相关论文: Data-driven polynomial chaos expansions: a weighte…
This paper discusses a methodology for determining a functional representation of a random process from a collection of scattered pointwise samples. The present work specifically focuses onto random quantities lying in a high dimensional…
In modern process industries, data-driven models are important tools for real-time monitoring when key performance indicators are difficult to measure directly. While accurate predictions are essential, reliable uncertainty quantification…
In this work we introduce a manifold learning-based surrogate modeling framework for uncertainty quantification in high-dimensional stochastic systems. Our first goal is to perform data mining on the available simulation data to identify a…
Uncertainty quantification (UQ) is a crucial but challenging task in many high-dimensional regression or learning problems to increase the confidence of a given predictor. We develop a new data-driven approach for UQ in regression that…
Quasi-Monte Carlo (QMC) integration over unbounded domains $\mathbb{R}^s$ remains challenging due to the high dimensionality of sampling space and the boundary growth of the integrand. In applications such as uncertainty quantification…
Consistency-based methods have emerged as an effective approach to uncertainty quantification (UQ) in large language models. These methods typically rely on several generations obtained via multinomial sampling, measuring their agreement…
The noisy matrix completion problem, which aims to recover a low-rank matrix $\mathbf{X}$ from a partial, noisy observation of its entries, arises in many statistical, machine learning, and engineering applications. In this paper, we…
In this work, we discuss the problem of approximating a multivariate function via $\ell_1$ minimization method, using a random chosen sub-grid of the corresponding tensor grid of Gaussian points. The independent variables of the function…
Fractional statistical moments are utilized for various tasks of uncertainty quantification, including the estimation of probability distributions. However, an estimation of fractional statistical moments of costly mathematical models by…
We provide a framework for the numerical approximation of distributed optimal control problems, based on least-squares finite element methods. Our proposed method simultaneously solves the state and adjoint equations and is $\inf$--$\sup$…
A probabilistic performance-oriented controller design approach based on polynomial chaos expansion and optimization is proposed for flight dynamic systems. Unlike robust control techniques where uncertainties are conservatively handled,…
Coupled problems with various combinations of multiple physics, scales, and domains can be found in numerous areas of science and engineering. A key challenge in the formulation and implementation of corresponding coupled models is to…
In recent years, large language models (LLMs) have become increasingly prevalent, offering remarkable text generation capabilities. However, a pressing challenge is their tendency to make confidently wrong predictions, highlighting the…
The stochastic linear--quadratic regulator problem subject to Gaussian disturbances is well known and usually addressed via a moment-based reformulation. Here, we leverage polynomial chaos expansions, which model random variables via series…
Polynomial chaos expansions (PCE) allow us to propagate uncertainties in the coefficients of differential equations to the statistics of their solutions. Their main advantage is that they replace stochastic equations by systems of…
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…
A gradient-based method is proposed for solving the linear quadratic regulator (LQR) problem for linear systems with nonlinear dependence on time-invariant probabilistic parametric uncertainties. The approach explicitly accounts for model…
We consider the problem of providing optimal uncertainty quantification (UQ) --- and hence rigorous certification --- for partially-observed functions. We present a UQ framework within which the observations may be small or large in number,…
This letter proposes a data-driven sparse polynomial chaos expansion-based surrogate model for the stochastic economic dispatch problem considering uncertainty from wind power. The proposed method can provide accurate estimations for the…
Accurate and efficient uncertainty quantification is essential for resilience assessment of modern power systems under high impact and low probability disturbances. Data driven sparse polynomial chaos expansion (DDSPCE) provides a…