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We study the Allen-Cahn equation with a cubic-quintic nonlinear term and a stochastic $Q$-trace-class stochastic forcing in two spatial dimensions. This stochastic partial differential equation (SPDE) is used as a test case to understand,…
We derive computable error estimates for finite element approximations of linear elliptic partial differential equations (PDE) with rough stochastic coefficients. In this setting, the exact solutions contain high frequency content that…
We present a space-time multiscale method for a parabolic model problem with an underlying coefficient that may be highly oscillatory with respect to both the spatial and the temporal variables. The method is based on the framework of the…
We consider the problem of extracting a low-dimensional, linear latent variable structure from high-dimensional random variables. Specifically, we show that under mild conditions and when this structure manifests itself as a linear space…
Considering stochastic partial differential equations of parabolic type with random coefficients in vector-valued H\"older spaces, we obtain a sharp Schauder estimate. As an application, the existence and uniqueness of solution to the…
The article deals with the problem of synthesis of an adaptive observer of state variables of a linear time-varying SISO dynamic system. It is assumed that the control signal and the output variable are measurable. It is assumed that the…
This paper introduces an adaptive time splitting technique for the solution of stiff evolutionary PDEs that guarantees an effective error control of the simulation, independent of the fastest physical time scale for highly unsteady…
Correlated with the trend of increasing degrees of freedom in robotic systems is a similar trend of rising interest in Spatio-Temporal systems described by Partial Differential Equations (PDEs) among the robotics and control communities.…
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 studies the problem of estimating a large coefficient matrix in a multiple response linear regression model when the coefficient matrix could be both of low rank and sparse in the sense that most nonzero entries concentrate on a…
Parametric estimation of stochastic differential equations (SDEs) has been a subject of intense studies already for several decades. The Heston model for instance is driven by two coupled SDEs and is often used in financial mathematics for…
This paper addresses the problem of estimating the modes of an observed non-stationary mixture signal in the presence of an arbitrary distributed noise. A novel Bayesian model is introduced to estimate the model parameters from the…
Stochastic partial differential equations (SPDEs) are ubiquitous in engineering and computational sciences. The stochasticity arises as a consequence of uncertainty in input parameters, constitutive relations, initial/boundary conditions,…
We study non-parametric estimation of choice models, which were introduced to alleviate unreasonable assumptions in traditional parametric models, and are prevalent in several application areas. Existing literature focuses only on the…
In various practical situations, we encounter data from stochastic processes which can be efficiently modelled by an appropriate parametric model for subsequent statistical analyses. Unfortunately, the most common estimation and inference…
We propose an improved method for estimating partial differential equations and delay partial differential equations from data, using Bayesian optimization and the Bayesian information criterion to automatically find suitable…
For parameter identification problems the Fr\'echet-derivative of the parameter-to-state map is of particular interest. In many applications, e.g. in seismic tomography, the unknown quantity is modeled as a coefficient in a linear…
We propose an adaptive Hermite spectral method for the three-dimensional velocity space of the Boltzmann equation guided by a newly developed frequency indicator. For the homogeneous problem, the indicator is defined by the contribution of…
This paper aims to investigate the numerical approximation of a general second order parabolic stochastic partial differential equation(SPDE) driven by multiplicative and additive noise. Our main interest is on such SPDEs where the…
In this work, we propose a novel probabilistic sequence model that excels at capturing high variability in time series data, both across sequences and within an individual sequence. Our method uses temporal latent variables to capture…