相关论文: A Bi-fidelity Ensemble Kalman Method for PDE-Const…

In this work, we develop a multi-fidelity Bayesian experimental design framework to efficiently quantify the extreme-event statistics of an input-to-response (ItR) system with given input probability and expensive function evaluations. The…

The ensemble Kalman filter (EnKF) (Evensen, 2009) has proven effective in quantifying uncertainty in a number of challenging dynamic, state estimation, or data assimilation, problems such as weather forecasting and ocean modeling. In these…

Ensemble Kalman inversion is a parallelizable methodology for solving inverse or parameter estimation problems. Although it is based on ideas from Kalman filtering, it may be viewed as a derivative-free optimization method. In its most…

We propose a new class of filtering and smoothing methods for inference in high-dimensional, nonlinear, non-Gaussian, spatio-temporal state-space models. The main idea is to combine the ensemble Kalman filter and smoother, developed in the…

We propose a methodology to address two analysis problems concerning complex systems, namely bounding state functionals of stochastic differential equations (SDEs) and verifying set avoidance of systems described by partial differential…

Bayesian experimental design (BED) for complex physical systems is often limited by the nested inference required to estimate the expected information gain (EIG) or its gradients. Each outer sample induces a different posterior, creating a…

We develop an efficient and reliable adaptive finite element method (AFEM) for the nonlinear Poisson-Boltzmann equation (PBE). We first examine the regularization technique of Chen, Holst, and Xu; this technique made possible the first a…

This paper focuses on inverse problems to identify parameters by incorporating information from measurements. These generally ill-posed problems are formulated here in a probabilistic setting based on Bayes's theorem because it leads to a…

The present paper proposes a Bayesian framework for inverse problems that seamlessly integrates optimization and inversion to enable rapid surrogate modeling, accurate parameter inference, and rigorous uncertainty quantification. Bayesian…

Accurately reconstructing and forecasting high-resolution (HR) states from computationally cheap low-resolution (LR) observations is central to estimation-and-control of spatio-temporal PDE systems. We develop a unified superresolution…

The scaled boundary finite element method (SBFEM) is a relatively recent boundary element method that allows the approximation of solutions to PDEs without the need of a fundamental solution. A theoretical framework for the convergence…

Ensemble methods have become ubiquitous for the solution of Bayesian inference problems. State-of-the-art Langevin samplers such as the Ensemble Kalman Sampler (EKS), Affine Invariant Langevin Dynamics (ALDI) or its extension using weighted…

The increasing availability of data presents an opportunity to calibrate unknown parameters which appear in complex models of phenomena in the biomedical, physical and social sciences. However, model complexity often leads to…

Among the class of nonlinear particle filtering methods, the Ensemble Kalman Filter (EnKF) has gained recent attention for its use in solving inverse problems. We review the original method and discuss recent developments in particular in…

This paper extends the ensemble Kalman filter (EnKF) for inverse problems to identify trending model coefficients. This is done by repeatedly inflating the ensemble while maintaining the mean of the particles. As a benchmark serves a…

The fundamental computational issues in Bayesian inverse problems (BIP) governed by partial differential equations (PDEs) stem from the requirement of repeated forward model evaluations. A popular strategy to reduce such costs is to replace…

Applications of free-flying robots range from entertainment purposes to aerospace applications. The control algorithm for such systems requires accurate estimation of their states based on sensor feedback. The objective of this paper is to…

Bayesian models have many desirable properties, most notable is their ability to generalize from limited data and to properly estimate the uncertainty in their predictions. However, these benefits come at a steep computational cost as…

Likelihood-free Bayesian inference algorithms are popular methods for calibrating the parameters of complex, stochastic models, required when the likelihood of the observed data is intractable. These algorithms characteristically rely…

Ensemble Kalman Inversion (EKI) has been a very popular algorithm used in Bayesian inverse problems. It samples particles from a prior distribution, and introduces a motion to move the particles around in pseudo-time. As the pseudo-time…