Quantization Effects on Dynamic Mode Decomposition for Koopman Operator Estimation
The core message of this work is that the estimation of the Koopman operator using Dynamic Mode Decomposition (DMD) with quantized data can be interpreted as a regularized DMD problem with unquantized data, where the regularization parameter depends on the quantization resolution. This connection provides a framework to potentially recover the unquantized Koopman operator estimate from the quantized data.
Efficient Trajectory Classification and Parameterization via Adaptive Birkhoff Reduced Rank Extrapolation
A modified reduced rank extrapolation (Birkhoff RRE) method is introduced to efficiently classify trajectories as chaotic, invariant circles, or islands, and parameterize the invariant circles and islands.
Discovering Constants of Motion from Machine-Learned Dynamical Models for Conserved and Non-conserved Systems
The existence of constants of motion in both conserved and non-conserved dynamical systems can be discovered by combining machine learning techniques (FJet) to model the dynamics with Lie symmetry analysis.
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