相关论文: Uncertainty Quantification with Bayesian Higher Or…
This paper explores uncertainty quantification (UQ) methods in the context of Kolmogorov-Arnold Networks (KANs). We apply an ensemble approach to KANs to obtain a heuristic measure of UQ, enhancing interpretability and robustness in…
Uncertainty quantification (UQ) plays a pivotal role in scientific machine learning, especially when surrogate models are used to approximate complex systems. Although multilayer perceptions (MLPs) are commonly employed as surrogates, they…
Kolmogorov-Arnold Networks have emerged as interpretable alternatives to traditional multi-layer perceptrons. However, standard implementations lack principled uncertainty quantification capabilities essential for many scientific…
We develop a novel deep learning method for uncertainty quantification in stochastic partial differential equations based on Bayesian neural network (BNN) and Hamiltonian Monte Carlo (HMC). A BNN efficiently learns the posterior…
Kolmogorov-Arnold Networks (KANs) offer a theoretically grounded alternative to multi-layer perceptrons by representing multivariate functions as compositions of univariate basis functions. However, a critical limitation of KANs is the need…
Fractional calculus provides a rigorous mathematical framework to describe anomalous stochastic processes by generalizing the notion of classical differential equations to their fractional-order counterparts. By introducing the fractional…
The Kolmogorov-Arnold network (KAN) is a regression model that is based on a representation of an arbitrary continuous multivariate function by a composition of functions of a single variable. Experimentally-obtained datasets for regression…
Uncertainty quantification is an important and challenging problem in deep learning. Previous methods rely on dropout layers which are not present in modern deep architectures or batch normalization which is sensitive to batch sizes. In…
Because of its strong predictive skills, deep learning has emerged as an essential tool in many industries, including healthcare. Traditional deep learning models, on the other hand, frequently lack interpretability and omit to take…
This paper proposes a novel uncertainty quantification framework for computationally demanding systems characterized by a large vector of non-Gaussian uncertainties. It combines state-of-the-art techniques in advanced Monte Carlo sampling…
Uncertainty-quantification methods are applied to estimate the confidence of deep-neural-networks classifiers over their predictions. However, most widely used methods are known to be overconfident. We address this problem by developing an…
We explore probability modelling of discretization uncertainty for system states defined implicitly by ordinary or partial differential equations. Accounting for this uncertainty can avoid posterior under-coverage when likelihoods are…
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…
Finding solutions to partial differential equations (PDEs) is an important and essential component in many scientific and engineering discoveries. One of the common approaches empowered by deep learning is Physics-informed Neural Networks…
Neural networks (NNs) are currently changing the computational paradigm on how to combine data with mathematical laws in physics and engineering in a profound way, tackling challenging inverse and ill-posed problems not solvable with…
We overview some recent results in the field of uncertainty quantification for kinetic equations and related problems with random inputs. Uncertainties may be due to various reasons, such as lack of knowledge on the microscopic interaction…
Kolmogorov-Arnold Networks (KANs) have recently emerged as a powerful alternative to traditional multilayer perceptrons. However, their reliance on predefined, bounded grids restricts their ability to approximate functions on unbounded…
Large language models (LLMs) exhibit impressive fluency, but often produce critical errors known as "hallucinations". Uncertainty quantification (UQ) methods are a promising tool for coping with this fundamental shortcoming. Yet, existing…
Uncertainty quantification is an important task in machine learning - a task in which standardneural networks (NNs) have traditionally not excelled. This can be a limitation for safety-critical applications, where uncertainty-aware methods…
Bayesian Neural Networks (BNNs) place priors over the parameters in a neural network. Inference in BNNs, however, is difficult; all inference methods for BNNs are approximate. In this work, we empirically compare the quality of predictive…