Speaker
Description
Learning compact surrogate models from data has become a major application area of machine learning techniques. Such models are required to describe dynamical behavior of processes in the presence of time series data and the absence of explicit mechanistic models. This may be the case if only measurement data is available or simulation data is obtained via proprietary software. Prominent techniques in this area are dictionary learning via sparse regression or operator inference which allow to infer nonlinear models describing the data in some optimal way. If stable behavior of the underlying process is expected, be it Lyapunov or global stability, or some sort of attractor dynamics, the classical system identification approaches can not guarantee this intrinsic property of the physical process. We discuss how several stability concepts can be encoded in the inferred model structure using structured matrices so that the obtained surrogate models are guaranteed to have the desired stability property. We discuss in particular quadratic and cubic nonlinearities as it is known that these are sufficiently expressive for many nonlinear dynamical systems. We also discuss the extension of the suggested encodings to parametric and control systems.
This talk is based on prior work with Pawan K. Goyal, Siddarth Mamidisetti, and Igor Pontes Duff.