相关论文: Deep Multi-fidelity Gaussian Processes

In spatial statistics, a common objective is to predict values of a spatial process at unobserved locations by exploiting spatial dependence. Kriging provides the best linear unbiased predictor using covariance functions and is often…

We provide a new approach to approximate emulation of large computer experiments. By focusing expressly on desirable properties of the predictive equations, we derive a family of local sequential design schemes that dynamically define the…

We introduce a new framework for verifying systems with a parametric number of concurrently running processes. The systems we consider are well-structured with respect to a specific well-quasi order. This allows us to decide a wide range of…

Dirichlet-to-Neumann maps enable the coupling of multiphysics simulations across computational subdomains by ensuring continuity of state variables and fluxes at artificial interfaces. We present a novel method for learning…

In this work we introduce a fully-connected graph structure in the Deep Gaussian Conditional Random Field (G-CRF) model. For this we express the pairwise interactions between pixels as the inner-products of low-dimensional embeddings,…

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…

In biomanufacturing, developing an accurate model to simulate the complex dynamics of bioprocesses is an important yet challenging task. This is partially due to the uncertainty associated with bioprocesses, high data acquisition cost, and…

In many numerical schemes, the computational complexity scales non-linearly with the problem size. Solving a linear system of equations using direct methods or most iterative methods is a typical example. Algebraic multi-grid (AMG) methods…

Verification plays an essential role in the formal analysis of safety-critical systems. Most current verification methods have specific requirements when working on Deep Neural Networks (DNNs). They either target one particular network…

We propose a Bayesian framework for uncertainty quantification and comparison in brain connectivity graph analysis. Standard graph-based approaches typically rely on point estimates of correlation matrices, overlooking the uncertainty…

A large collection of time series poses significant challenges for classical and neural forecasting approaches. Classical time series models fail to fit data well and to scale to large problems, but succeed at providing uncertainty…

In many real-world applications we are interested in approximating costly functions that are analytically unknown, e.g. complex computer codes. An emulator provides a fast approximation of such functions relying on a limited number of…

Artificial intelligence has made great progress in medical data analysis, but the lack of robustness and trustworthiness has kept these methods from being widely deployed. As it is not possible to train networks that are accurate in all…

We propose a framework of generative adversarial networks with multiple discriminators, which collaborate to represent a real dataset more effectively. Our approach facilitates learning a generator consistent with the underlying data…

Modern scientific problems are often multi-disciplinary and require integration of computer models from different disciplines, each with distinct functional complexities, programming environments, and computation times. Linked Gaussian…

Increasingly sophisticated mathematical modelling processes from Machine Learning are being used to analyse complex data. However, the performance and explainability of these models within practical critical systems requires a rigorous and…

While machine learning models have proven effective across various scenarios, it is widely acknowledged that many models are vulnerable to adversarial attacks. Recently, there have emerged numerous efforts in adversarial defense. Among…

Modern scientific research and applications very often encounter "fragmentary data" which brings big challenges to imputation and prediction. By leveraging the structure of response patterns, we propose a unified and flexible framework…

In this paper we consider the problem of a measure that allows us to describe the spatial and temporal dependence structure of multivariate time series with innovations having infinite variance. By using recent results obtained in the…

We propose a novel single-image super-resolution approach based on the geostatistical method of kriging. Kriging is a zero-bias minimum-variance estimator that performs spatial interpolation based on a weighted average of known…