相关论文: Residual-driven online Generalized Multiscale Fini…

The aggregated unfitted finite element method (AgFEM) is a methodology recently introduced in order to address conditioning and stability problems associated with embedded, unfitted, or extended finite element methods. The method is based…

Pre-trained Foundation Models (PFMs) have ushered in a paradigm-shift in Artificial Intelligence, due to their ability to learn general-purpose representations that can be readily employed in a wide range of downstream tasks. While PFMs…

Offline reinforcement learning seeks to utilize offline (observational) data to guide the learning of (causal) sequential decision making strategies. The hope is that offline reinforcement learning coupled with function approximation…

Machine learning has been successfully applied to various fields of scientific computing in recent years. In this work, we propose a sparse radial basis function neural network method to solve elliptic partial differential equations (PDEs)…

Projection-based reduced order models are effective at approximating parameter-dependent differential equations that are parametrically separable. When parametric separability is not satisfied, which occurs in both linear and nonlinear…

In this article, we propose a data-driven reduced basis (RB) method for the approximation of parametric eigenvalue problems. The method is based on the offline and online paradigms. In the offline stage, we generate snapshots and construct…

Modern applications in sensitive domains such as biometrics and medicine frequently require the use of non-decomposable loss functions such as precision@k, F-measure etc. Compared to point loss functions such as hinge-loss, these offer much…

We introduce quantitative and robust tools to control the numerical accuracy in simulations performed using the Multiscale Finite Element Method (MsFEM). First, we propose a guaranteed and fully computable a posteriori error estimate for…

This paper establishes the theoretical foundations of the online scaled gradient methods (OSGM), a framework that utilizes online learning to adapt stepsizes and provably accelerate first-order methods. OSGM quantifies the effectiveness of…

We propose an online inference method for censored quantile regression with streaming data sets. A key strategy is to approximate the martingale-based unsmooth objective function with a quadratic loss function involving a well-justified…

To efficiently tackle parametrized multi and/or large scale problems, we propose an adaptive localized model order reduction framework combining both local offline training and local online enrichment with localized error control. For the…

Offline reinforcement learning enables agents to leverage large pre-collected datasets of environment transitions to learn control policies, circumventing the need for potentially expensive or unsafe online data collection. Significant…

We consider the robust estimation of the parameters of multivariate Gaussian linear regression models. To this aim we consider robust version of the usual (Mahalanobis) least-square criterion, with or without Ridge regularization. We…

We present a novel approach for the construction of basis functions to be employed in selective or adaptive h-refined finite element applications with arbitrary-level hanging node configurations. Our analysis is not restricted to…

Offline reinforcement learning (offline RL) is an emerging field that has recently begun gaining attention across various application domains due to its ability to learn strategies from earlier collected datasets. Offline RL proved very…

The task of repeatedly solving parametrized partial differential equations (pPDEs) in, e.g. optimization or interactive applications, makes it imperative to design highly efficient and equally accurate surrogate models. The reduced basis…

Multi-fidelity models are of great importance due to their capability of fusing information coming from different numerical simulations, surrogates, and sensors. We focus on the approximation of high-dimensional scalar functions with low…

We present statistical methods for big data arising from online analytical processing, where large amounts of data arrive in streams and require fast analysis without storage/access to the historical data. In particular, we develop…

We develop an online learning method for prediction, which is important in problems with large and/or streaming data sets. We formulate the learning approach using a covariance-fitting methodology, and show that the resulting predictor has…

We study the generalization performance of online learning algorithms trained on samples coming from a dependent source of data. We show that the generalization error of any stable online algorithm concentrates around its regret--an easily…