Speaker
Description
In this talk we discuss a machine learning method (Method of Multiple Trajectories [1]) for fitting time series data into a non-linear dynamical system. When restricted to a specific basin of attraction, the long-term forecast of the process can be associated with the tendency towards the attracting stationary point. Following M.W. Hirsch's definition of dissipativity (a system with a global attractor [2])
we define the dissipative restriction of the system to be the system on the restricted domain. Some dissipative properties can be discussed for this restricted system.
Within the basin of dissipative restriction, our method allows to achieve high accuracy short-term predictions of the process development (compare to [3]).
However, our method also provides us with several long-term trends that can be associated with various scenarios of the long-term process development. These scenarios are associated with different basins of attraction of the dynamical system, when the system is not restricted to a single basin.
In our examples (in the fields of economics and epidemiology), the dynamics can be driven into different basins of attraction via random external effects. For this reason, our long-term forecasts consist of multiple scenarios.
We want to use external forces for moving the dynamics into a desired basin of attraction. We are interested in extending the machine learning technique to find optimal control that allows the dynamics to be transferred from one basin to another.
References:
[1] V. Rayskin, Multivariate time series approximation by multiple trajectories of a dynamical system. Applications to internet traffic and COVID-19 data, American Institute of Physics Conference Proceedings, 2302 060011 (2020)
[2] M.W. Hirsch, (1996). "Dynamical Systems." In P. Smolensky, M. C. Mozer, & D. E. Rumelhart (Eds.), Mathematical Perspectives on Neural Networks (pp. 271–324). Lawrence Erlbaum Associates.
[3] E. Bradley, H. Kantz, Nonlinear time-series analysis revisited (2015), Chaos, 25(9)