Accurate simulations of gas flow within pipeline networks provide crucial insights for transmission and design operators. This importance intensifies with the growing integration of hydrogen-blended fuels in hydrogen-based energy systems. Existing models predominantly address single-component, one-dimensional flow within individual pipe segments, interconnected at network junctions. Recently,...
In the usual one-precision environment the Bartels--Stewart algorithm is the standard algorithm for solving small dense Sylvester matrix equations AX+XB=C. their algorithm consists of three steps, including the computation of the Schur decompositions, the substitution for solving the Sylvester equation with quasi-triangular coefficients, and the final recovering transformation.
In the new...
Numerical algorithms and computational tools are essential for managing and analyzing complex data processing tasks. As meta-data and parameter-driven simulations have become more prevalent, the need for automated workflows to reproduce computational experiments across platforms has significantly increased. In general, a computational workflow is defined as a step-by-step description for...
The class of bilinear dynamical systems often arises in the description and approximation of large-scale nonlinear systems with analytic nonlinearities. This bilinear structure allows the extension of various established model order reduction (MOR) approaches, from their linear counterparts. In this work, our aim is to introduce a realization-free, data-based MOR method, inspired by the...
The increasing complexity in design and manufacturing has driven the need for advanced techniques for fast modeling problems with high-dimensional parameter spaces. Avoiding high-fidelity finite element models while achieving fast and accurate simulations in such contexts is challenging. Projection-based parametric model order reduction (pMOR) has drawn significant attention in recent years....
pyMOR, a Python toolbox for building reduced order models, supports a variety of solver backends, such as dune-gdt, FEniCS, NGSolve, NumPy and potentially MPI distributed variants. An abstract interface, the VectorArray, is used to wrap vectors and matrices from these backends on which pyMOR's algorithms work. For compatibility reasons direct access of entries has to be avoided, which...
Solving the Schrödinger equation is a central task in quantum chemistry. Diffusion Monte Carlo (DMC) is a stochastic method that utilizes the connection between this equation and those governing diffusion phenomena to obtain accurate estimates of the eigenvalues and eigenfunctions involved.
This is made possible by the well-known Feynman-Kac formula, which allows the Schrödinger equation to...
For the standard algebraic generalized Riccati equation
$C^TQC+ A^TXE + E^TXA -E^TXBR^{-1}B^TXE = 0$
different algorithms inspired by the low-rank alternating directions implicit (LR-ADI) iteration and Krylov subspace projection have successfully been applied, based on the $ZZ^T$ factorization of the iterates, when $Q, R$ are both symmetric, and $Q\geq0$ and $R>0$.
In this...
We study the problem of constructing solutions [1, 2] $X \in \mathbb{R}^{\alpha \times \beta}$ of a linear matrix equation
$LX = F, F \in \mathbb{R}^{\gamma \times \delta},$ (1)
where $L : \mathbb{R}^{\alpha \times \beta} \rightarrow \mathbb{R}^{\gamma \times \delta}$ is a linear bounded matrix functional. A partial case of the matrix algebraic equation (1) is the well-known Sylvester and...
Biomolecular processes often involve transitions between metastable states governing molecular function. Extracting this information is challenging due to the high dimensionality of simulation data. Kernel methods are a powerful tool for automated analysis of complex systems, yet their need for pairwise kernel evaluations leads to scalability issues, particularly in large datasets.
To address...
We analyze two classes of mathematical models describing chemical reactions of the type "$A \to$ product," conducted in tubular reactors. The first class involves nonlinear hyperbolic partial differential equations modeling a plug flow reactor (PFR) in the presence of an inert component. For this system, an isoperimetric optimal control problem is formulated to maximize the mean product yield...
There have been a number of works in the literature dealing with the stabilization of processes with input delays for a reaction-diffusion partial differential equation, mainly by using finite-time control strategies, where their settling time depends on the initial conditions. However, in many practical applications, it is difficult or even impossible to obtain system initial values in...
We present a novel machine learning approach to develop energy-preserving reduced-order models (ROMs) by exploiting the multi-symplectic structure of partial differential equations (PDEs). Traditional energy-preserving ROMs often rely on the symplectic Galerkin projection, which requires fully discrete operators - often unavailable in black-box PDE solvers. Our method circumvents this...
The numerical integration of Hamiltonian systems is a central topic in computational physics and theoretical chemistry. Intrinsic structure-preserving symplectic networks (SympNets) [1] are a widely used tool when it comes to learning symplectic integrators for Hamiltonian systems from data. More often then not Hamiltonian systems of interest depend on a set of parameters. Currently, SympNets...
Model-order Reduction (MOR) is a technique used to reduce the complexity of high-dimensional dynamical systems while preserving their essential properties. It has been been successfully used in many scientific and engineering fields, such as Fluid Dynamics and Control Theory by methods like Proper Orthogonal Decomposition (POD), Autoencoder, Dynamic Mode decomposition (DMD) and so on. However,...
Data-driven modelling and optimisation play a fundamental role in science and engineering. In particular, hybrid models, i.e., those that combine physical models (white-box modelling) with data-driven machine learning approaches (black-box modelling), have great potential for simulating and controlling vector-borne diseases, including dengue virus, yellow fever virus, Chikungunya virus, and...
