Inferring the dimensionality of dynamical systems automatically using machine learning

Summary

This research will develop methods to infer the dimensionality of a dynamical system automatically, by adapting dimensionality reduction methods to high-dimensional time-series feature spaces.

Supervisor(s)

Dr Ben Fulcher

Research Location

School of Physics

Program Type

Masters/PHD

Synopsis

Finding simple principles that can explain the complexity of the world around us often relies on finding lower-dimensional representations (or manifolds) of high-dimensional data. The complex dynamics of many real-world systems can be well-approximated by the variation of only a handful of parameters. Successful inference of these parameters in a data-driven way would be a major advance with an impact felt across science and industry. For example, if we understand the hidden patterns underlying variability across patients with a given disease, doctors could learn what minimal set of tests to run on their patients in order to recommend the optimal treatment. In this project, the student will apply a new highly comparative analysis framework, hctsa, to time-series datasets to develop new data-driven methods to automatically infer the parametric dimensionality of a range of physical (and other real-world) systems.

Additional Information

Excellent facilities are available to carry out all aspects of the work, including access to computing resources and large collections of time-series data. There is much flexibility to adjust the specific project to the interests of the student, who should have a strong interest in data science (with a quantitative background in e.g., physics, mathematics, statistics, engineering, or computer science). Top-up funding is available for the highest quality of applicants, with additional funding available to support travel to present research results at national and international conferences (or to visit collaborators, e.g., at Monash University or Imperial College London).


HDR Inherent Requirements

In addition to the academic requirements set out in the Science Postgraduate Handbook, you may be required to satisfy a number of inherent requirements to complete this degree. Example of inherent requirement may include:

- Confidential disclosure and registration of a disability that may hinder your performance in your degree;
- Confidential disclosure of a pre-existing or current medical condition that may hinder your performance in your degree (e.g. heart disease, pace-maker, significant immune suppression, diabetes, vertigo, etc.);
- Ability to perform independently and/or with minimal supervision;
- Ability to undertake certain physical tasks (e.g. heavy lifting);
- Ability to undertake observatory, sensory and communication tasks;
- Ability to spend time at remote sites (e.g. One Tree Island, Narrabri and Camden);
- Ability to work in confined spaces or at heights;
- Ability to operate heavy machinery (e.g. farming equipment);
- Hold or acquire an Australian driver’s licence;
- Hold a current scuba diving license;
- Hold a current Working with Children Check;
- Meet initial and ongoing immunisation requirements (e.g. Q-Fever, Vaccinia virus, Hepatitis, etc.)

You must consult with your nominated supervisor regarding any identified inherent requirements before completing your application.

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Keywords

Machine learning, time-series analysis, dynamical systems, complex systems, nonlinear dynamics, Applied mathematics, dimensionality reduction, manifold learning, data science, feature spaces

Opportunity ID

The opportunity ID for this research opportunity is: 2388

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