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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…

We present a Julia-based interface to the precompiled HALLaR and cuHALLaR binaries for large-scale semidefinite programs (SDPs). Both solvers are established as fast and numerically stable, and accept problem data in formats compatible with…

At many scales in neuroscience, appropriate mathematical models take the form of complex dynamical systems. Parametrising such models to conform to the multitude of available experimental constraints is a global nonlinear optimisation…

Scorio.jl is a Julia package for evaluating and ranking systems from repeated responses to shared tasks. It provides a common tensor-based interface for direct score-based, pairwise, psychometric, voting, graph, and listwise methods, so the…

For scientific machine learning tasks with a lot of custom code, picking the right Automatic Differentiation (AD) system matters. Our Julia package DifferentiationInterface$.$jl provides a common frontend to a dozen AD backends, unlocking…

The GRAPE$.$jl package (https://github.com/JuliaQuantumControl/GRAPE.jl) implements Gradient Ascent Pulse Engineering, a widely used method of quantum optimal control. Its purpose is to find controls that steer a quantum system in a…

This article introduces a software package release for geometrically reasoning about the \textit{safety} desiderata of (complex) dynamical systems via level set methods. In emphasis, safety is analyzed with Hamilton-Jacobi equations. In…

We present JuliaReach, a toolbox for set-based reachability analysis of dynamical systems. JuliaReach consists of two main packages: Reachability, containing implementations of reachability algorithms for continuous and hybrid systems, and…

JuMP is an open-source modeling language that allows users to express a wide range of optimization problems (linear, mixed-integer, quadratic, conic-quadratic, semidefinite, and nonlinear) in a high-level, algebraic syntax. JuMP takes…

We present ForwardDiff, a Julia package for forward-mode automatic differentiation (AD) featuring performance competitive with low-level languages like C++. Unlike recently developed AD tools in other popular high-level languages such as…

Thermodynamic models are often vital when characterising complex systems, particularly natural gas, electrolyte, polymer, pharmaceutical and biological systems. However, their implementations have historically been abstruse and cumbersome,…

This paper presents the Julia package CCOpt, built on top of the interior-point solver MadNLP. CCOpt implements a suite of algorithms for Mathematical Programs with Complementarity Constraints (MPCCs). The solver additionally comes with…

We present an open source computational framework geared towards the efficient numerical investigation of open quantum systems written in the Julia programming language. Built exclusively in Julia and based on standard quantum optics…

Hierarchical optimization architectures are used in power systems to manage disturbances and phenomena that arise at multiple spatial and temporal scales. We present a graph modeling abstraction for representing such architectures and an…

This paper describes open-source scientific contributions in python surrounding the numerical solutions to hyperbolic Hamilton-Jacobi (HJ) partial differential equations viz., their implicit representation on co-dimension one surfaces;…

This paper introduces the algorithmic design and implementation of Tulip, an open-source interior-point solver for linear optimization. It implements a regularized homogeneous interior-point algorithm with multiple centrality corrections,…

The Fast Fourier Transform (FFT) is a fundamental numerical technique with widespread application in a range of scientific problems. As scientific simulations attempt to exploit exascale systems, there has been a growing demand for…

In this paper we use memory-distributed level set-based topology optimisation to design three-dimensional periodic piezoelectric materials with enhanced properties. We compare and assess several existing iterative solvers with respect to…

InvertibleNetworks.jl is a Julia package designed for the scalable implementation of normalizing flows, a method for density estimation and sampling in high-dimensional distributions. This package excels in memory efficiency by leveraging…

We present a general graph-based modeling abstraction for optimization that we call an OptiGraph. Under this abstraction, any optimization problem is treated as a hierarchical hypergraph in which nodes represent optimization subproblems and…