The field of dynamical systems is being transformed by the mathematical tools and
algorithms emerging from modern computing and data science. First-principles derivations …

Generation and analysis of time-series data is relevant to many quantitative fields ranging
from economics to fluid mechanics. In the physical sciences, structures such as metastable …

Recurrent neural networks are widely used on time series data, yet such models often
ignore the underlying physical structures in such sequences. A new class of physics-based …

Research in modern data-driven dynamical systems is typically focused on the three key
challenges of high dimensionality, unknown dynamics and nonlinearity. The dynamic mode …

Cavitation is a quasi-periodic process, and its non-stationarity leads to increasingly complex
flow field structures. On the other hand, characterizing the flow field with greater precision …

Dynamic mode decomposition (DMD) provides a regression framework for adaptively
learning a best-fit linear dynamics model over snapshots of temporal, or spatio-temporal …

Dynamic mode decomposition (DMD) is a powerful tool for extracting spatial and temporal
patterns from multi-dimensional time series, and it has been used successfully in a wide …

We study numerical approaches to computation of spectral properties of composition
operators. We provide a characterization of Koopman Modes in Banach spaces using …

Koopman decomposition is a nonlinear generalization of eigen-decomposition, and is being
increasingly utilized in the analysis of spatio-temporal dynamics. Well-known techniques …

The Bellman equation and its continuous form, the Hamilton-Jacobi-Bellman (HJB)
equation, are ubiquitous in reinforcement learning (RL) and control theory. However, these …