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While significant progress has been made in specifying neural networks capable of representing uncertainty, deep networks still often suffer from overconfidence and misaligned predictive distributions. Existing approaches for measuring this…
With more and more data being collected, data-driven modeling methods have been gaining in popularity in recent years. While physically sound, classical gray-box models are often cumbersome to identify and scale, and their accuracy might be…
This article is devoted to providing a review of mathematical formulations in which Polynomial Chaos Theory (PCT) has been incorporated into stochastic model predictive control (SMPC). In the past decade, PCT has been shown to provide a…
This article considers the $\mathcal{H}_\infty$ static output-feedback control for linear time-invariant uncertain systems with polynomial dependence on probabilistic time-invariant parametric uncertainties. By applying polynomial chaos…
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…
Learning data representations under uncertainty is an important task that emerges in numerous scientific computing and data analysis applications. However, uncertainty quantification techniques are computationally intensive and become…
This work suggests an interpolation-based stochastic collocation method for the non-intrusive and adaptive construction of sparse polynomial chaos expansions (PCEs). Unlike pseudo-spectral projection and regression-based stochastic…
Probabilistic Circuits (PCs) are a promising avenue for probabilistic modeling. They combine advantages of probabilistic graphical models (PGMs) with those of neural networks (NNs). Crucially, however, they are tractable probabilistic…
We present Causal Posterior Estimation (CPE), a novel method for Bayesian inference in simulator models, i.e., models where the evaluation of the likelihood function is intractable or too computationally expensive, but where one can…
Physics-informed neural networks (PINNs) have recently emerged as an alternative way of solving partial differential equations (PDEs) without the need of building elaborate grids, instead, using a straightforward implementation. In…
Effective properties of composite materials are defined as the ensemble average of property-specific PDE solutions over the underlying microstructure distributions. Traditionally, predicting such properties can be done by solving PDEs…
Probabilistic encoding introduces Gaussian noise into neural networks, enabling a smooth transition from deterministic to uncertain states and enhancing generalization ability. However, the randomness of Gaussian noise distorts point-based…
Sparse principal component analysis (PCA) is a well-established dimensionality reduction technique that is often used for unsupervised feature selection (UFS). However, determining the regularization parameters is rather challenging, and…
Gradient-enhanced Uncertainty Quantification (UQ) has received recent attention, in which the derivatives of a Quantity of Interest (QoI) with respect to the uncertain parameters are utilized to improve the surrogate approximation.…
Polynomial Chaos Expansions represent a powerful tool to simulate stochastic models of dynamical systems. Yet, deriving the expansion's coefficients for complex systems might require a significant and non-trivial manipulation of the model,…
Ensemble learning has gain attention in resent deep learning research as a way to further boost the accuracy and generalizability of deep neural network (DNN) models. Recent ensemble training method explores different training algorithms or…
Deep learning has been the engine powering many successes of data science. However, the deep neural network (DNN), as the basic model of deep learning, is often excessively over-parameterized, causing many difficulties in training,…
Establishing associations between the structure and the generalisation ability of deep neural networks (DNNs) is a challenging task in modern machine learning. Producing solutions to this challenge will bring progress both in the…
Bayesian Neural Networks (BNNs) offer a principled and natural framework for proper uncertainty quantification in the context of deep learning. They address the typical challenges associated with conventional deep learning methods, such as…
This paper presents a detailed comparison between 3 methods for emulating CPU-intensive reactive transport models (RTMs): Gaussian processes (GPs), polynomial chaos expansion (PCE) and deep neural networks (DNNs). Besides direct emulation…