Smithells</a> Scholarships are available to UK applicants. &nbsp;<a href="https://phd.leeds.ac.uk/funding/60-alumni-bursary">Alumni Bursary</a> is available to graduates of the University of Leeds.&nbsp;</p> <p><strong>Non-UK</strong>&nbsp;&ndash; The&nbsp;<a href="https://phd.leeds.ac.uk/funding/53-school-of-computing-scholarship">School of Computing Scholarship&nbsp;</a>&nbsp;is available to support the additional academic fees of Non-UK applicants. The&nbsp;<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>&nbsp;is available to nationals of China. The&nbsp;<a href="https://phd.leeds.ac.uk/funding/73-leeds-marshall-scholarship">Leeds Marshall Scholarship</a>&nbsp;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>The&nbsp;<a href="https://www.ukcisa.org.uk/">UKCISA</a>&nbsp;website will be updated in due course with information regarding Fee Status for Non-UK Nationals starting from September/October 2021.</p>

<p>For further information regarding the project, please contact:&nbsp; Dr He Wang: <a href="mailto:h.e.wang@leeds.ac.uk">h.e.wang@leeds.ac.uk</a></p> <p>For further information regarding your application, please contact Doctoral College Admissions:&nbsp; e:&nbsp;<a href="mailto:phd@engineering.leeds.ac.uk">phd@engineering.leeds.ac.uk</a></p>