Learning dynamical systems from data: a simple cross-validation perspective, part I: parametric kernel flows
Regressing the vector field of a dynamical system from a finite number of observed states is
a natural way to learn surrogate models for such systems. We present variants of cross …
a natural way to learn surrogate models for such systems. We present variants of cross …
Infinite-dimensional reservoir computing
Reservoir computing approximation and generalization bounds are proved for a new
concept class of input/output systems that extends the so-called generalized Barron …
concept class of input/output systems that extends the so-called generalized Barron …
One-shot learning of stochastic differential equations with data adapted kernels
We consider the problem of learning Stochastic Differential Equations of the form d X t= f (X
t) d t+ σ (X t) d W t from one sample trajectory. This problem is more challenging than …
t) d t+ σ (X t) d W t from one sample trajectory. This problem is more challenging than …
[HTML][HTML] Learning dynamical systems from data: A simple cross-validation perspective, part iv: case with partial observations
A simple and interpretable way to learn a dynamical system from data is to interpolate its
governing equations with a kernel. In particular, this strategy is highly efficient (both in terms …
governing equations with a kernel. In particular, this strategy is highly efficient (both in terms …
[PDF][PDF] Learning dynamical systems from data: a simple cross-validation perspective, part ii: nonparametric kernel flows
In previous work, we showed that learning dynamical system [21] with kernel methods can
achieve state of the art, both in terms of accuracy and complexity, for predicting …
achieve state of the art, both in terms of accuracy and complexity, for predicting …
Learning dynamical systems from data: A simple cross-validation perspective, part v: Sparse kernel flows for 132 chaotic dynamical systems
Regressing the vector field of a dynamical system from a finite number of observed states is
a natural way to learn surrogate models for such systems. A simple and interpretable way to …
a natural way to learn surrogate models for such systems. A simple and interpretable way to …
Kernel-based models for system analysis
HJ Van Waarde, R Sepulchre - IEEE Transactions on Automatic …, 2022 - ieeexplore.ieee.org
This article introduces a computational framework to identify nonlinear input–output
operators that fit a set of system trajectories while satisfying incremental integral quadratic …
operators that fit a set of system trajectories while satisfying incremental integral quadratic …
Approximation of Lyapunov functions from noisy data
Methods have previously been developed for the approximation of Lyapunov functions
using radial basis functions. However these methods assume that the evolution equations …
using radial basis functions. However these methods assume that the evolution equations …
Kernel methods for center manifold approximation and a weak data-based version of the center manifold theorem
For dynamical systems with a non hyperbolic equilibrium, it is possible to significantly
simplify the study of stability by means of the center manifold theory. This theory allows to …
simplify the study of stability by means of the center manifold theory. This theory allows to …
Kernel methods for the approximation of nonlinear systems
We introduce a data-driven model approximation method for nonlinear control systems,
drawing on recent progress in machine learning and statistical-dimensionality reduction …
drawing on recent progress in machine learning and statistical-dimensionality reduction …