相关论文: Importance sampling for rare event tracking within…
The Ensemble Kalman Filter (EnKF) belongs to the class of iterative particle filtering methods and can be used for solving control--to--observable inverse problems. In this context, the EnKF is known as Ensemble Kalman Inversion (EKI). In…
Langevin dynamics has found a large number of applications in sampling, optimization and estimation. Preconditioning the gradient in the dynamics with the covariance - an idea that originated in literature related to solving estimation and…
Importance sampling (IS) as an elegant and efficient variance reduction (VR) technique for the acceleration of stochastic optimization problems has attracted many researches recently. Unlike commonly adopted stochastic uniform sampling in…
We study two adaptive importance sampling schemes for estimating the probability of a rare event in the high-dimensional regime $d \to \infty$ with $d$ the dimension. The first scheme is the prominent cross-entropy (CE) method, and the…
Enforcing sparse structure within learning has led to significant advances in the field of data-driven discovery of dynamical systems. However, such methods require access not only to time-series of the state of the dynamical system, but…
An important step in the design of autonomous systems is to evaluate the probability that a failure will occur. In safety-critical domains, the failure probability is extremely small so that the evaluation of a policy through Monte Carlo…
Importance sampling (IS) and numerical integration methods are usually employed for approximating moments of complicated target distributions. In its basic procedure, the IS methodology randomly draws samples from a proposal distribution…
The presence of erratic or unstable paths in standard kinetic Monte Carlo simulations significantly undermines the accurate simulation and sampling of transition pathways. While typically reliable methods, such as the Gillespie algorithm,…
Approximate inference in probability models is a fundamental task in machine learning. Approximate inference provides powerful tools to Bayesian reasoning, decision making, and Bayesian deep learning. The main goal is to estimate the…
Exploiting stochastic path integral theory, we obtain \emph{by simulation} substantial gains in efficiency for the computation of reaction rates in one-dimensional, bistable, overdamped stochastic systems. Using a well-defined measure of…
We present an Extended Kalman Filter framework for system identification and control of a stochastic high-dimensional epidemic model. The scale and severity of the COVID-19 emergency have highlighted the need for accurate forecasts of the…
We present a novel algorithm based on the ensemble Kalman filter to solve inverse problems involving multiscale elliptic partial differential equations. Our method is based on numerical homogenization and finite element discretization and…
The inefficiency of using an unbiased estimator in a Monte Carlo procedure can be quantified using an inefficiency constant, equal to the product of the variance of the estimator and its mean computational cost. We develop methods for…
In areas such as finance, engineering, and science, we often face situations that change quickly and unpredictably. These situations are tough to handle and require special tools and methods capable of understanding and predicting what…
The ensemble Kalman filter (EnKF) has become a standard methodology for state estimation in high-dimensional systems, yet its various stochastic and deterministic formulations often appear conceptually disconnected. In this paper, a unified…
Although many computational methods for rare event sampling exist, this type of calculation is not usually practical for general nonequilibrium conditions, with macroscopically irreversible dynamics and away from both stationary and…
We study the Extended Kalman Filter in constant dynamics, offering a bayesian perspective of stochastic optimization. We obtain high probability bounds on the cumulative excess risk in an unconstrained setting. In order to avoid any…
This paper uses a probabilistic approach to analyze the converge of an ensemble Kalman filter solution to an exact Kalman filter solution in the simplest possible setting, the scalar case, as it allows us to build upon a rich literature of…
Multifidelity modeling has been steadily gaining attention as a tool to address the problem of exorbitant model evaluation costs that makes the estimation of failure probabilities a significant computational challenge for complex real-world…
Importance sampling (IS) is a powerful Monte Carlo methodology for the approximation of intractable integrals, very often involving a target probability density function. The performance of IS heavily depends on the appropriate selection of…