Mathematics Seminar: Data to Equations: A Mathematical Approach | Manjunath Gandhi

Online Mathematics seminar by Dr Manjunath Gandhi (University of Pretoria
), held on 3 March 2022.

Abstract: Our ability to record rich and complex data has greatly improved, as has our anticipation of using the data to build models from them. Machine learning algorithms often out-perform mathematically based methods like the Takens delay embedding methods. However, they usually conduct prediction tasks rather than developing a model to relate to the dynamics underlying the data, resulting in inconsistent long-term results. Our goal to construct models that are resilient to noise and, in theory, allow for a precise representation of the data lies at the heart of this churning between intuition and qualitative understanding. In the same way that delay-coordinates are universal observables for embedding time-series data from a discrete-time dynamical system into a Euclidean space, observables that are obtained from a driven dynamical system through "causal embedding" are universal. The benefit of such an embedding is stability and robustness, which entails topologically and statistically consistent models over long periods of time.

Bio: Dr. Manjunath Gandhi has a Ph.D from the Indian Institute of Science. He is currently affiliated with the Mathematics department, University of Pretoria, where he is a Senior Lecturer. His research interests include topological dynamics and stability theory of autonomous and nonautonomous dynamical systems, data-driven modeling, and topics of machine learning that overlap with dynamical systems. His contributions include the extension of the celebrated Conley-decomposition theorem for Random Difference Equations and a zero-one stability law for driven dynamical systems.