相关论文: A data-driven framework for sparsity-enhanced surr…

Recently, the introduction of the generative adversarial network (GAN) and its variants has enabled the generation of realistic synthetic samples, which has been used for enlarging training sets. Previous work primarily focused on data…

When training a machine learning model with observational data, it is often encountered that some values are systemically missing. Learning from the incomplete data in which the missingness depends on some covariates may lead to biased…

The quantification of uncertainties of computer simulations due to input parameter uncertainties is paramount to assess a model's credibility. For computationally expensive simulations, this is often feasible only via surrogate models that…

We propose an efficient surrogate modeling technique for uncertainty quantification. The method is based on a well-known dimension-adaptive collocation scheme. We improve the scheme by enhancing sparse polynomial surrogates with conformal…

In the regression problem, L1 and L2 are the most commonly used loss functions, which produce mean predictions with different biases. However, the predictions are neither robust nor adequate enough since they only capture a few conditional…

This work presents a data-driven method for learning low-dimensional time-dependent physics-based surrogate models whose predictions are endowed with uncertainty estimates. We use the operator inference approach to model reduction that…

We propose a new stochastic first-order algorithmic framework to solve stochastic composite nonconvex optimization problems that covers both finite-sum and expectation settings. Our algorithms rely on the SARAH estimator introduced in…

Many modern big data applications feature large scale in both numbers of responses and predictors. Better statistical efficiency and scientific insights can be enabled by understanding the large-scale response-predictor association network…

We propose a multi-fidelity neural network surrogate sampling method for the uncertainty quantification of physical/biological systems described by ordinary or partial differential equations. We first generate a set of low/high-fidelity…

Distributionally robust stochastic optimization (DRSO) is a framework for decision-making problems under certainty, which finds solutions that perform well for a chosen set of probability distributions. Many different approaches for…

We propose a novel method for establishing the sparsity of the coefficients of the Laguerre generalized polynomial chaos expansion of solutions to parametric elliptic PDEs with log-gamma inputs on $\mathbb{R}_+^\infty$. The established…

We derive an efficient stochastic algorithm for inverse problems that present an unknown linear forcing term and a set of nonlinear parameters to be recovered. It is assumed that the data is noisy and that the linear part of the problem is…

Constructing approximations that can accurately mimic the behavior of complex models at reduced computational costs is an important aspect of uncertainty quantification. Despite their flexibility and efficiency, classical surrogate models…

Multilayer (or deep) networks are powerful probabilistic models based on multiple stages of a linear transform followed by a non-linear (possibly random) function. In general, the linear transforms are defined by matrices and the non-linear…

This paper proposes a novel computationally efficient dynamic bi-orthogonality based approach for calibration of a computer simulator with high dimensional parametric and model structure uncertainty. The proposed method is based on a…

Inferring dependence structure through undirected graphs is crucial for uncovering the major modes of multivariate interaction among high-dimensional genomic markers that are potentially associated with cancer. Traditionally, conditional…

In many problem settings, parameter vectors are not merely sparse but dependent in such a way that non-zero coefficients tend to cluster together. We refer to this form of dependency as "region sparsity." Classical sparse regression…

Significant effort has been made to solve computationally expensive optimization problems in the past two decades, and various optimization methods incorporating surrogates into optimization have been proposed. Most research focuses on…

Sparse identification of differential equations aims to compute the analytic expressions from the observed data explicitly. However, there exist two primary challenges. Firstly, it exhibits sensitivity to the noise in the observed data,…

A multifidelity method for the nonlinear propagation of uncertainties in the presence of stochastic accelerations is presented. The proposed algorithm treats the uncertainty propagation (UP) problem by separating the propagation of the…