相关论文: Non-linear Gaussian smoothing with Taylor moment e…

We consider the problem of joint learning of multiple linear dynamical systems. This has received significant attention recently under different types of assumptions on the model parameters. The setting we consider involves a collection of…

We present and analyze a structure-preserving method for the approximation of solutions to nonlinear cross-diffusion systems, which combines a Local Discontinuous Galerkin spatial discretization with the backward Euler time-stepping scheme.…

In this paper, we consider two distinct challenges in the resolution of nonsmooth stochastic optimization. Of these, the first pertains to the pronounced dependence of dimension in Gaussian smoothing-enabled zeroth-order schemes, impeding…

Computational multi-scale methods capitalize on a large time-scale separation to efficiently simulate slow dynamics over long time intervals. For stochastic systems, one often aims at resolving the statistics of the slowest dynamics. This…

In this paper, we prove convergence rates for time discretisation schemes for semi-linear stochastic evolution equations with additive or multiplicative Gaussian noise, where the leading operator $A$ is the generator of a strongly…

In this work we develop a scalable computational framework for the solution of PDE-constrained optimal control under high-dimensional uncertainty. Specifically, we consider a mean-variance formulation of the control objective and employ a…

Using state-space representation, mobile object positioning problems can be described as dynamic systems, with the state representing the unknown location and the observations being the information gathered from the location sensors. For…

Gaussian smoothing (GS) is a derivative-free optimization (DFO) algorithm that estimates the gradient of an objective using perturbations of the current parameters sampled from a standard normal distribution. We generalize it to sampling…

A new truncation scheme based on the cumulant expansion of the one-particle phase-space distribution function for dark matter particles is developed. Extending the method of moments in relativistic kinetic theory, we derive evolution…

Recent work suggests unstable recurrent solutions of the equations governing fluid flow can play an important role in structuring the dynamics of turbulence. Here we present a method for detecting intervals of time where turbulence…

We introduce a nonlinear generalized tensorial Maxwell-type constitutive equation to describe shear-thinning glass-forming fluids, motivated by a recent microscopic approach to the nonlinear rheology of colloidal suspensions. The model…

In this work, we propose a nonlinear stabilization technique for scalar conservation laws with implicit time stepping. The method relies on an artificial diffusion method, based on a graph-Laplacian operator. It is nonlinear, since it…

This paper develops meshless methods for probabilistically describing discretisation error in the numerical solution of partial differential equations. This construction enables the solution of Bayesian inverse problems while accounting for…

We propose two nonlinear Kalman smoothers that rely on Student's t distributions. The T-Robust smoother finds the maximum a posteriori likelihood (MAP) solution for Gaussian process noise and Student's t observation noise, and is extremely…

We apply the linear delta expansion to the quantum mechanical version of the slow rollover transition which is an important feature of inflationary models of the early universe. The method, which goes beyond the Gaussian approximation,…

In this paper we investigate a sub-diffusion equation for simulating the anomalous diffusion phenomenon in real physical environment. Based on an equivalent transformation of the original sub-diffusion equation followed by the use of a…

We study the problem of parameter estimation for a univariate discretely observed ergodic diffusion process given as a solution to a stochastic differential equation. The estimation procedure we propose consists of two steps. In the first…

We propose an alternative approach towards cost mitigation in volatility-managed portfolios based on smoothing the predictive density of an otherwise standard stochastic volatility model. Specifically, we develop a novel variational Bayes…

Whitening is a classical technique in unsupervised learning that can facilitate estimation tasks by standardizing data. An important application is the estimation of latent variable models via the decomposition of tensors built from…

The paper studies the optimal density steering problem for nonlinear continuous-time stochastic systems. To accurately capture nonlinear dynamics in high-uncertainty regions that deviate significantly from a nominal linearization point, we…