DataScience@BI seminar with Tomás C. Simões

DataScience@BI seminar with Tomás C. Simões, PhD student, University of Vienna

Abstract:
Path-dependent controlled differential equations (CDEs) provide a very general framework for modelling dynamical systems with memory: systems whose future evolution depends not only on their current state, but also on their past history, and that are driven by an external signal, called the control path. While this level of generality is mathematically appealing, it also creates practical challenges when modelling real path-dependent phenomena. In particular, how can one represent or learn an unknown dependence on the past?

In this talk, I will discuss these questions and then give a brief introduction to path signatures. This leads to signature controlled differential equations (Sig-CDEs), a structured and flexible class of path-dependent dynamical systems. The key message is that Sig-CDEs provide a concrete architecture for modelling memory effects, while still being rich enough to approximate the dynamics of any well-posed path-dependent system. This is based on joint work with Christa Cuchiero, Paul Hager, and Fabian Harang. 

Research areas:
Signature-based methods, Rough Path Theory, Machine Learning

• Read more about the speaker
• Visit our website to read more about the Department of Data Science and Analytics