相关论文: Symbolic Manipulation of Flows of Nonlinear Evolut…

This paper demonstrates how certified computational tools can be used to address various problems in control theory. In particular, we introduce PACE.jl, a Julia package that implements symbolic elimination techniques, including (among…

Accurate and efficient methods to simulate nonadiabatic and quantum nuclear effects in high-dimensional and dissipative systems are crucial for the prediction of chemical dynamics in condensed phase. To facilitate effective development,…

We present an efficient numerical implementation of the quasi-classical doorway-window approximation, specifically designed for on-the-fly simulations of time-resolved nonlinear spectroscopic signals in the Julia package WaveMixings.jl. The…

HarmonicBalance.jl is a publicly available Julia package designed to simplify and solve systems of periodic time-dependent nonlinear ordinary differential equations. Time dependence of the system parameters is treated with the harmonic…

Gaussian processes are a class of flexible nonparametric Bayesian tools that are widely used across the sciences, and in industry, to model complex data sources. Key to applying Gaussian process models is the availability of well-developed…

Proprietary closed-source software is still the norm in advanced process control. Transparency and reproducibility are key aspects of scientific research. Free and open-source toolkit can contribute to the development, sharing and…

Taylor series methods show a newfound promise for the solution of non-stiff ordinary differential equations (ODEs) given the rise of new compiler-enhanced techniques for calculating high order derivatives. In this paper we detail a new…

Sequential sampling models (SSMs) are a widely used framework describing decision-making as a stochastic, dynamic process of evidence accumulation. SSMs popularity across cognitive science has driven the development of various software…

The state of numerical computing is currently characterized by a divide between highly efficient yet typically cumbersome low-level languages such as C, C++, and Fortran and highly expressive yet typically slow high-level languages such as…

We introduce Metatheory.jl: a lightweight and performant general purpose symbolics and metaprogramming framework meant to simplify the act of writing complex Julia metaprograms and to significantly enhance Julia with a native term rewriting…

Efficiently solving nonlinear equations underpins numerous scientific and engineering disciplines, yet scaling these solutions for challenging system models remains a challenge. This paper presents NonlinearSolve.jl -- a suite of…

In this paper we present BilevelJuMP, a new Julia package to support bilevel optimization within the JuMP framework. The package is a Julia library that enables the user to describe both upper and lower-level optimization problems using the…

Biological systems with intertwined feedback loops pose a challenge to mathematical modeling efforts. Moreover, rare events, such as mutation and extinction, complicate system dynamics. Stochastic simulation algorithms are useful in…

Prior work on computable defect-based local error estimators for (linear) time-reversible integrators is extended to nonlinear and nonautonomous evolution equations. We prove that the asymptotic results from the linear case [W. Auzinger and…

This article introduces new acceleration methods for fixed-point iterations. Extrapolations are computed using two or three mappings alternately and a new type of step length is proposed with good properties for nonlinear applications. The…

We present an open-source Julia-based software toolkit for solving the phase problem using dual-space iterative algorithms. The toolkit is specifically designed for aperiodic crystals and quasicrystals, supporting general space group…

We present the Julia package Manifolds$.$jl, providing a fast and easy-to-use library of Riemannian manifolds and Lie groups. This package enables working with data defined on a Riemannian manifold, such as the circle, the sphere, symmetric…

Symbolic computation is an important approach in automated program analysis. Most state-of-the-art tools perform symbolic computation as interpreters and directly maintain symbolic data. In this paper, we show that it is feasible, and in…

The julia package integrates the Julia programming language into Stata. Users can transfer data between Stata and Julia, issue Julia commands to analyze and plot, and pass results back to Stata. Julia's econometric ecosystem is not as…

OptControl.jl(OptControl) implements that modeling optimal control problems with symbolic algebra system based on Julia language, and generates the corresponding numerical optimization codes to solve them with packages from Julia.…