相关论文: Lagrangian uncertainty quantification and informat…

We propose a data-driven technique to automatically learn contextual uncertainty sets in robust optimization, resulting in excellent worst-case and average-case performance while also guaranteeing constraint satisfaction. Our method…

Uncertainty Quantification (UQ) is essential in probabilistic machine learning models, particularly for assessing the reliability of predictions. In this paper, we present a systematic framework for estimating both epistemic and aleatoric…

Inference on unknown quantities in dynamical systems via observational data is essential for providing meaningful insight, furnishing accurate predictions, enabling robust control, and establishing appropriate designs for future…

Past research on pedestrian trajectory forecasting mainly focused on deterministic predictions which provide only point estimates of future states. These future estimates can help an autonomous vehicle plan its trajectory and avoid…

The accessibility of spatially distributed data, enabled by affordable sensors, field, and numerical experiments, has facilitated the development of data-driven solutions for scientific problems, including climate change, weather…

This paper presents a hierarchical Bayesian modeling framework for the uncertainty quantification in modal identification of linear dynamical systems using multiple vibration data sets. This novel framework integrates the state-of-the-art…

We propose a rigorous framework for Uncertainty Quantification (UQ) in which the UQ objectives and the assumptions/information set are brought to the forefront. This framework, which we call \emph{Optimal Uncertainty Quantification} (OUQ),…

We develop a stochastic model for Lagrangian velocity as it is observed in experimental and numerical fully developed turbulent flows. We define it as the unique statistically stationary solution of a causal dynamics, given by a stochastic…

Neural networks predictions are unreliable when the input sample is out of the training distribution or corrupted by noise. Being able to detect such failures automatically is fundamental to integrate deep learning algorithms into robotics.…

We introduce a method based on Gaussian process regression to identify discrete variational principles from observed solutions of a field theory. The method is based on the data-based identification of a discrete Lagrangian density. It is a…

Artificial intelligence (AI)-based data-driven weather forecasting models have experienced rapid progress over the last years. Recent studies, with models trained on reanalysis data, achieve impressive results and demonstrate substantial…

In many problems of data-driven modeling for dynamical systems, the governing equations are not known a priori and must be selected phenomenologically from a large set of candidate interactions and basis functions. In such situations, point…

Uncertainty quantification has been a core of the statistical machine learning, but its computational bottleneck has been a serious challenge for both Bayesians and frequentists. We propose a model-based framework in quantifying…

Computational models support high-stakes decisions across engineering and science, and practitioners increasingly seek probabilistic predictions to quantify uncertainty in such models. Existing approaches generate predictions either by…

We present an information-based uncertainty quantification method for general Markov Random Fields. Markov Random Fields (MRF) are structured, probabilistic graphical models over undirected graphs, and provide a fundamental unifying…

This paper introduces a novel uncertainty quantification framework for regression models where the response takes values in a separable metric space, and the predictors are in a Euclidean space. The proposed algorithms can efficiently…

Effective inclusion of physics-based knowledge into deep neural network models of dynamical systems can greatly improve data efficiency and generalization. Such a-priori knowledge might arise from physical principles (e.g., conservation…

We study the empirical likelihood approach to construct confidence intervals for the optimal value and the optimality gap of a given solution, henceforth quantify the statistical uncertainty of sample average approximation, for optimization…

Uncertainty quantification is at the core of the reliability and robustness of machine learning. In this paper, we provide a theoretical framework to dissect the uncertainty, especially the \textit{epistemic} component, in deep learning…

Autonomous driving systems face the formidable challenge of navigating intricate and dynamic environments with uncertainty. This study presents a unified prediction and planning framework that concurrently models short-term aleatoric…