Related papers: Tensor network approximation of Koopman operators
The rigorous linking of exact stochastic models to mean-field approximations is studied. Starting from the differential equation point of view the stochastic model is identified by its Kolmogorov equations, which is a system of linear ODEs…
Information networks are ubiquitous and are ideal for modeling relational data. Networks being sparse and irregular, network embedding algorithms have caught the attention of many researchers, who came up with numerous embeddings algorithms…
This paper proposes a data-driven framework to learn a finite-dimensional approximation of a Koopman operator for approximating the state evolution of a dynamical system under noisy observations. To this end, our proposed solution has two…
The Koopman operator provides a linear perspective on non-linear dynamics by focusing on the evolution of observables in an invariant subspace. Observables of interest are typically linearly reconstructed from the Koopman eigenfunctions.…
We study the approximation by tensor networks (TNs) of functions from classical smoothness classes. The considered approximation tool combines a tensorization of functions in $L^p([0,1))$, which allows to identify a univariate function with…
In one dimension, the area law and its implications for the approximability by Matrix Product States are the key to efficient numerical simulations involving quantum states. Similarly, in simulations involving quantum operators, the…
Recently Koopman operator has become a promising data-driven tool to facilitate real-time control for unknown nonlinear systems. It maps nonlinear systems into equivalent linear systems in embedding space, ready for real-time linear control…
Group equivariant convolutional networks (GCNNs) endow classical convolutional networks with additional symmetry priors, which can lead to a considerably improved performance. Recent advances in the theoretical description of GCNNs revealed…
We obtain a time-evolution operator for a forced optomechanical quantum system using Lie algebraic methods when the normalized coupling between the electromagnetic field and a mechanical oscillator, $G/\omega_m$, is not negligible compared…
We develop a new approach for detecting changes in the behavior of stochastic processes and random fields based on tensor product representations such as the Karhunen-Lo\`{e}ve expansion. From the associated eigenspaces of the covariance…
Applying the techniques resulting the existence of almost invariant half-spaces, similarity models $\wh T$ can be given for upper triangular operator-matrices $T= \left[\begin{matrix}A&C\\ 0&B\end{matrix}\right]$. The model $\wh T$ is also…
This paper introduces a data-dependent approximation of the forward kinematics map for certain types of animal motion models. It is assumed that motions are supported on a low-dimensional, unknown configuration manifold $Q$ that is…
Tensor regression has attracted significant attention in statistical research. This study tackles the challenge of handling covariates with smooth varying structures. We introduce a novel framework, termed functional tensor regression,…
The Koopman operator is beneficial for analyzing nonlinear and stochastic dynamics; it is linear but infinite-dimensional, and it governs the evolution of observables. The extended dynamic mode decomposition (EDMD) is one of the famous…
Recent advances in {matrix-mimetic} tensor frameworks have made it possible to preserve linear algebraic properties for multilinear data analysis and, as a result, to obtain optimal representations of multiway data. Matrix mimeticity arises…
The Koopman operator approach to the state estimation problem for nonlinear systems is a promising research area. The main goal of this paper is an attempt to provide a rigorous theoretical framework for this approach. In particular, the…
We develop a novel EDMD-type algorithm that captures the spectrum of the Koopman operator defined on a reproducing kernel Hilbert space of analytic functions. This method, which we call analytic EDMD, relies on an orthogonal projection on…
Analyzing the long-term behavior of high-dimensional nonlinear dynamical systems remains a significant challenge. While the Koopman operator framework provides a powerful global linearization tool, current methods for approximating its…
The prediction of photon echoes is a crucial technique for understanding optical quantum systems. However, it typically requires numerous simulations with varying parameters and input pulses, rendering numerical studies computationally…
We introduce an encoder-only approach to learn the evolution operators of large-scale non-linear dynamical systems, such as those describing complex natural phenomena. Evolution operators are particularly well-suited for analyzing systems…