Related papers: Stochastic parareal: an application of probabilist…
Gaussian processes are a powerful framework for quantifying uncertainty and for sequential decision-making but are limited by the requirement of solving linear systems. In general, this has a cubic cost in dataset size and is sensitive to…
Probabilistic numerical solvers for ordinary differential equations (ODEs) treat the numerical simulation of dynamical systems as problems of Bayesian state estimation. Aside from producing posterior distributions over ODE solutions and…
Sample-based Bayesian inference provides a route to uncertainty quantification in the geosciences, and inverse problems in general, though is very computationally demanding in the naive form that requires simulating an accurate computer…
A widely used heuristic for solving stochastic optimization problems is to use a deterministic rolling horizon procedure, which has been modified to handle uncertainty (e.g. buffer stocks, schedule slack). This approach has been criticized…
We consider stochastic algorithms derived from methods for solving deterministic optimization problems, especially comparison-based algorithms derived from stochastic approximation algorithms with a constant step-size. We develop a…
This paper is dedicated to enhancing the computational efficiency of traditional parallel-in-time methods for solving stochastic initial-value problems. The standard parareal algorithm often suffers from slow convergence when applied to…
Stochastic optimization algorithms update models with cheap per-iteration costs sequentially, which makes them amenable for large-scale data analysis. Such algorithms have been widely studied for structured sparse models where the sparsity…
We consider learning problems over training sets in which both, the number of training examples and the dimension of the feature vectors, are large. To solve these problems we propose the random parallel stochastic algorithm (RAPSA). We…
We present adaptive sequential SAA (sample average approximation) algorithms to solve large-scale two-stage stochastic linear programs. The iterative algorithm framework we propose is organized into \emph{outer} and \emph{inner} iterations…
The stochastic interpolant framework offers a powerful approach for constructing generative models based on ordinary differential equations (ODEs) or stochastic differential equations (SDEs) to transform arbitrary data distributions.…
There is a recent interest on first-order methods for linear programming (LP). In this paper,we propose a stochastic algorithm using variance reduction and restarts for solving sharp primal-dual problems such as LP. We show that the…
While recent advances in deep learning have shown promising efficiency gains in solving time-dependent partial differential equations (PDEs), matching the accuracy of conventional numerical solvers still remains a challenge. One strategy to…
For time-dependent partial differential equations, parallel-in-time integration using the "parallel full approximation scheme in space and time" (PFASST) is a promising way to accelerate existing space-parallel approaches beyond their…
Physical models with uncertain inputs are commonly represented as parametric partial differential equations (PDEs). That is, PDEs with inputs that are expressed as functions of parameters with an associated probability distribution.…
In this paper, we present a method that enables solving in parallel the Euler-Lagrange system associated with the optimal control of a parabolic equation. Our approach is based on an iterative update of a sequence of intermediate targets…
In this work (Part I), we study three time-discretization procedures of the Dynamical Low-Rank Approximation (DLRA) of high-dimensional stochastic differential equations (SDEs). Specifically, we consider the Dynamically Orthogonal (DO)…
Stochastic sampling methods are arguably the most direct and least intrusive means of incorporating parametric uncertainty into numerical simulations of partial differential equations with random inputs. However, to achieve an overall error…
We consider an $n$ agents distributed optimization problem with imperfect information characterized in a parametric sense, where the unknown parameter can be solved by a distinct distributed parameter learning problem. Though each agent…
We present the Wavelet-based Edge Multiscale Parareal (WEMP) Algorithm, recently proposed in [Li and Hu, {\it J. Comput. Phys.}, 2021], for efficiently solving subdiffusion equations with heterogeneous coefficients in long time. This…
Time-varying stochastic optimization problems frequently arise in machine learning practice (e.g. gradual domain shift, object tracking, strategic classification). Although most problems are solved in discrete time, the underlying process…