Related papers: Predictability of Observables of Dynamical Systems
Nonlinear ordinary differential equations (ODEs) are powerful tools for modeling real-world dynamical systems. However, propagating initial state uncertainty through nonlinear dynamics, especially when the ODE is unknown and learned from…
We study the existence and uniqueness of (locally) absolutely continuous trajectories of a dynamical system governed by a nonexpansive operator. The weak convergence of the orbits to a fixed point of the operator is investigated by relying…
In applications of nonlinear and complex dynamical systems, a common situation is that the system can be measured but its structure and the detailed rules of dynamical evolution are unknown. The inverse problem is to determine the system…
Time-invariant linear dynamical system arises in many real-world applications,and its usefulness is widely acknowledged. A practical limitation with this model is that its latent dimension that has a large impact on the model capability…
Stability of linear systems with uncertain bounded time-varying delays is studied under assumption that the nominal delay values are not equal to zero. An input-output approach to stability of such systems is known to be based on the bound…
This paper presents a closed-form notion of controllability and observability for systems with communication delays, actuation delays, and locality constraints. The formulation reduces to classical notions of controllability and…
We study prediction-assimilation systems, which have become routine in meteorology and oceanography and are rapidly spreading to other areas of the geosciences and of continuum physics. The long-term, nonlinear stability of such a system…
We propose a method for learning dynamical systems from high-dimensional empirical data that combines variational autoencoders and (spatio-)temporal attention within a framework designed to enforce certain scientifically-motivated…
Nonlinear systems of affine control inputs overarch many sensor fusion instances. Analyzing whether a state variable in such a nonlinear system can be estimated (i.e., observability) informs better estimator design. Among the research on…
An efficient representation of observed data has many benefits in various domains of engineering and science. Representing static data sets, such as images, is a living branch in machine learning and eases downstream tasks, such as…
We start by reviewing recent probabilistic results on ergodic sums in a large class of (non-uniformly) hyperbolic dynamical systems. Namely, we describe the central limit theorem, the almost-sure convergence to the gaussian and other stable…
In this paper we present a radically new approach to design state observers for nonlinear systems, with particular emphasis on physical ones. Our objective is to obtain an algebraic relation between the unmeasurable part of the state and…
A faithful description of the state of a complex dynamical network would require, in principle, the measurement of all its $d$ variables, an infeasible task for systems with practical limited access and composed of many nodes with high…
The adiabatic criterion, widely used in astronomical dynamics, is based on the harmonic oscillator. It asserts that the change in action under a slowly varying perturbation is exponentially small. Recent mathematical results precisely…
Time-invariant finite-dimensional systems, under reasonable continuity assumptions, exhibit the property that if solutions exist for all future times, the set of vectors reachable from a bounded set of initial conditions over bounded time…
This paper provides an algorithmic pipeline for studying the intrinsic structure of a finite discrete dynamical system (DDS) modelling an evolving phenomenon. Here, by intrinsic structure we mean, regarding the dynamics of the DDS under…
Stability of the zero solution plays an important role in the investigation of positive systems. In this note, we revisit the $\mu$-stability of positive nonlinear systems with unbounded time-varying delays. The system is modelled by…
Limit theorems for a linear dynamical system with random interactions are established. These theorems enable us to characterize the dynamics of a large complex system in details and assess whether a large complex system is stable or…
In this paper we investigate a problem of state estimation for the dynamical system described by the linear operator equation with unknown parameters in Hilbert space. We present explicit expressions for linear minimax estimation and error…
Numerous studies have focused on learning and understanding the dynamics of physical systems from video data, such as spatial intelligence. Artificial intelligence requires quantitative assessments of the uncertainty of the model to ensure…