Physics

Nonlinear system

Dynamic mode decomposition

Mathematics

Dynamical systems theory

Biology

Noise (video)

Algorithm

Image (mathematics)

Statistics

Mathematical optimization

Machine learning

Decomposition

Mathematical analysis

Series (stratigraphy)

Paleontology

Artificial intelligence

Variable (mathematics)

Ecology

Dynamical system (definition)

Computer science

Flexibility (engineering)

Quantum mechanics

Projection (relational algebra)

SIAM Journal on Applied Dynamical Systems

The dynamic mode decomposition (DMD) has become a leading tool for data-driven modeling of dynamical systems, providing a regression framework for fitting linear dynamical models to time-series measurement data. We present a simple algorithm for computing an optimized version of the DMD for data which may be collected at unevenly spaced sample times. By making use of the variable projection method for nonlinear least squares problems, the algorithm is capable of solving the underlying nonlinear optimization problem efficiently. We explore the performance of the algorithm with some numerical examples for synthetic and real data from dynamical systems and find that the resulting decomposition displays less bias in the presence of noise than standard DMD algorithms. Because of the flexibility of the algorithm, we also present some interesting new options for DMD-based analysis.

Variable Projection Methods for an Optimized Dynamic Mode Decomposition