Dynamic Mode Decomposition

The Dynamic Mode Decomposition (DMD) functions are designed to compute an evolution operator from data snapshots, enabling efficient analysis of linear dynamics in extended phase spaces. The methods provide memory-efficient representations of evolution operators, with DynamicModeDecompositionQR incorporating QR-based data compression for improved computational efficiency.

The Dynamic mode decomposition (DMD) method is an algorithm for searching for an evolution operator (inverse operator problem solutions) in a finite-dimensional problem solution space (numerical or experimentally obtained) in a set of solutions (slices, "snapshots") in some consecutive moments of time. Expansion of the phase space due to the use of a nonlinear basis (relative to the variables of the problem) allows us to construct a global linear operator describing a linear evolution in the extended "rectifying space" (the Coopman operator) and the Perron-Frobenius operator that is its adjoint one. The DMD method is equivalent to a compressed representation of a linear evolution operator in the form of a product of rectangular matrices, which provides significant savings in the required memory during calculations.