Related papers: A survey of unsupervised learning methods for high…

Many high-dimensional uncertainty quantification problems are solved by polynomial dimensional decomposition (PDD), which represents Fourier-like series expansion in terms of random orthonormal polynomials with increasing dimensions. This…

Machine learning methods are increasingly widely used in high-risk settings such as healthcare, transportation, and finance. In these settings, it is important that a model produces calibrated uncertainty to reflect its own confidence and…

On top of machine learning models, uncertainty quantification (UQ) functions as an essential layer of safety assurance that could lead to more principled decision making by enabling sound risk assessment and management. The safety and…

Uncertainty quantification in automated image analysis is highly desired in many applications. Typically, machine learning models in classification or segmentation are only developed to provide binary answers; however, quantifying the…

We propose UnCLe, the first standardized benchmark for Unsupervised Continual Learning of a multimodal 3D reconstruction task: Depth completion aims to infer a dense depth map from a pair of synchronized RGB image and sparse depth map. We…

In this paper, we develop new high-order numerical methods for hyperbolic systems of nonlinear partial differential equations (PDEs) with uncertainties. The new approach is realized in the semi-discrete finite-volume framework and is based…

We propose a non-intrusive method to build surrogate models that approximate the solution of parameterized partial differential equations (PDEs), capable of taking into account the dependence of the solution on the shape of the…

Impressive advances in acquisition and sharing technologies have made the growth of multimedia collections and their applications almost unlimited. However, the opposite is true for the availability of labeled data, which is needed for…

Spatial scene understanding, including monocular depth estimation, is an important problem in various applications, such as robotics and autonomous driving. While improvements in unsupervised monocular depth estimation have potentially…

We describe a computational framework linking Uncertainty Quantification (UQ) methods for continuum problems depending on random parameters with Equation-Free (EF) methods for performing continuum deterministic numerics by acting directly…

Researchers have proposed several approaches for neural network (NN) based uncertainty quantification (UQ). However, most of the approaches are developed considering strong assumptions. Uncertainty quantification algorithms often perform…

Unsupervised 3D object detection aims to identify objects of interest from unlabeled raw data, such as LiDAR points. Recent approaches usually adopt pseudo 3D bounding boxes (3D bboxes) from clustering algorithm to initialize the model…

Traditional deep learning (DL) models are powerful classifiers, but many approaches do not provide uncertainties for their estimates. Uncertainty quantification (UQ) methods for DL models have received increased attention in the literature…

Mixed-dimensional partial differential equations (PDEs) are characterized by coupled operators defined on domains of varying dimensions and pose significant computational challenges due to their inherent ill-conditioning. Moreover, the…

Many important problems in science and engineering require solving the so-called parametric partial differential equations (PDEs), i.e., PDEs with different physical parameters, boundary conditions, shapes of computational domains, etc.…

Deterministic uncertainty quantification (UQ) in deep learning aims to estimate uncertainty with a single pass through a network by leveraging outputs from the network's feature extractor. Existing methods require that the feature extractor…

Unsupervised learning is becoming more and more important recently. As one of its key components, the autoencoder (AE) aims to learn a latent feature representation of data which is more robust and discriminative. However, most AE based…

Neural differential equations offer a powerful approach for learning dynamics from data. However, they do not impose known constraints that should be obeyed by the learned model. It is well-known that enforcing constraints in surrogate…

High-dimensional partial differential equations (PDEs) pose significant challenges for numerical computation due to the curse of dimensionality, which limits the applicability of traditional mesh-based methods. Since 2017, the Deep BSDE…

Large Language Models (LLMs) have demonstrated remarkable capabilities across various tasks due to large training datasets and powerful transformer architecture. However, the reliability of responses from LLMs remains a question.…