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PhD Studentship: Physics-informed Sparse Spectral Statistical Learning: Wind Flow Reconstruction

Mathematical Sciences

Location:  UK Other
Closing Date:  Wednesday 15 March 2023
Reference:  SCI2144

Machine learning strategies for fluid flows have been extensively developed in recent years. Particular attention has been paid to physics-informed deep neural networks in a statistical learning context. Such models combine measurements with physical properties to improve the reconstruction quality, especially when there are not enough velocity measurements. In this project, we reconstruct the velocity field of incompressible flows given a finite set of measurements. For the spatial approximation, we developed the Sparse Fourier divergence-free approximation based on a discrete $L^2$ projection. Within this physics-informed type of statistical learning framework, we adaptively build a sparse set of Fourier basis functions with corresponding coefficients by solving a sequence of minimization problems where the set of basis functions is augmented greedily at each optimization problem. We regularize our minimization problems with the seminorm of the fractional Sobolev space in a Tikhonov fashion. In the Fourier setting, the incompressibility (divergence-free) constraint becomes a finite set of linear algebraic equations. We couple our spatial approximation with the truncated Singular Value Decomposition (SVD) of the flow measurements for temporal compression.

Our computational framework thus combines supervised and unsupervised learning techniques.

With support for Home-UK PhD student

Entry requirements:

2:1 in mathematics or a closely related subject with substantial mathematical content.

To secure funding you will need a First Class degree or Distinction.

Application Process:

All applications are to be made directly to the University, selecting PhD Mathematics (36 months duration) as the course. Please apply at:

In the research proposal section please only include “Espath advertised PhD position” in the title. You are required to upload the following documents to your application:

  • C.V.
  • Personal statement (maximum 1 page) describing why the candidate is interested in pursuing a PhD and any relevant research experience.
  • Either two references (in a non-editable format such as pdf, on headed paper and signed by the referee) or the details (email addresses) of two referees that we can contact. One of the references must be academic.

If you have any questions about the application process through MyNottingham, please contact for further advice.

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