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Over the past decade, Finite Element Method (FEM) has served as a foundational numerical framework for approximating the terms of Time Series Expansion (TSE) as solutions to transient Partial Differential Equation (PDE). However, the…
In this work, we investigate data fitting problems with random noises. A randomized progressive iterative regularization method is proposed. It works well for large-scale matrix computations and converges in expectation to the least-squares…
In this paper, we propose a novel \emph{uncertainty-aware graph self-training} approach for semi-supervised node classification. Our method introduces an Expectation-Maximization (EM) regularization scheme to incorporate an uncertainty…
Regression by composition provides a flexible framework for constructing conditional distributions through sequential group actions. However, when multiple flows act on the same distribution, the model becomes non-identifiable, leading to…
This paper develops a Hierarchical Bayesian Modeling (HBM) framework for uncertainty quantification of Finite Element (FE) models based on modal information. This framework uses an existing Fast Fourier Transform (FFT) approach to identify…
This paper focuses on the study of the Filament Based Lamellipodium Model (FBLM) and the corresponding Finite Element Method (FEM) from a numerical point of view. We study fundamental numerical properties of the FEM and justify the further…
In this paper, a non-probabilistic method based on fuzzy logic is used to update finite element models (FEMs). Model updating techniques use the measured data to improve the accuracy of numerical models of structures. However, the measured…
Optimization, a key tool in machine learning and statistics, relies on regularization to reduce overfitting. Traditional regularization methods control a norm of the solution to ensure its smoothness. Recently, topological methods have…
An extension of the framework of the Finite Integration Technique (FIT) including dynamic and adaptive mesh refinement is presented. After recalling the standard formulation of the FIT, the proposed mesh adaptation procedure is described.…
Regularization is a core component of modern inverse problems, as it helps establish the well-posedness of the solution of interest. Popular regularization approaches include variational regularization and iterative regularization. The…
We consider an inverse problem involving the reconstruction of the solution to a nonlinear partial differential equation (PDE) with unknown boundary conditions. Instead of direct boundary data, we are provided with a large dataset of…
Unsupervised registration strategies bypass requirements in ground truth transforms or segmentations by optimising similarity metrics between fixed and moved volumes. Among these methods, a recent subclass of approaches based on…
Electrical impedance tomography (EIT) provides functional images of an electrical conductivity distribution inside the human body. Since the 1980s, many potential clinical applications have arisen using inexpensive portable EIT devices. EIT…
During the inversion of discrete linear systems noise in data can be amplified and result in meaningless solutions. To combat this effect, characteristics of solutions that are considered desirable are mathematically implemented during…
Solving inverse problems involving measurement noise and modeling errors requires regularization in order to avoid data overfit. Geophysical inverse problems, in which the Earth's highly heterogeneous structure is unknown, present a…
The state space dynamics representation is the most general approach for nonlinear systems and often chosen for system identification. During training, the state trajectory can deform significantly leading to poor data coverage of the state…
This paper presents a new finite element (FE) formulation for liquid shells that is based on an explicit, 3D surface discretization using $C^1$-continuous finite elements constructed from NURBS interpolation. Both displacement-based and…
The classical approach to linear system identification is given by parametric Prediction Error Methods (PEM). In this context, model complexity is often unknown so that a model order selection step is needed to suitably trade-off bias and…
Deep learning-based fault diagnosis (FD) approaches require a large amount of training data, which are difficult to obtain since they are located across different entities. Federated learning (FL) enables multiple clients to collaboratively…
Modern data analysis depends increasingly on estimating models via flexible high-dimensional or nonparametric machine learning methods, where the identification of structural parameters is often challenging and untestable. In linear…