A new opportunity has arisen to extend the Dedalus framework (see http://dedalus-project.org) for the Direct Statistical Simulation of partial differential equations (PDEs) in multi-scale physics and fluid dynamics (see for instance https://arxiv.org/pdf/1708.07805.pdf). The project (funded by the European Research Council) is to work with the Dedalus developer team (specifically Geoff Vasil, Jeff Oishi and Keaton Burns) together with Profs. Steven Tobias (Leeds) and Brad Marston (Brown) to provide a flexible package to generate and solve systems of equations for the statistical properties of fluid flows in Cartesian, spherical and cylindrical geometries. The project would involve utilising Python’s functionality to derive the relevant mathematical equations and using Dedalus’ highly accurate machinery to solve the resulting systems.
Possible relevant expertise required includes object-oriented and functional programming practices, particularly with Python; mathematical statistics; multi-scale modelling and model-reduction techniques for PDEs; or spectral numerical methods. A background in Machine Learning or computational optimisation would also provide many relevant skills. The Dedalus project is a community-developed code with a large and diverse user base, and this project will engage in a collaborative development process including public peer-review of code. This project combines several new areas in statistics, PDEs, and automated computational science. More than anything, the project requires an eagerness to learn several different mathematical and computational techniques, and apply them to diverse physical applications. The timeframe for starting this project may be somewhat flexible for an interested candidate with the right background and skills.
Please contact Prof. Steve Tobias or me directly if you would like more information regarding this opportunity.