相关论文: Non-linear estimation is easy

Neural ordinary differential equations (NODE) have been recently proposed as a promising approach for nonlinear system identification tasks. In this work, we systematically compare their predictive performance with current state-of-the-art…

We consider reduction of dimension for nonlinear dynamical systems. We demonstrate that in some cases, one can reduce a nonlinear system of equations into a single equation for one of the state variables, and this can be useful for…

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 connection between the state estimation problem and the separability problem is noticed and exploited to find efficient numerical algorithms to solve the first one. Based on these ideas, we also derive a systematic method to obtain upper…

Nonlinear thermoelastic systems play a crucial role in understanding thermal conductivity, stresses, elasticity, and temperature interactions. This research focuses on finding solutions to these systems in their fractional forms, which is a…

The problem of separating structured information representing phenomena of differing natures is considered. A structure is assumed to be independent of the others if can be represented in a complementary subspace. When the concomitant…

This paper introduces a novel optimization-based approach for parametric nonlinear system identification. Building upon the prediction error method framework, traditionally used for linear system identification, we extend its capabilities…

Ordinary differential equations (ODE's) are widespread models in physics, chemistry and biology. In particular, this mathematical formalism is used for describing the evolution of complex systems and it might consist of high-dimensional…

In this article, it is described how to use statistical data analysis to obtain models directly from data. The focus is put on finding nonlinearities within a generalized additive model. These models are found by the means of backfitting…

Applications of structural equation models (SEMs) are often restricted to linear associations between variables. Maximum likelihood (ML) estimation in non-linear models may be complex and require numerical integration. Furthermore, ML…

Nonlinear systems are capable of displaying complex behavior even if this is the result of a small number of interacting time scales. A widely studied case is when complex dynamics emerges out of a nonlinear system being forced by a simple…

A numerical framework based on network partition and operator splitting is developed to solve nonlinear differential equations of large-scale dynamic processes encountered in physics, chemistry and biology. Under the assumption that those…

Inference for streaming time-series is tightly coupled with the problem of Bayesian on-line state and parameter inference. In this paper we will introduce Dynamic Generalised Linear Models, the class of models often chosen to model…

We consider a nonparametric regression model with continuous endogenous independent variables when only discrete instruments are available that are independent of the error term. Although this framework is very relevant for applied…

In increasingly digitalized and metered distribution networks, state estimation is generally recognized as a key enabler of advanced network management functionalities. However, despite decades of research, the real-life adoption of state…

Linear regression is a fundamental and popular statistical method. There are various kinds of linear regression, such as mean regression and quantile regression. In this paper, we propose a new one called distribution regression, which…

The numerical solution of differential equations can be formulated as an inference problem to which formal statistical approaches can be applied. However, nonlinear partial differential equations (PDEs) pose substantial challenges from an…

This paper presents a method for jointly estimating the state, input, and parameters of linear systems in an online fashion. The method is specially designed for measurements that are corrupted with non-Gaussian noise or outliers, which are…

Nonlinear (systems of) ordinary differential equations (ODEs) are common tools in the analysis of complex one-dimensional dynamic systems. In this paper we propose a smoothing approach regularized by a quasilinearized ODE-based penalty in…

We provide another look at the statistical calibration problem in computer models. This viewpoint is inspired by two overarching practical considerations of computer models: (i) many computer models are inadequate for perfectly modeling…