Related papers: Data Driven Estimation of Stochastic Switched Line…

The paper suggests a generalization of the Sign-Perturbed Sums (SPS) finite sample system identification method for the identification of closed-loop observable stochastic linear systems in state-space form. The solution builds on the…

We address the problem of data-driven pattern identification and outlier detection in time series. To this end, we use singular value decomposition (SVD) which is a well-known technique to compute a low-rank approximation for an arbitrary…

We prove that the ordinary least-squares (OLS) estimator attains nearly minimax optimal performance for the identification of linear dynamical systems from a single observed trajectory. Our upper bound relies on a generalization of…

This paper presents a two-stage online algorithm for recovery of low-rank parameter matrix in non-stationary stochastic systems. The first stage applies the recursive least squares (RLS) estimator combined with its singular value…

The forecasting and computation of the stability of chaotic systems from partial observations are tasks for which traditional equation-based methods may not be suitable. In this computational paper, we propose data-driven methods to (i)…

Recent advances in digitization have led to the availability of multivariate time series data in various domains, enabling real-time monitoring of operations. Identifying abnormal data patterns and detecting potential failures in these…

The problem of estimating parameters of switched affine systems with noisy input-output observations is considered. The switched affine models is transformed into a switched linear one by removing its intersection subspace, which is…

This paper considers the stabilization of unknown switched linear systems using data. Instead of a full system model, we have access to a finite number of trajectories of each of the different modes prior to the online operation of the…

We propose a hybrid method combining the deep long short-term memory (LSTM) model with the inexact empirical model of dynamical systems to predict high-dimensional chaotic systems. The deep hierarchy is encoded into the LSTM by…

A heuristic procedure based on novel recursive formulation of sinusoid (RFS) and on regression with predictive least-squares (LS) enables to decompose both uniformly and nonuniformly sampled 1-d signals into a sparse set of sinusoids (SSS).…

Linear Dynamical System (LDS) is an elegant mathematical framework for modeling and learning multivariate time series. However, in general, it is difficult to set the dimension of its hidden state space. A small number of hidden states may…

We consider the problem of high-dimensional filtering of state-space models (SSMs) at discrete times. This problem is particularly challenging as analytical solutions are typically not available and many numerical approximation methods can…

We study a fundamental class of regression models called the second order linear model (SLM). The SLM extends the linear model to high order functional space and has attracted considerable research interest recently. Yet how to efficiently…

In this work, we present the novel mathematical framework of latent dynamics models (LDMs) for reduced order modeling of parameterized nonlinear time-dependent PDEs. Our framework casts this latter task as a nonlinear dimensionality…

Many natural systems, such as neurons firing in the brain or basketball teams traversing a court, give rise to time series data with complex, nonlinear dynamics. We can gain insight into these systems by decomposing the data into segments…

Data-driven modelling and scientific machine learning have been responsible for significant advances in determining suitable models to describe data. Within dynamical systems, neural ordinary differential equations (ODEs), where the system…

This paper investigates the problem of identifying state-dependent switching systems, a class of hybrid dynamical systems that combine multiple linear or nonlinear modes. We propose two broad classes of switching systems: switching linear…

Second-order Latent Factor (SLF) model, a class of low-rank representation learning methods, has proven effective at extracting node-to-node interaction patterns from High-dimensional and Incomplete (HDI) data. However, its optimization is…

State space subspace algorithms for input-output systems have been widely applied but also have a reasonably well-developedasymptotic theory dealing with consistency. However, guaranteeing the stability of the estimated system matrix is a…

We develop an approach to subspace system identification using multiple data records and present a simple rank-based test for the adequacy of these data for fitting the unique linear, noise-free, dynamic model of prescribed state-vector,…