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A new approach for the parallel forward modeling of transient electromagnetic (TEM) fields is presented. It is based on a family of uniform-in-time rational approximants to the matrix exponential that share a common denominator independent…

The diffusive transport of particles in anisotropic media is a fundamental phenomenon in computational, medical and biological disciplines. While deterministic models (partial differential equations) of such processes are well established,…

This paper introduces a novel spatiotemporal feature representation model designed to address the limitations of traditional methods in multidimensional time series (MTS) analysis. The proposed approach converts MTS into one-dimensional…

For linear parabolic initial-boundary value problems with self-adjoint, time-homogeneous elliptic spatial operator in divergence form with Lipschitz-continuous coefficients, and for incompatible, time-analytic forcing term in…

In these lecture notes we give a technical overview of tangent-space methods for matrix product states in the thermodynamic limit. We introduce the manifold of uniform matrix product states, show how to compute different types of…

Spectral methods of moments provide a powerful tool for learning the parameters of latent variable models. Despite their theoretical appeal, the applicability of these methods to real data is still limited due to a lack of robustness to…

A method for dimension reduction with clustering, classification, or discriminant analysis is introduced. This mixture model-based approach is based on fitting generalized hyperbolic mixtures on a reduced subspace within the paradigm of…

Numerical schemes for the solution of the Euler equations have recently been developed, which involve the discretisation of the internal energy equation, with corrective terms to ensure the correct capture of shocks, and, more generally,…

Time-varying nanostructures allow us to control the spatial and temporal properties of light. The temporal modulation of the nanostructures constitutes an additional degree of freedom to control their scattering properties on demand and in…

We consider a time-stepping scheme of Crank-Nicolson type for the heat equation on a moving domain in Eulerian coordinates. As the spatial domain varies between subsequent time steps, an extension of the solution from the previous time step…

We propose a modification technique for discrete time systems for exponentially fast convergence to compact sets. The extension technique allows us to use tools defined on Euclidean spaces to systems evolving on manifolds by modifying the…

A space-time domain decomposition approach is presented as a natural extension of the enhanced velocity mixed finite element (EVMFE) [Wheeler et. al] for spatial domain decomposition. The proposed approach allows for different space-time…

A general method is introduced for constructing two-dimensional (2D) surface meshes embedded in three-dimensional (3D) space time, and 3D hypersurface meshes embedded in four-dimensional (4D) space time. In particular, we begin by dividing…

Thinking of the flow through biological or technical valves, there is a variety of applications in which the topology of a fluid domain changes over time. This topology change is characteristic for the physical behaviour, but poses a…

Large tensors are frequently encountered in various fields such as computer vision, scientific simulations, sensor networks, and data mining. However, these tensors are often too large for convenient processing, transfer, or storage.…

We develop a machine learning method for mapping data originating from both Standard Model processes and various theories beyond the Standard Model into a unified representation (latent) space while conserving information about the…

We introduce a new tiling algorithm for hyperbolic 3-manifolds. We use it to compute the maximal cusp area matrix; this completely characterizes the space of all embedded and disjoint cusp neighborhoods. As another application of our work,…

Many important problems in astrophysics, space physics, and geophysics involve flows of (possibly ionized) gases in the vicinity of a spherical object, such as a star or planet. The geometry of such a system naturally favors numerical…

On the example of the Poynting-Thomson-Zener rheological model for solids, which exhibits both dissipation and wave propagation - with nonlinear dispersion relation -, we introduce and investigate a finite difference numerical scheme. Our…

In this work, we present a numerical method that remedies the instabilities of the conventional FDTD approach for solving Maxwell's equations in a space-time dependent magneto-electric medium with direct application to the simulation of the…