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math.DS2019★ 148 cited
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★ 73 cited
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…