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math.DS2019
Physics-Informed Probabilistic Learning of Linear Embeddings of Non-linear Dynamics With Guaranteed Stability
Shaowu Pan, Karthik Duraisamy
The Koopman operator has emerged as a powerful tool for the analysis of nonlinear dynamical systems as it provides coordinate transformations to globally linearize the dynamics. Wh…
math.DS2019
On the Structure of Time-delay Embedding in Linear Models of Non-linear Dynamical Systems
Shaowu Pan, Karthik Duraisamy
This work addresses fundamental issues related to the structure and conditioning of linear time-delayed models of non-linear dynamics on an attractor. While this approach has been…
math.DS2018
Data-driven Discovery of Closure Models
Shaowu Pan, Karthik Duraisamy
Derivation of reduced order representations of dynamical systems requires the modeling of the truncated dynamics on the retained dynamics. In its most general form, this so-called…