Related papers: Efficient Statistically Accurate Algorithms for th…
This work extends the high-resolution isogeometric analysis approach established for scalar transport equations to the equations of gas dynamics. The group finite element formulation is adopted to obtain an efficient assembly procedure for…
The Fokker-Planck equations describe time evolution of probability densities of stochastic dynamical systems and are thus widely used to quantify random phenomena such as uncertainty propagation. For dynamical systems driven by non-Gaussian…
The Fokker--Planck equation is a key ingredient of many models in physics, and related subjects, and arises in a diverse array of settings. Analytical solutions are limited to special cases, and resorting to numerical simulation is often…
Gaussian mixture filters for nonlinear systems usually rely on severe approximations when calculating mixtures in the prediction and filtering step. Thus, offline approximations of noise densities by Gaussian mixture densities to reduce the…
Machine learning algorithms often struggle to control complex real-world systems. In the case of nuclear fusion, these challenges are exacerbated, as the dynamics are notoriously complex, data is poor, hardware is subject to failures, and…
We introduce a novel numerical scheme for solving the Fokker-Planck equation of discretized Dean-Kawasaki models with a functional tensor network ansatz. The Dean-Kawasaki model describes density fluctuations of interacting particle…
We investigate a numerical behaviour of robust deterministic optimal control problem subject to a convection diffusion equation containing uncertain inputs. Stochastic Galerkin approach, turning the original optimization problem containing…
In this paper, we study efficient approximate sampling for probability distributions known up to normalization constants. We specifically focus on a problem class arising in Bayesian inference for large-scale inverse problems in science and…
High-performance learned image compression codecs require flexible probability models to fit latent representations. Gaussian Mixture Models (GMMs) were proposed to satisfy this demand, but suffer from a significant runtime performance…
In collisionless and weakly collisional plasmas, the particle distribution function is a rich tapestry of the underlying physics. However, actually leveraging the particle distribution function to understand the dynamics of a weakly…
A recently introduced nonlinear Fokker-Planck equation, derived directly from a master equation, comes out as a very general tool to describe phenomenologically systems presenting complex behavior, like anomalous diffusion, in the presence…
In this work, we study a class of nonlocal-in-time kinetic models of incompressible dilute polymeric fluids. The system couples a macroscopic balance of linear momentum equation with a mezoscopic subdiffusive Fokker-Planck equation…
We present a framework, which, from the trajectories detailing the spatiotemporal dynamics of a population, simultaneously reconstructs a transport map as well as the Fokker-Planck equation governing the coarse-grained probability…
In this paper, we introduce an adaptive kernel method for solving the optimal filtering problem. The computational framework that we adopt is the Bayesian filter, in which we recursively generate an optimal estimate for the state of a…
The discrete unified gas kinetic scheme (DUGKS) has emerged as a promising Boltzmann solver capable of effectively capturing flow physics across all Knudsen numbers. However, simulating rarefied flows at high Knudsen numbers remains…
We demonstrate a method which allows the stochastic modelling of quantum systems for which the generalised Fokker-Planck equation in the phase space contains derivatives of higher than second order. This generalises quantum stochastics far…
We describe a general technique that yields the first {\em Statistical Query lower bounds} for a range of fundamental high-dimensional learning problems involving Gaussian distributions. Our main results are for the problems of (1) learning…
This paper deals with Gibbs samplers that include high dimensional conditional Gaussian distributions. It proposes an efficient algorithm that avoids the high dimensional Gaussian sampling and relies on a random excursion along a small set…
In this letter, we present an extensive study of the linearly forced isotropic turbulence. By using analytical method, we identify two parametric choices, of which they seem to be new as far as our knowledge goes. We prove that the…
In this paper, we study numerical methods for the homogenization of linear second-order elliptic equations in nondivergence-form with periodic diffusion coefficients and large drift terms. Upon noting that the effective diffusion matrix can…