Data driven analysis of dynamical systems

Host Faculty: Engineering
General Subject Area: Applied Mathematics
Project Level: PhD
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Dynamical systems arise as solutions of differential equations, or in any situation where the state of a system updates iteratively with the passage of time steps (e.g., a descent algorithm for training a deep learning network). The local and global behaviour of dynamical systems is often determined by invariants of various kinds: fixed points, periodic orbits, invariant manifolds, invariant probability distributions. When the system is complex (due to very strong nonlinearities and/or high dimension), these objects are hard to find and analyse. In the last decade, a new family of tools has developed, loosely under the umbrella name of "Dynamic mode decomposition". These methods use samples from the dynamical system to build approximate transfer operators, from which eigenvectors can be extracted. The theory behind these methods remains undeveloped, there is a plethora of possible computational strategies, and any dynamical system can be analysed in this way. The emphasis in this project can be tailored to student interest.  


Supervisor: Rua Murray

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