Related papers: A pathwise parameterisation for stochastic transpo…
In this paper, we study a semi-martingale optimal transport problem and its application to the calibration of Local-Stochastic Volatility (LSV) models. Rather than considering the classical constraints on marginal distributions at initial…
We study a novel alternative approach for the computation of transport coefficients at mesoscales. While standard nonequilibrium molecular dynamics (NEMD) approaches fix the forcing and measure the average induced flux in the system driven…
The PARAFAC2 is a multimodal factor analysis model suitable for analyzing multi-way data when one of the modes has incomparable observation units, for example because of differences in signal sampling or batch sizes. A fully probabilistic…
Fluids can behave in a highly irregular, turbulent way. It has long been realised that, therefore, some weak notion of solution is required when studying the fundamental partial differential equations of fluid dynamics, such as the…
We present the fundamentals of a measure transport approach to sampling. The idea is to construct a deterministic coupling---i.e., a transport map---between a complex "target" probability measure of interest and a simpler reference measure.…
This paper investigates the pathwise uniform convergence in probability of fully discrete finite-element approximations for the two-dimensional stochastic Navier-Stokes equations with multiplicative noise, subject to no-slip boundary…
A new vehicular traffic flow model based on a stochastic jump process in vehicle acceleration and braking is introduced. It is based on a master equation for the single car probability density in space, velocity and acceleration with an…
A machine-learning strategy for investigating the stability of fluid flow problems is proposed herein. The goal is to provide a simple yet robust methodology to find a nonlinear mapping from the parametric space to an indicator representing…
We introduce and test methods for the calibration of the diffusion term in Stochastic Partial Differential Equations (SPDEs) describing fluids. We take two approaches, one uses ideas from the singular value decomposition and the Biot-Savart…
This paper introduces a randomized tamed Euler scheme tailored for L\'evy-driven stochastic differential equations (SDEs) with superlinear random coefficients and Carath\'eodory-type drift. Under assumptions that allow for time-irregular…
We propose a mathematical methodology to derive a stochastic parameterization of bulk warm cloud micro-physics properties. Unlike previous bulk parameterizations, the stochastic parameterization does not assume any particular droplet size…
In this paper, we are concerned with the quantification of uncertainties that arise from intra-day oscillations in the demand for natural gas transported through large-scale networks. The short-term transient dynamics of the gas flow is…
We study a rather general class of optimal "ballistic" transport problems for matrix-valued measures. These problems naturally arise, in the spirit of \emph{Y. Brenier. Comm. Math. Phys. (2018) 364(2) 579-605}, from a certain dual…
We survey some of our recent results on existence, uniqueness and regularity of function solutions to parabolic and transport type partial differential equations driven by non-differentiable noises. When applied pathwise to random…
The task of sampling from a probability density can be approached as transporting a tractable density function to the target, known as dynamical measure transport. In this work, we tackle it through a principled unified framework using…
Most inverse problems from physical sciences are formulated as PDE-constrained optimization problems. This involves identifying unknown parameters in equations by optimizing the model to generate PDE solutions that closely match measured…
This paper proposes a new stochastic model of traffic dynamics in Lagrangian coordinates. The source of uncertainty is heterogeneity in driving behavior, captured using driver-specific speed-spacing relations, i.e., parametric uncertainty.…
Many dynamical systems are subjected to stochastic influences, such as random excitations, noise, and unmodeled behavior. Tracking the system's state and parameters based on a physical model is a common task for which filtering algorithms,…
We present and study a Particle method for the stationary solutions of a class of transport equations. This method is inspired by non-stationary Particle methods, the time variable being replaced by one spatial variable. Particles…
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…