Related papers: A machine learning approach for efficient uncertai…
We propose a data-driven, coarse-graining formulation in the context of equilibrium statistical mechanics. In contrast to existing techniques which are based on a fine-to-coarse map, we adopt the opposite strategy by prescribing a…
The introduction of the Segment Anything Model (SAM) has paved the way for numerous semantic segmentation applications. For several tasks, quantifying the uncertainty of SAM is of particular interest. However, the ambiguous nature of the…
In this article a novel approach for training deep neural networks using Bayesian techniques is presented. The Bayesian methodology allows for an easy evaluation of model uncertainty and additionally is robust to overfitting. These are…
In spatial statistics, fast and accurate parameter estimation, coupled with a reliable means of uncertainty quantification, can be challenging when fitting a spatial process to real-world data because the likelihood function might be slow…
This paper concerns the study of optimal (supremum and infimum) uncertainty bounds for systems where the input (or prior) probability measure is only partially/imperfectly known (e.g., with only statistical moments and/or on a coarse…
Deep Learning is a consolidated, state-of-the-art Machine Learning tool to fit a function when provided with large data sets of examples. However, in regression tasks, the straightforward application of Deep Learning models provides a point…
Deep learning as a means to inferencing has proliferated thanks to its versatility and ability to approach or exceed human-level accuracy. These computational models have seemingly insatiable appetites for computational resources not only…
While deep neural networks have become the go-to approach in computer vision, the vast majority of these models fail to properly capture the uncertainty inherent in their predictions. Estimating this predictive uncertainty can be crucial,…
This article describes a multivariate polynomial regression method where the uncertainty of the input parameters are approximated with Gaussian distributions, derived from the central limit theorem for large weighted sums, directly from the…
Scientific Machine Learning is a new class of approaches that integrate physical knowledge and mechanistic models with data-driven techniques for uncovering governing equations of complex processes. Among the available approaches, Universal…
The construction of efficient methods for uncertainty quantification in kinetic equations represents a challenge due to the high dimensionality of the models: often the computational costs involved become prohibitive. On the other hand,…
In this paper, we propose a local model reduction approach for subsurface flow problems in stochastic and highly heterogeneous media. To guarantee the mass conservation, we consider the mixed formulation of the flow problem and aim to solve…
Proper quantification of predictive uncertainty is essential for the use of machine learning in safety-critical applications. Various uncertainty measures have been proposed for this purpose, typically claiming superiority over other…
Model calibration is essential for ensuring that the predictions of deep neural networks accurately reflect true probabilities in real-world classification tasks. However, deep networks often produce over-confident or under-confident…
Popular approaches for quantifying predictive uncertainty in deep neural networks often involve distributions over weights or multiple models, for instance via Markov Chain sampling, ensembling, or Monte Carlo dropout. These techniques…
We propose a multiscale approach for an elliptic multiscale setting with general unstructured diffusion coefficients that is able to achieve high-order convergence rates with respect to the mesh parameter and the polynomial degree. The…
While Deep Neural Networks (DNNs) achieve state-of-the-art accuracy in various applications, they often fall short in accurately estimating their predictive uncertainty and, in turn, fail to recognize when these predictions may be wrong.…
Uncertainty quantification based on generalized polynomial chaos has been used in many applications. It has also achieved great success in variation-aware design automation. However, almost all existing techniques assume that the parameters…
Quantifying the predictive uncertainty emerged as a possible solution to common challenges like overconfidence or lack of explainability and robustness of deep neural networks, albeit one that is often computationally expensive. Many…
This contribution presents a hierarchical multigrid approach for the solution of large-scale finite cell problems on both uniform grids and multi-level hp-discretizations. The proposed scheme leverages the hierarchical nature of the basis…