Related papers: Discrete gradients for computational Bayesian infe…
A crucial task in predictive maintenance is estimating the remaining useful life of physical systems. In the last decade, deep learning has improved considerably upon traditional model-based and statistical approaches in terms of predictive…
Approximate Bayesian inference methods that scale to very large datasets are crucial in leveraging probabilistic models for real-world time series. Sparse Markovian Gaussian processes combine the use of inducing variables with efficient…
Kalman filtering and smoothing are the foundational mechanisms for efficient inference in Gauss-Markov models. However, their time and memory complexities scale prohibitively with the size of the state space. This is particularly…
Practical Bayes filters often assume the state distribution of each time step to be Gaussian for computational tractability, resulting in the so-called Gaussian filters. When facing nonlinear systems, Gaussian filters such as extended…
We perform a numerical approximation of coherent sets in finite-dimensional smooth dynamical systems by computing singular vectors of the transfer operator for a stochastically perturbed flow. This operator is obtained by solution of a…
Modelling incompressible ideal fluids as a finite collection of vortex filaments is important in physics (super-fluidity, models for the onset of turbulence) as well as for numerical algorithms used in computer graphics for the real time…
A widely used method to create a continuous representation of a discrete data-set is regression analysis. When the regression model is not based on a mathematical description of the physics underlying the data, heuristic techniques play a…
We consider finite-volume approximations of Fokker-Planck equations on bounded convex domains in $\mathbb{R}^d$ and study the corresponding gradient flow structures. We reprove the convergence of the discrete to continuous Fokker-Planck…
A computational tool for coarse-graining nonlinear systems of ordinary differential equations in time is discussed. Three illustrative model examples are worked out that demonstrate the range of capability of the method. This includes the…
A new and very general technique for simulating solid-fluid suspensions is described; its most important feature is that the computational cost scales linearly with the number of particles. The method combines Newtonian dynamics of the…
We study an approximation method for the one-dimensional nonlinear filtering problem, with discrete time and continuous time observation. We first present the method applied to the Fokker-Planck equation. The convergence of the…
A new method that enables easy and convenient discretization of partial differential equations with derivatives of arbitrary real order (so-called fractional derivatives) and delays is presented and illustrated on numerical solution of…
Discrete gradient methods are geometric integration techniques that can preserve the dissipative structure of gradient flows. Due to the monotonic decay of the function values, they are well suited for general convex and nonconvex…
In this paper we present a novel inference methodology to perform Bayesian inference for spatiotemporal Cox processes where the intensity function depends on a multivariate Gaussian process. Dynamic Gaussian processes are introduced to…
We propose and analyze a mixed formulation for the Brinkman-Forchheimer equations for unsteady flows. Our approach is based on the introduction of a pseudostress tensor related to the velocity gradient, leading to a mixed formulation where…
This paper introduces a novel approach to compute the numerical fluxes at the cell boundaries for a cell-centered conservative numerical scheme. Explicit gradients used in deriving the reconstruction polynomials are replaced by high-order…
Attaining reliable profile gradients is of utmost relevance for many physical systems. In most situations, the estimation of gradient can be inaccurate due to noise. It is common practice to first estimate the underlying system and then…
We develop fully noncommutative Feynman-Kac formulae by employing quantum stochastic processes. To this end we establish some theory for perturbing quantum stochastic flows on von Neumann algebras by multiplier cocycles. Multiplier cocycles…
Bayesian calibration is widely used for inverse analysis and uncertainty analysis for complex systems in the presence of both computer models and observation data. In the present work, we focus on large-scale fluid-structure interaction…
Including the effect of thermal fluctuations in traditional computational fluid dynamics requires developing numerical techniques for solving the stochastic partial differential equations of fluctuating hydrodynamics. These Langevin…