Interpolatory Model Reduction for Structured Stochastic and Nonlinear Systems

Explore advanced mathematical techniques for reducing the computational complexity of high-dimensional nonlinear stochastic dynamical systems in this 57-minute conference talk. Discover how physical properties are encoded in differential structures like second-order time derivatives in mechanical systems and time-delay terms, and understand why the high-dimensional nature of these systems creates computational bottlenecks in real-world modeling applications. Learn about model order reduction as a solution for constructing efficient surrogate models that maintain accuracy while using significantly fewer differential equations. Examine how nonlinear and stochastic phenomena can be equivalently modeled using bilinear and quadratic terms, and how these dynamical systems can be represented in the Laplace domain through multivariate rational functions. Gain insights into a novel structure-preserving model reduction framework that enables simulation-free construction of computationally efficient surrogate models for nonlinear dynamical systems while preserving their internal structures through multivariate rational function interpolation.