相关论文: A detectability criterion and data assimilation fo…

We study the problem of nonparametric estimation of density functions with a product form on the domain $\triangle=\{( x_1, \ldots, x_d)\in \mathbb{R}^d, 0\leq x_1\leq \dots \leq x_d \leq 1\}$. Such densities appear in the random truncation…

A coupled computational approach to simultaneously learn a vector field and the region of attraction of an equilibrium point from generated trajectories of the system is proposed. The nonlinear identification leverages the local stability…

Variational data assimilation is a technique for combining measured data with dynamical models. It is a key component of Earth system state estimation and is commonly used in weather and ocean forecasting. The approach involves a…

We present a new algorithm for computing the Lyapunov exponents spectrum based on a matrix differential equation. The approach belongs to the so called continuous type, where the rate of expansion of perturbations is obtained for all times,…

We revisit the numerical calculation of generalized Lyapunov exponents, $L$($q$), in deterministic dynamical systems. The standard method consists of adding noise to the dynamics in order to use importance sampling algorithms. Then $L$($q$)…

Data assimilation, in its most comprehensive form, addresses the Bayesian inverse problem of identifying plausible state trajectories that explain noisy or incomplete observations of stochastic dynamical systems. Various approaches have…

We introduce new machine-learning techniques for analyzing chaotic dynamical systems. The primary objectives of the study include the development of a new and simple method for calculating the Lyapunov exponent using only two trajectory…

This paper is concerned with relationships of Lyapunov exponents with sensitivity and stability for non-autonomous discrete systems. Some new concepts are introduced for non-autonomous discrete systems, including Lyapunov exponents, strong…

The problem of sampling according to the probability distribution minimizing a given free energy, using interacting particles unadjusted kinetic Langevin Monte Carlo, is addressed. In this setting, three sources of error arise, related to…

This paper introduces a novel anomaly detection framework that combines the robust statistical principles of density-estimation-based anomaly detection methods with the representation-learning capabilities of deep learning models. The…

We propose a numerical approximation method for the Cahn-Hilliard equations that incorporates continuous data assimilation in order to achieve long time accuracy. The method uses a C$^0$ interior penalty spatial discretization of the fourth…

This work is concerned with robust filtering of nonlinear sampled-data systems with and without exact discrete-time models. A linear matrix inequality (LMI) based approach is proposed for the design of robust $H_{\infty}$ observers for a…

This paper focuses on continuous data assimilation (CDA) for the Navier-Stokes equations with nonlinear slip boundary conditions. CDA methods are typically employed to recover the original system when initial data or viscosity coefficients…

Complex nonlinear turbulent dynamical systems are ubiquitous in many areas. Recovering unobserved state variables is an important topic for the data assimilation of turbulent systems. In this article, an efficient continuous in time data…

Approximate Bayesian inference on the basis of summary statistics is well-suited to complex problems for which the likelihood is either mathematically or computationally intractable. However the methods that use rejection suffer from the…

This paper develops a flexible distribution-free method for collective outlier detection and enumeration, designed for situations in which the presence of outliers can be detected powerfully even though their precise identification may be…

This work proposes an accelerated primal-dual dynamical system for affine constrained convex optimization and presents a class of primal-dual methods with nonergodic convergence rates. In continuous level, exponential decay of a novel…

A novel distributed control law for consensus of networked double integrator systems with biased measurements is developed in this article. The agents measure relative positions over a time-varying, undirected graph with an unknown and…

Data assimilation plays a crucial role in numerical modeling, enabling the integration of real-world observations into mathematical models to enhance the accuracy and predictive capabilities of simulations. This approach is widely applied…

This paper deals with the problem of finite-time learning for unknown discrete-time nonlinear systems' dynamics, without the requirement of the persistence of excitation. Two finite-time concurrent learning methods are presented to…