Steffen W.R. Werner: Interpolatory Model Reduction for Structured Stochastic and Nonlinear Systems скачать в хорошем качестве

Steffen W.R. Werner: Interpolatory Model Reduction for Structured Stochastic and Nonlinear Systems

For the accurate modeling of time-dependent real-world phenomena, high-dimensional nonlinear stochastic dynamical systems are indispensable. Thereby, many physical properties are encoded in the internal differential structure of these systems. Typical differential structures are second-order time derivatives in mechanical systems or time-delay terms. When using such models in computational settings, the high-dimensional nature represented by a large number of differential equations that describe the dynamics becomes the main computational bottleneck. A remedy to this problem is model order reduction, which is concerned with the construction of cheap-to-evaluate surrogate models that are described by a significantly smaller number of differential equations while accurately approximating the input-to-output behavior of the original high-dimensional systems. It has been shown that many nonlinear and stochastic phenomena can be equivalently modeled using only bilinear and quadratic terms. Dynamical systems with such terms can be represented in the Laplace domain using multivariate rational functions. In this work, we present a structure-preserving model reduction framework for nonlinear dynamical systems via multivariate rational function interpolation. This new approach allows the simulation-free construction of cheap-to-evaluate surrogate models for nonlinear dynamical systems with internal structures.