Related papers: Quantifying model uncertainty for the observed non…
We develop a mean-field approach for multicomponent stochastic spatially extended systems and use it to obtain a multivariate nonlinear self-consistent Fokker-Planck equation defining the probability density of the state of the system,…
Complex-valued Gaussian processes are commonly used in Bayesian frequency-domain system identification as prior models for regression. If each realization of such a process were an $H_\infty$ function with probability one, then the same…
The problem of determining dynamical models and trajectories that describe observed time-series data allowing for the understanding, prediction and possibly control of complex systems in nature is of a great interest in a wide variety of…
Gaussian process modeling is a standard tool for building emulators for computer experiments, which are usually used to study deterministic functions, for example, a solution to a given system of partial differential equations. This work…
We address the issue of quantifying the non-Gaussian character of a bosonic quantum state and introduce a non-Gaussianity measure based on the Hilbert-Schmidt distance between the state under examination and a reference Gaussian state. We…
The stochastic variational approach for geophysical fluid dynamics was introduced by Holm (Proc Roy Soc A, 2015) as a framework for deriving stochastic parameterisations for unresolved scales. This paper applies the variational stochastic…
In this paper, we derive a novel procedure for set-membership estimation of dynamical systems affected by stochastic noise with unbounded support. Employing a bound on the sample covariance matrix, we are able to provide a finite- sample…
This work aims at identifying and quantifying uncertainties related to elastic and viscoelastic parameters, which characterize the arterial wall behavior, in one-dimensional modeling of the human arterial hemodynamics. The chosen uncertain…
Models and methods that are able to accurately and efficiently predict the flows of low-speed rarefied gases are in high demand, due to the increasing ability to manufacture devices at micro and nano scales. One such model and method is a…
The homotopy analysis method known from its successful applications to obtain quasi-analytical approximations of solutions of ordinary and partial differential equations is applied to stochastic differential equations with Gaussian…
How to distinguish and quantify deterministic and random influences on the statistics of turbulence data in meteorology cases is discussed from first principles. Liquid water path (LWP) changes in clouds, as retrieved from radio signals,…
For a model nonlinear dynamical system, we show how one may obtain its bifurcation behavior by introducing noise into the dynamics and then studying the resulting Langevin dynamics in the weak-noise limit. A suitable quantity to capture the…
Inferring the driving equations of a dynamical system from population or time-course data is important in several scientific fields such as biochemistry, epidemiology, financial mathematics and many others. Despite the existence of…
The article focuses on determining the predictive uncertainty of a model on the example of atrial fibrillation detection problem by a single-lead ECG signal. To this end, the model predicts parameters of the beta distribution over class…
An uncertainty inequality is presented that establishes a lower limit for the product of the variance of the time-averaged intensity of a mode of a quantized electromagnetic field and the degree of its spatial localization. The lower limit…
Inverse problems in physical or biological sciences often involve recovering an unknown parameter that is random. The sought-after quantity is a probability distribution of the unknown parameter, that produces data that aligns with…
Gaussian process is a theoretically appealing model for nonparametric analysis, but its computational cumbersomeness hinders its use in large scale and the existing reduced-rank solutions are usually heuristic. In this work, we propose a…
In this work, we present methodologies for the quantification of confidence in bottom-up coarse-grained models for molecular and macromolecular systems. Coarse-graining methods have been extensively used in the past decades in order to…
We present a dynamical description of slow relaxation processes based on the extension of Onsager's fluctuation theory to systems in local quasi-equilibrium. A non-Markovian Fokker-Planck equation for the conditional probability density is…
Parameter inference of dynamical systems is a challenging task faced by many researchers and practitioners across various fields. In many applications, it is common that only limited variables are observable. In this paper, we propose a…