Related papers: Multivariate sensitivity-adaptive polynomial chaos…
Efficient surrogate modelling is a key requirement for uncertainty quantification in data-driven scenarios. In this work, a novel approach of using Sparse Random Features for surrogate modelling in combination with self-supervised…
Background: Scatterometry is a fast, indirect and non-destructive optical method for quality control in the production of lithography masks. To solve the inverse problem in compliance with the upcoming need for improved accuracy, a…
Polynomial expansions are important in the analysis of neural network nonlinearities. They have been applied thereto addressing well-known difficulties in verification, explainability, and security. Existing approaches span classical Taylor…
A novel approach for non-intrusive uncertainty propagation is proposed. Our approach overcomes the limitation of many traditional methods, such as generalised polynomial chaos methods, which may lack sufficient accuracy when the quantity of…
Crash simulations play an essential role in improving vehicle safety, design optimization, and injury risk estimation. Unfortunately, numerical solutions of such problems using state-of-the-art high-fidelity models require significant…
Assessing the safety and environmental impacts of subsurface resource exploitation and management is critical and requires robust geomechanical modeling. However, uncertainties stemming from model assumptions, intrinsic variability of…
In this paper we present applications of methods from wavelet analysis to polynomial approximations for a number of accelerator physics problems. According to variational approach in the general case we have the solution as a…
Multivariate global polynomial approximations - such as polynomial chaos or stochastic collocation methods - are now in widespread use for sensitivity analysis and uncertainty quantification. The pseudospectral variety of these methods uses…
Accurate modeling of radio wave propagation over irregular terrains is crucial for designing reliable wireless communication systems in such environments, yet uncertainties in the antenna configuration are not quantified within…
This paper proposes a new algorithm for compensating external disturbances for class of multi-channel linear systems. The solution to this problem is based on the use of the internal model principle and the extended error adaptation…
This work proposes an adaptive framework to solve a robust structural shape optimization problem governed by linear elasticity models that account for uncertainties in the loading and material inputs. A posteriori error estimators are…
Recent studies have shown that chaotic maps are well-suited for applications requiring unpredictable behaviour, making them a valuable tool for enhancing unpredictability and complexity. A method is developed using 3D parametric equations…
We present a new adaptive method for electronic structure calculations based on novel fast algorithms for reduction of multivariate mixtures. In our calculations, spatial orbitals are maintained as Gaussian mixtures whose terms are selected…
Extreme response assessment is important in the design and operation of engineering structures, and is a crucial part of structural risk and reliability analyses. Structures should be designed in a way that enables them to withstand the…
Adaptive designs are increasingly used in clinical trials and online experiments to improve participant outcomes by dynamically updating treatment allocation as data accumulate. In practice, experimenters often consider multiple candidate…
This paper extends the subjects dicussed in the Data Analysis and Dynamical Systems courses by looking at the subject of modelling data. This task is nontrivial as the underlying process could be non-linear. In the paper some common…
Orthogonal polynomial approximations form the foundation to a set of well-established methods for uncertainty quantification known as polynomial chaos. These approximations deliver models for emulating physical systems in a variety of…
In modern engineering, physical processes are modelled and analysed using advanced computer simulations, such as finite element models. Furthermore, concepts of reliability analysis and robust design are becoming popular, hence, making…
Highly accurate datasets from numerical or physical experiments are often expensive and time-consuming to acquire, posing a significant challenge for applications that require precise evaluations, potentially across multiple scenarios and…
Compressive sampling has been widely used for sparse polynomial chaos (PC) approximation of stochastic functions. The recovery accuracy of compressive sampling highly depends on the incoherence properties of the measurement matrix. In this…