Related papers: Data-driven computation methods for quasi-stationa…
We present a method to compute the stochastic reachability safety probabilities for high-dimensional stochastic dynamical systems. Our approach takes advantage of a nonparametric learning technique known as conditional distribution…
We study a class of multi-species birth-and-death processes going almost surely to extinction and admitting a unique quasi-stationary distribution (qsd for short). When rescaled by $K$ and in the limit $K\to+\infty$, the realizations of…
Though quasi-Newton methods have been extensively studied in the literature, they either suffer from local convergence or use a series of line searches for global convergence which is not acceptable in the distributed setting. In this work,…
Computer experiments are becoming increasingly important in scientific investigations. In the presence of uncertainty, analysts employ probabilistic sensitivity methods to identify the key-drivers of change in the quantities of interest.…
Many stochastic optimization problems include chance constraints that enforce constraint satisfaction with a specific probability; however, solving an optimization problem with chance constraints assumes that the solver has access to the…
This paper develops solutions of fractional Fokker-Planck equations describing subdiffusion of probability densities of stochastic dynamical systems driven by non-Gaussian L\'evy processes, with space-time-dependent drift, diffusion and…
Covariance matrix estimation is an important problem in multivariate data analysis, both from theoretical as well as applied points of view. Many simple and popular covariance matrix estimators are known to be severely affected by model…
This paper presents a robust version of the stratified sampling method when multiple uncertain input models are considered for stochastic simulation. Various variance reduction techniques have demonstrated their superior performance in…
Stochastic transport processes on networked domains (modelled on metric graphs) arise in a variety of applications where diffusion and drift mechanisms interact with an underlying graph structure. The Fokker--Planck equation provides a…
Statistical (machine learning) tools for equation discovery require large amounts of data that are typically computer generated rather than experimentally observed. Multiscale modeling and stochastic simulations are two areas where learning…
Stochastic partial differential equations (SPDEs) have become a key modelling tool in applications. Yet, there are many classes of SPDEs, where the existence and regularity theory for solutions is not completely developed. Here we…
Multifidelity methods are widely used for estimating quantities of interest (QoI) in computational science by employing numerical simulations of differing costs and accuracies. Many methods approximate numerical-valued statistics that…
Accurate approximation of probability measures is essential in numerical applications. This paper explores the quantization of probability measures using the maximum mean discrepancy (MMD) distance as a guiding metric. We first investigate…
Stochastic differential equations play an important role in various applications when modeling systems that have either random perturbations or chaotic dynamics at faster time scales. The time evolution of the probability distribution of a…
We formulate a data-driven method for constructing finite volume discretizations of a dynamical system's underlying Continuity / Fokker-Planck equation. A method is employed that allows for flexibility in partitioning state space,…
Stochastic models of chemical systems are often analysed by solving the corresponding Fokker-Planck equation which is a drift-diffusion partial differential equation for the probability distribution function. Efficient numerical solution of…
We develop a new computing paradigm, which we refer to as data-driven computing, according to which calculations are carried out directly from experimental material data and pertinent constraints and conservation laws, such as compatibility…
We demonstrate a data-driven method to solve for the invariant probability density function of a randomly perturbed dynamical system. The key idea is to replace the boundary condition of numerical schemes by a least squares problem…
This paper focuses on finding an approximate solution of a kind of Fokker-Planck equation with time-dependent perturbations. A formulation of the approximate solution of the equation is constructed, and then the existence of the formulation…
We study the long-time behavior of stochastic models with an absorbing state, conditioned on survival. For a large class of processes, in which saturation prevents unlimited growth, statistical properties of the surviving sample attain…