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We present a proximal algorithm that performs a variational recursion on the space of joint probability measures to propagate the stochastic uncertainties in power system dynamics over high dimensional state space. The proposed algorithm…
We present a computationally efficient framework, called $\texttt{FlowDRO}$, for solving flow-based distributionally robust optimization (DRO) problems with Wasserstein uncertainty sets while aiming to find continuous worst-case…
We study a nonlinear, degenerate cross-diffusion model which involves two densities with two different drift velocities. A general framework is introduced based on its gradient flow structure in Wasserstein space to derive a notion of…
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…
Efficiently and accurately simulating partial differential equations (PDEs) in and around arbitrarily defined geometries, especially with high levels of adaptivity, has significant implications for different application domains. A key…
Applications in quantitative finance such as optimal trade execution, risk management of options, and optimal asset allocation involve the solution of high dimensional and nonlinear Partial Differential Equations (PDEs). The connection…
This paper solves the discretised multiphase flow equations using tools and methods from machine-learning libraries. The idea comes from the observation that convolutional layers can be used to express a discretisation as a neural network…
We investigate the single-point velocity probability density function (PDF) in three-dimensional fully developed homogeneous isotropic turbulence within the framework of PDF equations focussing on deviations from Gaussianity. A joint…
Natural gas consumption by users of pipeline networks is subject to increasing uncertainty that originates from the intermittent nature of electric power loads serviced by gas-fired generators. To enable computationally efficient…
In this paper, we propose stochastic structure-preserving schemes to compute the effective diffusivity for particles moving in random flows. We first introduce the motion of particles using the Lagrangian formulation, which is modeled by…
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…
We devise a distributed asynchronous stochastic epsilon-gradient-based algorithm to enable a network of computing and communicating nodes to solve a constrained discrete-time time-varying stochastic convex optimization problem. Each node…
Motivated by the modeling of the spatial structure of the velocity field of three-dimensional turbulent flows, and the phenomenology of cascade phenomena, a linear dynamics has been recently proposed able to generate high velocity gradients…
We study a model of crowd motion following a gradient vector field, with possibly additional interaction terms such as attraction/repulsion, and we present a numerical scheme for its solution through a Lagrangian discretization. The density…
The superior performance of ensemble methods with infinite models are well known. Most of these methods are based on optimization problems in infinite-dimensional spaces with some regularization, for instance, boosting methods and convex…
We propose a variational finite volume scheme to approximate the solutions to Wasserstein gradient flows. The time discretization is based on an implicit linearization of the Wasserstein distance expressed thanks to Benamou-Brenier formula,…
Wasserstein gradient flows are continuous time dynamics that define curves of steepest descent to minimize an objective function over the space of probability measures (i.e., the Wasserstein space). This objective is typically a divergence…
Many physical questions in fluid dynamics can be recast in terms of norm constrained optimisation problems; which in-turn, can be further recast as unconstrained problems on spherical manifolds. Due to the nonlinearities of the governing…
We introduce a simple, rigorous, and unified framework for solving nonlinear partial differential equations (PDEs), and for solving inverse problems (IPs) involving the identification of parameters in PDEs, using the framework of Gaussian…
We consider Markov models of large-scale networks where nodes are characterized by their local behavior and by a mobility model over a two-dimensional lattice. By assuming random walk, we prove convergence to a system of partial…