Related papers: Stochastic model reduction for slow-fast systems w…
Traditional methods for solving linear systems have quickly become impractical due to an increase in the size of available data. Utilizing massive amounts of data is further complicated when the data is incomplete or has missing entries. In…
We propose new continuous-time formulations for first-order stochastic optimization algorithms such as mini-batch gradient descent and variance-reduced methods. We exploit these continuous-time models, together with simple Lyapunov analysis…
The diffusion of molecules in complex intracellular environments can be strongly influenced by spatial heterogeneity and stochasticity. A key challenge when modelling such processes using stochastic random walk frameworks is that negative…
A reduced chemical scheme involving a small number of variables is often sufficient to account for the deterministic evolution of the concentrations of the main species contributing to a reaction. However its predictions are questionable in…
In this paper, we study stochastic homogenization of a coupled diffusion-reaction system. The diffusion-reaction system is coupled to stochastic differential equations, which govern the changes in the media properties. Though homogenization…
We introduce a variant of the asymmetric random average process with continuous state variables where the maximal transport is restricted by a cutoff. For periodic boundary conditions, we show the existence of a phase transition between a…
Data-driven reduced order modeling of chaotic dynamics can result in systems that either dissipate or diverge catastrophically. Leveraging non-linear dimensionality reduction of autoencoders and the freedom of non-linear operator inference…
We consider a class of stochastic programming problems where the implicitly decision-dependent random variable follows a nonparametric regression model with heteroscedastic error. The Clarke subdifferential and surrogate functions are not…
We construct a finite element approximation of a strain-limiting elastic model on a bounded open domain in $\mathbb{R}^d$, $d \in \{2,3\}$. The sequence of finite element approximations is shown to exhibit strong convergence to the unique…
We study a family of numerical schemes applied to a class of multiscale systems of stochastic differential equations. When the time scale separation parameter vanishes, a well-known homogenization or Wong--Zakai diffusion approximation…
A surrogate model approximates the outputs of a solver of Partial Differential Equations (PDEs) with a low computational cost. In this article, we propose a method to build learning-based surrogates in the context of parameterized PDEs,…
We present a scalable methodology to verify stochastic hybrid systems. Using the Mori-Zwanzig reduction method, we construct a finite state Markov chain reduction of a given stochastic hybrid system and prove that this reduced Markov chain…
We study decision dependent distributionally robust optimization models, where the ambiguity sets of probability distributions can depend on the decision variables. These models arise in situations with endogenous uncertainty. The developed…
We give the first mathematically rigorous analysis of an emerging approach to finite element analysis (see, e.g., Bauer et al. [Appl. Numer. Math., 2017]), which we hereby refer to as the surrogate matrix methodology. This methodology is…
Time distributed optimization is an implementation strategy that can significantly reduce the computational burden of model predictive control by exploiting its robustness to incomplete optimization. When using this strategy, optimization…
For microscale heterogeneous PDEs, this article further develops novel theory and methodology for their macroscale mathematical/asymptotic homogenization. This article specifically encompasses the case of quasi-periodic heterogeneity with…
Different stochastic extensions of hybrid automata have been proposed in the past, with unclear expressivity relations between them. To structure and relate these modeling languages, in this paper we formalize two alternative approaches to…
We address the application of stochastic optimization methods for the simultaneous control of parameter-dependent systems. In particular, we focus on the classical Stochastic Gradient Descent (SGD) approach of Robbins and Monro, and on the…
We present and characterize a method to accelerate the relaxation of a Brownian object between two distinct equilibrium states. Instead of relying on a deterministic time-dependent control parameter, we use stochastic resetting to guide and…
We develop the method of stochastic modified equations (SME), in which stochastic gradient algorithms are approximated in the weak sense by continuous-time stochastic differential equations. We exploit the continuous formulation together…