Related papers: Joint Maximum a Posteriori State Path and Paramete…

Although the governing equations of many systems, when derived from first principles, may be viewed as known, it is often too expensive to numerically simulate all the interactions they describe. Therefore researchers often seek simpler…

In this work, we derive the maximum a posteriori (MAP) symbol detector for a multiple-input multiple-output system in the presence of Wiener phase noise due to noisy local oscillators. As in single-antenna systems, the computation of the…

This work aims efficiently estimating the posterior distribution of kinetic parameters for dynamic positron emission tomography (PET) imaging given a measurement of time of activity curve. Considering the inherent information loss from…

This study addresses the inverse problem of parameter estimation for Stochastic Differential Equations (SDEs) by minimizing a regularized discrepancy functional via Stochastic Gradient Descent (SGD). To achieve computational efficiency, we…

Motivated by emerging technologies for energy efficient analog computing and continuous-time processing, this paper proposes continuous-time minimum mean squared error estimation for multiple-input multiple-output (MIMO) systems based on an…

We study the dynamics of a continuous-time model of the Stochastic Gradient Descent (SGD) for the least-square problem. Indeed, pursuing the work of Li et al. (2019), we analyze Stochastic Differential Equations (SDEs) that model SGD either…

The measured spatiotemporal response of various physical processes is utilized to infer the governing partial differential equations (PDEs). We propose SimultaNeous Basis Function Approximation and Parameter Estimation (SNAPE), a technique…

For adaptive mixed finite element methods (AMFEM), we first introduce the data oscillation to analyze, without the restriction that the inverse of the coefficient matrix of the partial differential equations (PDEs) is a piecewise polynomial…

The mean square error (MSE)-optimal estimator is known to be the conditional mean estimator (CME). This paper introduces a parametric channel estimation technique based on Bayesian estimation. This technique uses the estimated channel…

We propose a variational autoencoder (VAE) approach for parameter estimation in nonlinear mixed-effects models based on ordinary differential equations (NLME-ODEs) using longitudinal data from multiple subjects. In moderate dimensions,…

The paper proposes a systematic framework for building data-driven stochastic differential equation (SDE) models from sparse, noisy observations. Unlike traditional parametric approaches, which assume a known functional form for the drift,…

We propose an optimization formulation for the simultaneous estimation of a latent variable and the identification of a linear continuous-time dynamic system, given a single input-output pair. We justify this approach based on Bayesian…

In this paper we study the problem of estimating the drift/viscosity coefficient for a large class of linear, parabolic stochastic partial differential equations (SPDEs) driven by an additive space-time noise. We propose a new class of…

This paper is concerned with high moment and pathwise error estimates for both velocity and pressure approximations of the Euler-Maruyama scheme for time discretization and its two fully discrete mixed finite element discretizations. The…

Estimating the parameters of max-stable parametric models poses significant challenges, particularly when some parameters lie on the boundary of the parameter space. This situation arises when a subset of variables exhibits extreme values…

We present an algorithm for the efficient sampling of conditional paths of stochastic differential equations (SDEs). While unconditional path sampling of SDEs is straightforward, albeit expensive for high dimensional systems of SDEs,…

In this work, we present methods for state estimation in continuous-discrete nonlinear systems involving stochastic differential equations. We present the extended Kalman filter, the unscented Kalman filter, the ensemble Kalman filter, and…

We consider the numerical approximation of general semilinear parabolic stochastic partial differential equations (SPDEs) driven by additive space-time noise. In contrast to the standard time stepping methods which uses basic increments of…

Real-time sea state estimation is vital for applications like shipbuilding and maritime safety. Traditional methods rely on accurate wave-vessel transfer functions to estimate wave spectra from onboard sensors. In contrast, our approach…

We derive globally reliable a posteriori error estimators for a PDE-constrained optimization problem involving linear models in fluid dynamics as state equation; control constraints are also considered. The corresponding local error…