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The context of this paper is the simulation of parameter-dependent partial differential equations (PDEs). When the aim is to solve such PDEs for a large number of parameter values, Reduced Basis Methods (RBM) are often used to reduce…
Nonnegative matrix factorization (NMF) has been shown recently to be tractable under the separability assumption, under which all the columns of the input data matrix belong to the convex cone generated by only a few of these columns.…
Nonnegative Matrix Factorization (NMF) is the problem of approximating a nonnegative matrix with the product of two low-rank nonnegative matrices and has been shown to be particularly useful in many applications, e.g., in text mining, image…
A fast inverse heat conduction model (IHCM) is developed for estimating unknown properties of multi-layer composites considering internal heat generation. This work builds on the validated analytical forward models presented in Part I.…
We discuss realization, properties and performance of the adaptive finite element approach to the design of nano-photonic components. Central issues are the construction of vectorial finite elements and the embedding of bounded components…
Agent-based cellular models simulate tissue evolution by capturing the behavior of individual cells, their interactions with neighboring cells, and their responses to the surrounding microenvironment. An important challenge in the field is…
We consider the reliable implementation of an adaptive high-order unfitted finite element method on Cartesian meshes for solving elliptic interface problems with geometrically curved singularities. We extend our previous work on the…
A high-dimensional and incomplete (HDI) matrix frequently appears in various big-data-related applications, which demonstrates the inherently non-negative interactions among numerous nodes. A non-negative latent factor (NLF) model performs…
Insufficient reference data is ubiquitous in data-driven computational fluid dynamics, as it is usually too expensive to compute or impossible to observe over long enough times needed for data-driven methods. The lack of data can…
Fractional calculus has been proved to be very effective in representing the visco-elastic relaxation response of materials with memory such as polymers. Moreover, in modelling the temperature dependency of the material functions in…
The magnetohydrodynamics (MHD) equations are continuum models used in the study of a wide range of plasma physics systems, including the evolution of complex plasma dynamics in tokamak disruptions. However, efficient numerical solution…
Finite element method (FEM) suffers from a serious mesh distortion problem when used for high velocity impact analyses. The smooth particle hydrodynamics (SPH) method is appropriate for this class of problems involving severe damages but at…
Nonnegative matrix factorization (NMF) is a linear dimensionality reduction technique for nonnegative data, with applications such as hyperspectral unmixing and topic modeling. NMF is a difficult problem in general (NP-hard), and its…
This article is concerned with the numerical solution of convex variational problems. More precisely, we develop an iterative minimisation technique which allows for the successive enrichment of an underlying discrete approximation space in…
The nonequilibrium Green's functions (NEGF) approach is a versatile theoretical tool, which allows to describe the electronic structure, spectroscopy and dynamics of strongly correlated systems. The applicability of this method is, however,…
Hypertension is a heterogeneous syndrome in need of improved subtyping using phenotypic and genetic measurements so that patients in different subtypes share similar pathophysiologic mechanisms and respond more uniformly to targeted…
Non-negative Matrix Factorization (NMF) is a key kernel for unsupervised dimension reduction used in a wide range of applications, including topic modeling, recommender systems and bioinformatics. Due to the compute-intensive nature of…
High-throughput methods enable accelerated discovery of novel materials in complex systems such as high-entropy alloys, which exhibit intricate phase stability across vast compositional spaces. Computational approaches, including Density…
Validity of fluid models breaks down for non-thermal or weakly collisional plasmas which often occur e.g. in the solar wind. In these regimes one has to resort to modelling through the first-principle Vlasov-Maxwell system, but its…
For manufacturing of aerospace composites, several parts may be processed simultaneously using convective heating in an autoclave. Due to uncertainties including tool placement, convective Boundary Conditions (BCs) vary in each run. As a…