相关论文: PoCET: a Polynomial Chaos Expansion Toolbox for Ma…
In this work, Uncertainty Quantification (UQ) based on non-intrusive Polynomial Chaos Expansion (PCE) is applied to the CFD problem of the flow past an airfoil with parameterized angle of attack and inflow velocity. To limit the…
Chaos Engineering (CE) is an engineering technique aimed at improving the resiliency of distributed systems. It involves artificially injecting specific failures into a distributed system and observing its behavior in response. Based on the…
There are already quite a few tools for solving the Satisfiability Modulo Theories (SMT) problems. In this paper, we present \texttt{VolCE}, a tool for counting the solutions of SMT constraints, or in other words, for computing the volume…
A 1-dimensional generalization of the well known Logistic Map is proposed. The proposed family of maps is referred to as the B-Exponential Map. The dynamics of this map are analyzed and found to have interesting properties. In particular,…
We present a MATLAB package called the Pha-sorArray Toolbox that has been developed to make harmonic analysis and control methods both practical and user-friendly. The toolbox adopts an object-oriented architecture that enables intuitive…
Mixture models are powerful statistical models used in many applications ranging from density estimation to clustering and classification. When dealing with mixture models, there are many issues that the experimenter should be aware of and…
We present an algorithm for computing sparse, least squares-based polynomial chaos expansions, incorporating both adaptive polynomial bases and sequential experimental designs. The algorithm is employed to approximate stochastic…
This work proposes a method for sparse polynomial chaos (PC) approximation of high-dimensional stochastic functions based on non-adapted random sampling. We modify the standard l1 -minimization algorithm, originally proposed in the context…
The Problem-oriented AutoML in Clustering (PoAC) framework introduces a novel, flexible approach to automating clustering tasks by addressing the shortcomings of traditional AutoML solutions. Conventional methods often rely on predefined…
Realistic physical phenomena exhibit random fluctuations across many scales in the input and output processes. Models of these phenomena require stochastic PDEs. For three-dimensional coupled (vector-valued) stochastic PDEs (SPDEs), for…
The Statistical Finite Element Method (statFEM) offers a Bayesian framework for integrating computational models with observational data, thus providing improved predictions for structural health monitoring and digital twinning. This paper…
Control of nonlinear distributed parameter systems (DPS) under uncertainty is a meaningful task for many industrial processes. However, both intrinsic uncertainty and high dimensionality of DPS require intensive computations, while…
We present our implementation autoCAS for fully automated multi-configurational calculations, which we also make available free of charge on our webpages. The graphical user interface of autoCAS connects a general electronic structure…
Machine learning interatomic potentials are revolutionizing large-scale, accurate atomistic modelling in material science and chemistry. Many potentials use atomic cluster expansion or equivariant message passing frameworks. Such frameworks…
We consider a Poisson process $\eta$ on an arbitrary measurable space with an arbitrary sigma-finite intensity measure. We establish an explicit Fock space representation of square integrable functions of $\eta$. As a consequence we…
Polynomial Chaos Expansions (PCEs) are widely recognized for their efficient computational performance in surrogate modeling. Yet, a robust framework to quantify local model errors is still lacking. While the local uncertainty of PCE…
In this paper, we consider the composition of two independent processes : one process corresponds to position and the other one to time. Such processes will be called iterated processes. We first propose an algorithm based on the Euler…
Artificial Intelligence and Machine learning have been widely used in various fields of mathematical computing, physical modeling, computational science, communication science, and stochastic analysis. Approaches based on Deep Artificial…
Power-of-two (PoT) quantization significantly reduces the size of deep neural networks (DNNs) and replaces multiplications with bit-shift operations for inference. Prior work has shown that PoT-quantized DNNs can preserve accuracy for tasks…
The present work addresses the issue of accurate stochastic approximations in high-dimensional parametric space using tools from uncertainty quantification (UQ). The basis adaptation method and its accelerated algorithm in polynomial chaos…