Related papers: A Sparse Bayesian Approach to the Identification o…

In recent years, identification of nonlinear dynamical systems from data has become increasingly popular. Sparse regression approaches, such as Sparse Identification of Nonlinear Dynamics (SINDy), fostered the development of novel governing…

We consider machine learning techniques to develop low-latency approximate solutions to a class of inverse problems. More precisely, we use a probabilistic approach for the problem of recovering sparse stochastic signals that are members of…

We propose a method to reconstruct sparse signals degraded by a nonlinear distortion and acquired at a limited sampling rate. Our method formulates the reconstruction problem as a nonconvex minimization of the sum of a data fitting term and…

In high-dimensional settings, sparse structures are critical for efficiency in term of memory and computation complexity. For a linear system, to find the sparsest solution provided with an over-complete dictionary of features directly is…

This work considers methods for imposing sparsity in Bayesian regression with applications in nonlinear system identification. We first review automatic relevance determination (ARD) and analytically demonstrate the need to additional…

We propose a nonparametric method for detecting nonlinear causal relationship within a set of multidimensional discrete time series, by using sparse additive models (SpAMs). We show that, when the input to the SpAM is a $\beta$-mixing time…

In this document, some general results in approximation theory and matrix analysis with applications to sparse identification of time series models and nonlinear discrete-time dynamical systems are presented. The aforementioned theoretical…

This paper presents a novel hybrid algorithm for minimizing the sum of a continuously differentiable loss function and a nonsmooth, possibly nonconvex, sparse regularization function. The proposed method alternates between solving a…

Likelihood-based inference in stochastic non-linear dynamical systems, such as those found in chemical reaction networks and biological clock systems, is inherently complex and has largely been limited to small and unrealistically simple…

Sparsity constraints on the control inputs of a linear dynamical system naturally arise in several practical applications such as networked control, computer vision, seismic signal processing, and cyber-physical systems. In this work, we…

Data-driven discovery of governing equations from data remains a fundamental challenge in nonlinear dynamics. Although sparse regression techniques have advanced system identification, they struggle with rational functions and noise…

This paper introduces new techniques for using convex optimization to fit input-output data to a class of stable nonlinear dynamical models. We present an algorithm that guarantees consistent estimates of models in this class when a small…

Discrete-time linear time-varying (LTV) systems form a powerful class of models to approximate complex dynamical systems with nonlinear dynamics for the purpose of analysis, design and control. Motivated by inference of spatio-temporal…

This paper presents an efficient Bayesian framework for solving nonlinear, high-dimensional model calibration problems. It is based on a Variational Bayesian formulation that aims at approximating the exact posterior by means of solving an…

The focus in this paper is Bayesian system identification based on noisy incomplete modal data where we can impose spatially-sparse stiffness changes when updating a structural model. To this end, based on a similar hierarchical sparse…

A new Bayesian approach to linear system identification has been proposed in a series of recent papers. The main idea is to frame linear system identification as predictor estimation in an infinite dimensional space, with the aid of…

Sparse signal reconstruction algorithms have attracted research attention due to their wide applications in various fields. In this paper, we present a simple Bayesian approach that utilizes the sparsity constraint and a priori statistical…

Automated model selection is an important application in science and engineering. In this work, we develop a learning approach for identifying structured dynamical systems from undersampled and noisy spatiotemporal data. The learning is…

An incremental/online state dynamic learning method is proposed for identification of the nonlinear Gaussian state space models. The method embeds the stochastic variational sparse Gaussian process as the probabilistic state dynamic model…

Sparsity and rank functions are important ways of regularizing under-determined linear systems. Optimization of the resulting formulations is made difficult since both these penalties are non-convex and discontinuous. The most common remedy…