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Imperfections and uncertainties in forecast models are often represented in ensemble prediction systems by stochastic perturbations of model equations. In this article, we present a new technique to generate model perturbations. The…
Verification is a critical process in the development of engineered systems. Through verification, engineers gain confidence in the correct functionality of the system before it is deployed into operation. Traditionally, verification…
The numerical simulation of complex physical processes requires the use of economical discrete models. This lecture presents a general paradigm of deriving a posteriori error estimates for the Galerkin finite element approximation of…
Recovery type a posteriori error estimators are popular, particularly in the engineering community, for their computationally inexpensive, easy to implement, and generally asymptotically exactness. Unlike the residual type error estimators,…
We present an adaptive finite element method for the incompressible Navier--Stokes equations based on a standard splitting scheme (the incremental pressure correction scheme). The presented method combines the efficiency and simplicity of a…
The finite element method (FEM) has several computational steps to numerically solve a particular problem, to which many efforts have been directed to accelerate the solution stage of the linear system of equations. However, the finite…
Energy-Based Models (EBMs) present a flexible and appealing way to represent uncertainty. Despite recent advances, training EBMs on high-dimensional data remains a challenging problem as the state-of-the-art approaches are costly, unstable,…
Generation planning approaches face challenges in managing the incompatible mathematical structures between stochastic production simulations for reliability assessment and optimization models for generation planning, which hinders the…
The phase field model is a widely used mathematical approach for describing crack propagation in continuum damage fractures. In the context of phase field fracture simulations, adaptive finite element methods (AFEM) are often employed to…
In this paper, we propose upper and lower error bounding techniques for reduced order modelling applied to the computational homogenisation of random composites. The upper bound relies on the construction of a reduced model for the stress…
This paper presents a comprehensive computational framework for investigating thermo-elastic fracture in transversely isotropic materials, where classical linear elasticity fails to predict physically realistic behavior near stress…
Inference-time steering is widely regarded as a lightweight and parameter-free mechanism for controlling large language model (LLM) behavior, and prior work has often suggested that simple activation-level interventions can reliably induce…
Test time adaptation (TTA) equips deep learning models to handle unseen test data that deviates from the training distribution, even when source data is inaccessible. While traditional TTA methods often rely on entropy as a confidence…
This paper proposes some efficient and accurate adaptive two-grid (ATG) finite element algorithms for linear and nonlinear partial differential equations (PDEs). The main idea of these algorithms is to utilize the solutions on the $k$-th…
Fault tolerance is a critical aspect of modern computing systems, ensuring correct functionality in the presence of faults. This paper presents a comprehensive survey of fault tolerance methods and software-based mitigation techniques in…
Fully computable a posteriori error estimates in the energy norm are given for singularly perturbed semilinear reaction-diffusion equations posed in polygonal domains. Linear finite elements are considered on anisotropic triangulations. To…
This paper introduces a simple framework for accurately predicting the fatigue lifetime of notched components by employing various machine learning algorithms applied to a wide range of materials, loading conditions, notch geometries, and…
In this paper, a new combination of a dynamic transformation method and a trajectory-based integration technique is proposed for the model independent computation of unstable equilibrium points (UEPs). The transformation method converts a…
Numerical simulations of physical systems exhibit discrepancies arising from unmodeled physics and idealizations, as well as numerical approximation errors stemming from discretization and solver tolerances. This article reviews techniques…
The growing complexity of safety-relevant systems causes an increasing effort for safety assurance. The reduction of development costs and time-to-market, while guaranteeing safe operation, is therefore a major challenge. In order to enable…