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 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 …
[HTML][HTML] Simplicity bias, algorithmic probability, and the random logistic map
Simplicity bias is an intriguing phenomenon prevalent in various input–output maps,
characterized by a preference for simpler, more regular, or symmetric outputs. Notably, these …
characterized by a preference for simpler, more regular, or symmetric outputs. Notably, these …
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 …
Kernel methods for the approximation of some key quantities of nonlinear systems
We introduce a data-based approach to estimating key quantities which arise in the study of
nonlinear control systems and random nonlinear dynamical systems. Our approach hinges …
nonlinear control systems and random nonlinear dynamical systems. Our approach hinges …
Learning dynamical systems from data: A simple cross-validation perspective, Part III: Irregularly-sampled time series
A simple and interpretable way to learn a dynamical system from data is to interpolate its
vector-field with a kernel. In particular, this strategy is highly efficient (both in terms of …
vector-field with a kernel. In particular, this strategy is highly efficient (both in terms of …
Learning dynamical systems from data: a simple cross-validation perspective, part iii: irregularly-sampled time series
A simple and interpretable way to learn a dynamical system from data is to interpolate its
vector-field with a kernel. In particular, this strategy is highly efficient (both in terms of …
vector-field with a kernel. In particular, this strategy is highly efficient (both in terms of …