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 …
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 …
Model reduction for nonlinear systems by balanced truncation of state and gradient covariance
Data-driven reduced-order models often fail to make accurate forecasts of high-dimensional
nonlinear dynamical systems that are sensitive along coordinates with low-variance …
nonlinear dynamical systems that are sensitive along coordinates with low-variance …
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 …
Kernel sum of squares for data adapted kernel learning of dynamical systems from data: A global optimization approach
This paper examines the application of the Kernel Sum of Squares (KSOS) method for
enhancing kernel learning from data, particularly in the context of dynamical systems …
enhancing kernel learning from data, particularly in the context of dynamical systems …
Dimensionality reduction of complex metastable systems via kernel embeddings of transition manifolds
We present a novel kernel-based machine learning algorithm for identifying the low-
dimensional geometry of the effective dynamics of high-dimensional multiscale stochastic …
dimensional geometry of the effective dynamics of high-dimensional multiscale stochastic …
Gaussian processes simplify differential equations
In this paper we use Gaussian processes (kernel methods) to learn mappings between
trajectories of distinct differential equations. Our goal is to simplify both the representation …
trajectories of distinct differential equations. Our goal is to simplify both the representation …