相关论文: Entropy based lower dimension bounds for finite-ti…

We consider model-based derivative-free optimization (DFO) for large-scale problems, based on iterative minimization in random subspaces. We provide the first worst-case complexity bound for such methods for convergence to approximate…

Recently, versions of neural networks with infinite-dimensional affine operators inside the computational units (``neural operator'' networks) have been applied to learn solutions to differential equations. To enable practical computations,…

Predicting the future behaviour of complex systems exhibiting critical-like dynamics is often considered to be an intrinsically hard task. Here, we study the predictability of the depinning dynamics of elastic interfaces in random media…

Estimating global properties of many-body quantum systems such as entropy or bipartite entanglement is a notoriously difficult task, typically requiring a number of measurements or classical post-processing resources growing exponentially…

This work is devoted to the investigation of the most probable transition time between metastable states for stochastic dynamical systems. Such a system is modeled by a stochastic differential equation with non-vanishing Brownian noise, and…

After a brief introduction to the concept of entanglement in quantum systems, I apply these ideas to many-body systems and show that the von Neumann entropy is an effective way of characterising the entanglement between the degrees of…

We establish upper and lower bounds for the metric entropy and bracketing entropy of the class of $d$-dimensional bounded monotonic functions under $L^p$ norms. It is interesting to see that both the metric entropy and bracketing entropy…

We address the problem of learning the parameters of a stable linear time invariant (LTI) system or linear dynamical system (LDS) with unknown latent space dimension, or order, from a single time--series of noisy input-output data. We focus…

We show how a recently introduced statistics [Patil et al, Phys. Rev. Lett. 81 5878 (2001)] provides a direct relationship between dimension and predictability in spatiotemporal chaotic systems. Regions of low dimension are identified as…

In this paper, we consider two questions about topological entropy of dynamical systems. We propose to resolve these questions by the same approach of using \'etale analogs of topological and algebraic dynamical systems. The first question…

Koopman operators linearize nonlinear dynamical systems, making their spectral information of crucial interest. Numerous algorithms have been developed to approximate these spectral properties, and Dynamic Mode Decomposition (DMD) stands…

Koopman decomposition is a non-linear generalization of eigen-decomposition, and is being increasingly utilized in the analysis of spatio-temporal dynamics. Well-known techniques such as the dynamic mode decomposition (DMD) and its linear…

We present a data-driven learning approach for unknown nonautonomous dynamical systems with time-dependent inputs based on dynamic mode decomposition (DMD). To circumvent the difficulty of approximating the time-dependent Koopman operators…

The present paper treats the identification of nonlinear dynamical systems using Koopman-based deep state-space encoders. Through this method, the usual drawback of needing to choose a dictionary of lifting functions a priori is…

We provide a mutual information lower bound that can be used to analyze the effect of training in models with unknown parameters. For large-scale systems, we show that this bound can be calculated using the difference between two…

In this paper, we introduce topological entropy for dynamical systems generated by a single local homeomorphism (Deaconu-Renault systems). More precisely, we generalize Adler, Konheim, and McAndrew's definition of entropy via covers and…

Koopman operators are infinite-dimensional operators that linearize nonlinear dynamical systems, facilitating the study of their spectral properties and enabling the prediction of the time evolution of observable quantities. Recent methods…

Given a factor code between sofic shifts X and Y, there is a family of decompositions of the original code into factor codes such that the entropies of the intermediate subshifts arising from the decompositions are dense in the interval…

Dynamic Mode Decomposition (DMD) is a data-driven and model-free decomposition technique. It is suitable for revealing spatio-temporal features of both numerically and experimentally acquired data. Conceptually, DMD performs a…

The Koopman operator and its data-driven approximations, such as extended dynamic mode decomposition (EDMD), are widely used for analysing, modelling, and controlling nonlinear dynamical systems. However, when the true Koopman…