相关论文: pythOS: A Python library for solving IVPs by opera…

Numerically solving ordinary differential equations (ODEs) is a naturally serial process and as a result the vast majority of ODE solver software are serial. In this manuscript we developed a set of parallelized ODE solvers using…

We present an open-source simulation framework for optically detected magnetic resonance, developed in Python. The framework allows users to construct, manipulate, and evolve multipartite quantum systems that consist of spins and electronic…

PYROBOCOP is a lightweight Python-based package for control and optimization of robotic systems described by nonlinear Differential Algebraic Equations (DAEs). In particular, the package can handle systems with contacts that are described…

Elliptic partial differential equations (PDEs) arise in many areas of computational sciences such as computational fluid dynamics, biophysics, engineering, geophysics and more. They are difficult to solve due to their global nature and…

Coupled multi-physics problems are encountered in countless applications and pose significant numerical challenges. Although monolithic approaches offer possibly the best solution strategy, they often require ad-hoc preconditioners and…

We present a method for constructing numerical schemes with up to 3rd strong convergence order for solution of a class of stochastic differential equations, including equations of the Langevin type. The construction proceeds in two stages.…

The KeOps library provides a fast and memory-efficient GPU support for tensors whose entries are given by a mathematical formula, such as kernel and distance matrices. KeOps alleviates the major bottleneck of tensor-centric libraries for…

We propose a hierarchical splitting approach to differential equations that provides a design principle for constructing splitting methods for $N$-split systems by iteratively applying splitting methods for two-split systems. We analyze the…

The recomputability and reproducibility of results from scientific software requires access to both the source code and all associated input and output data. However, the full collection of these resources often does not accompany the key…

It is common in classical mechanics to encounter systems whose Hamiltonian $H$ is the sum of an often exactly integrable Hamiltonian $H_0$ and a small perturbation $\epsilon H_1$ with $\epsilon\ll1$. Such near-integrability can be exploited…

We introduce an efficient variational hybrid quantum-classical algorithm designed for solving Caputo time-fractional partial differential equations. Our method employs an iterable cost function incorporating a linear combination of overlap…

In deterministic optimization, it is typically assumed that all problem parameters are fixed and known. In practice, however, some parameters may be a priori unknown but can be estimated from contextual information. A typical…

In this paper, we combine the operator splitting methodology for abstract evolution equations with that of stochastic methods for large-scale optimization problems. The combination results in a randomized splitting scheme, which in a given…

Recent years have seen a rise in the popularity of quality diversity (QD) optimization, a branch of optimization that seeks to find a collection of diverse, high-performing solutions to a given problem. To grow further, we believe the QD…

Partial Differential Equations (PDEs) are fundamental tools for modeling physical phenomena, yet most PDEs of practical interest cannot be solved analytically and require numerical approximations. The feasibility of such numerical methods,…

Background: Ad hoc parsers are pieces of code that use common string functions like split, trim, or slice to effectively perform parsing. Whether it is handling command-line arguments, reading configuration files, parsing custom file…

This paper discusses stochastic numerical methods of Runge-Kutta type with weak and strong convergences for systems of stochastic differential equations in It\^o form. At the beginning we give a brief overview of the stochastic numerical…

The explicit split-operator algorithm is often used for solving the linear and nonlinear time-dependent Schr\"{o}dinger equations. However, when applied to certain nonlinear time-dependent Schr\"{o}dinger equations, this algorithm loses…

Reduced basis methods are projection-based model order reduction techniques for reducing the computational complexity of solving parametrized partial differential equation problems. In this work we discuss the design of pyMOR, a freely…

This paper introduces OptimizedDP, a high-performance software library for several common grid-based dynamic programming (DP) algorithms used in control theory and robotics. Specifically, OptimizedDP provides functions to numerically solve…