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Matrix differential Riccati equation (DRE) typically exhibits transient and steady-state phases, posing challenges for fixed-step time integration methods, which may lack accuracy during transients or oversample in steady regimes. In this…
Exponential integrators that use Krylov approximations of matrix functions have turned out to be efficient for the time-integration of certain ordinary differential equations (ODEs). This holds in particular for linear homogeneous ODEs,…
Many real-world optimization problems exhibit dynamic characteristics, posing significant challenges for traditional optimization techniques. Evolutionary Dynamic Optimization Algorithms (EDOAs) are designed to address these challenges…
Projective Integration methods are explicit time integration schemes for stiff ODEs with large spectral gaps. In this paper, we show that all existing Projective Integration methods can be written as Runge-Kutta methods with an extended…
Large Language Models (LLMs) have recently demonstrated strong capabilities in tool use, yet progress in tool retrieval remains hindered by incomplete and heterogeneous tool documentation. To address this challenge, we introduce Tool-DE, a…
We present an automated framework for constructing Taylor series expansions of rovibrational kinetic and potential energy operators for arbitrary molecules, internal coordinate systems, and molecular frame embedding conditions. Expressing…
We present the new version of the Loop Acceleration Tool (LoAT), a powerful tool for proving non-termination and worst-case lower bounds for programs operating on integers. It is based on a novel calculus for loop acceleration, i.e.,…
Stress relaxation and oscillation damping of complex viscoelastic media often manifest history- and path-dependent physical behaviors and cannot accurately be described by the classical models. Recent research found that fractional…
The RooUnfold package provides a common framework to evaluate and use different unfolding algorithms, side-by-side. It currently provides implementations or interfaces for the Iterative Bayes, Singular Value Decomposition, and TUnfold…
This paper announces the availability of a fixed point toolbox for the Matlab compatible software package Octave. This toolbox is released under the GNU Public License, and can be used to model the losses in algorithms implemented in…
The eXtended CASA Line Analysis Software Suite (XCLASS) is a toolbox for the Common Astronomy Software Applications package (CASA) containing new functions for modeling interferometric and single dish data. Among the tools is the myXCLASS…
A variable stepsize exponential multistep integrator, with contour integral approximation of the operator-valued exponential functions, is proposed for solving semilinear parabolic equations with nonsmooth initial data. By this approach,…
Outstanding advances in solid-state laser technology, employing the optical parametric chirped-pulse-amplification (OPCPA) technique, have led physicists to focus laser pulses to highly-relativistic intensities which led to novel schemes…
This paper introduces an adaptive time splitting technique for the solution of stiff evolutionary PDEs that guarantees an effective error control of the simulation, independent of the fastest physical time scale for highly unsteady…
Nowadays, it has become a basic need to reuse existing Application Programming Interface (API), Class Libraries, and frameworks for rapid software development. Software developers often reuse this by calling the respective APIs or…
Timed model checking has been extensively researched in recent years. Many new formalisms with time extensions and tools based on them have been presented. On the other hand, Explicit-Time Description Methods aim to verify real-time systems…
Summary: ipd is an open-source R software package for the downstream modeling of an outcome and its associated features where a potentially sizable portion of the outcome data has been imputed by an artificial intelligence or machine…
Solving partial differential equations (PDEs) by numerical methods meet computational cost challenge for getting the accurate solution since fine grids and small time steps are required. Machine learning can accelerate this process, but…
This is the second in a series of papers on implementing a discontinuous Galerkin (DG) method as an open source Matlab / GNU Octave toolbox. The intention of this ongoing project is to offer a rapid prototyping package for application…
Deep learning inspired by differential equations is a recent research trend and has marked the state of the art performance for many machine learning tasks. Among them, time-series modeling with neural controlled differential equations…