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Sparsity-promoting algorithms for the discovery of informative Koopman invariant subspaces
Shaowu Pan, Nicholas Arnold-Medabalimi, Karthik Duraisamy
Koopman decomposition is a non-linear generalization of eigen-decomposition, and is being increasingly utilized in the analysis of spatio-temporal dynamics. Well-known techniques s…
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…
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…
The Adjoint Petrov-Galerkin Method for Non-Linear Model Reduction
Eric J. Parish, Christopher Wentland, Karthik Duraisamy
We formulate a new projection-based reduced-ordered modeling technique for non-linear dynamical systems. The proposed technique, which we refer to as the Adjoint Petrov-Galerkin (A…
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…