Related papers: Improved Initialization for Nonlinear State-Space …

Many problems in the geophysical sciences demand the ability to calibrate the parameters and predict the time evolution of complex dynamical models using sequentially-collected data. Here we introduce a general methodology for the joint…

We study a spectral initialization method that serves a key role in recent work on estimating signals in nonconvex settings. Previous analysis of this method focuses on the phase retrieval problem and provides only performance bounds. In…

We consider the problem of subspace estimation in situations where the number of available snapshots and the observation dimension are comparable in magnitude. In this context, traditional subspace methods tend to fail because the…

Nonlinear stochastic motion presents significant challenges for Bayesian particle tracking. To address this challenge, this paper proposes a framework to construct an invertible transformation that maps the nonlinear state-space model (SSM)…

The system identification problem is to estimate dynamical parameters from the output data, obtained by performing measurements on the output fields. We investigate system identification for quantum linear systems. Our main objectives are…

A large variety of dynamical systems, such as chemical and biomolecular systems, can be seen as networks of nonlinear entities. Prediction, control, and identification of such nonlinear networks require knowledge of the state of the system.…

Motivated by the maneuvering target tracking with sensors such as radar and sonar, this paper considers the joint and recursive estimation of the dynamic state and the time-varying process noise covariance in nonlinear state space models.…

For real-life nonlinear systems, the exact form of nonlinearity is often not known and the known governing equations are often based on certain assumptions and approximations. Such representation introduced model-form error into the system.…

Equation discovery methods enable modelers to combine domain-specific knowledge and system identification to construct models most suitable for a selected modeling task. The method described and evaluated in this paper can be used as a…

The identification of structured state-space model has been intensively studied for a long time but still has not been adequately addressed. The main challenge is that the involved estimation problem is a non-convex (or bilinear)…

It has been recognized that using time-varying initialization functions to solve the initial value problem of fractional-order systems (FOS) is both complex and essential in defining the dynamical behavior of the states of FOSs. In this…

We consider a characteristic initial value problem for a class of symmetric hyperbolic systems with initial data given on two smooth null intersecting characteristic surfaces. We prove existence of solutions on a future neighborhood of the…

Empirical modelling often aims for the simplest model consistent with the data. A new technique is presented which quantifies the consistency of the model dynamics as a function of location in state space. As is well-known, traditional…

Estimating the values of unknown parameters from corrupted measured data faces a lot of challenges in ill-posed problems. In such problems, many fundamental estimation methods fail to provide a meaningful stabilized solution. In this work,…

This paper focuses on the identification of dynamical systems with tailor-made model structures, where neural networks are used to approximate uncertain components and domain knowledge is retained, if available. These model structures are…

This paper investigates nonlinear panel regression models with interactive fixed effects and introduces a general framework for parameter estimation under potentially non-convex objective functions. We propose a computationally feasible…

Recent developments in system identification have brought attention to regularized kernel-based methods, where, adopting the recently introduced stable spline kernel, prior information on the unknown process is enforced. This reduces the…

Neural network modules conditioned by known priors can be effectively trained and combined to represent systems with nonlinear dynamics. This work explores a novel formulation for data-efficient learning of deep control-oriented nonlinear…

Probabilistic (or Bayesian) modeling and learning offers interesting possibilities for systematic representation of uncertainty using probability theory. However, probabilistic learning often leads to computationally challenging problems.…

Literatures in state space models focus on parametric inference and prediction, which fail if the state space model is not fully specified and the maximum likelihood estimation does not work. In this paper, we assume the state transition…