577 citations · 1.5k across the 23 of their papers we have counts for
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Recurrent Neural Networks for Dynamical Systems: Applications to Ordinary Differential Equations, Collective Motion, and Hydrological Modeling
Yonggi Park, Kelum Gajamannage, Dilhani I. Jayathilake +1
Classical methods of solving spatiotemporal dynamical systems include statistical approaches such as autoregressive integrated moving average, which assume linear and stationary re…
ERFit: Entropic Regression Fit Matlab Package, for Data-Driven System Identification of Underlying Dynamic Equations
Abd AlRahman AlMomani, Erik Bollt
Data-driven sparse system identification becomes the general framework for a wide range of problems in science and engineering. It is a problem of growing importance in applied mac…
Geometric Considerations of a Good Dictionary for Koopman Analysis of Dynamical Systems: Cardinality, 'Primary Eigenfunction,' and Efficient Representation
Erik Bollt
Representation of a dynamical system in terms of simplifying modes is a central premise of reduced order modelling and a primary concern of the increasingly popular DMD (dynamic mo…
Extended dynamic mode decomposition with dictionary learning: a data-driven adaptive spectral decomposition of the Koopman operator
Qianxiao Li, Felix Dietrich, Erik M. Bollt +1
Numerical approximation methods for the Koopman operator have advanced considerably in the last few years. In particular, data-driven approaches such as dynamic mode decomposition…