Defence of doctoral thesis in the field of Computer Science, M.Sc. Cagatay Yildiz

Differential equations are among the most prominent ways of representing physical quantities and their rates of change (the derivatives). These equations have been most commonly expressed using mechanistic models. Such models generate new hypotheses for an observed phenomenon by constructing mathematical formulations of causal mechanisms. Unfortunately, this process typically requires domain expertise and the resulting models tend to carry oversimplified assumptions. As opposed to the mechanistic paradigm, machine learning approaches are capable of learning complicated relations with very little or no domain knowledge. In this dissertation, we study how to build machine learning algorithms for differential equations and also how differential equations can be used within machine learning.

First, we examine the problems in which mechanistic modeling becomes too difficult, e.g., when we have only partial information about the observed system or when the system is too complicated for mechanistic modeling. We solve this problem using a well-established machine learning technique called Gaussian processes. Afterwards, we show that our ideas can be combined with recent deep learning techniques to predict the future frames of videos. Our subsequent work demonstrates how reinforcement learning, a sub-branch of machine learning, can benefit from our ideas to build intelligent decision-making agents. The last and most technical method in this work introduces an efficient numerical optimization technique to find the minimums of highly complicated functions.

Our approaches can be used as a direct replacement for mechanistic models; therefore, researchers lacking certain domain expertise can utilize our methods. Furthermore, we show that the proposed methods very accurately predict the future of different kinds of sequences such as physical systems, sensor measurements, videos, etc. Our reinforcement learning method provide a solid foundation to build intelligent agents for physical problems (such as pole balancing). Finally, our optimization technique allows machine learning researchers to optimize their models with desirable guarantees and hence boosts the research.

Opponent: Associate Professor Carl Henrik Ek, University of Cambridge, England

Custos: Professor Harri Lähdesmäki, Aalto University School of Science, Department of Computer Science

Contact details of the doctoral student: [email protected], +3584578718428

The public defence will be organised via Zoom. Link to the event

The thesis is publicly displayed 10 days before the defence in the publication archive Aaltodoc of Aalto University. 

Electronic thesis