Dependency Packages

NeuralNetDiffEq.jl755PhysicsInformed Neural Networks (PINN) and Deep BSDE Solvers of Differential Equations for Scientific Machine Learning (SciML) accelerated simulation

DiffEqTutorials.jl694Tutorials for doing scientific machine learning (SciML) and highperformance differential equation solving with open source software.

ApproxFun.jl486Julia package for function approximation

DiffEqOperators.jl279Linear operators for discretizations of differential equations and scientific machine learning (SciML)

DiffEqSensitivity.jl248A component of the DiffEq ecosystem for enabling sensitivity analysis for scientific machine learning (SciML). Optimizethendiscretize, discretizethenoptimize, adjoint methods, and more for ODEs, SDEs, DDEs, DAEs, etc.

Kinetic.jl96Universal modeling and simulation of fluid mechanics upon machine learning. From the Boltzmann equation, heading towards multiscale and multiphysics flows.

EconPDEs.jl91Solve forwardlooking PDEs (e.g. HJB equations).

OrbitalTrajectories.jl74OrbitalTrajectories.jl is a modern orbital trajectory design, optimisation, and analysis library for Julia, providing methods and tools for designing spacecraft orbits and transfers via highperformance simulations of astrodynamical models.

AtomicGraphNets.jl58Atomic graph models for molecules and crystals in Julia

SingularIntegralEquations.jl57Julia package for solving singular integral equations

ReactionMechanismSimulator.jl54The amazing Reaction Mechanism Simulator for simulating large chemical kinetic mechanisms

NonlinearSchrodinger.jl33A suite of tools for solving Nonlinear Schrodinger equations via higherorder algorithms and Darboux transformations.

ClassicalOrthogonalPolynomials.jl33A Julia package for classical orthogonal polynomials and expansions

PDSampler.jl31Piecewise Deterministic Sampler library (Bouncy particle sampler, Zig Zag sampler, ...)

InfiniteLinearAlgebra.jl30A Julia repository for linear algebra with infinite matrices

ODINN.jl27Global glacier model using Universal Differential Equations for climateglacier interactions

HarmonicOrthogonalPolynomials.jl24A Julia package for working with spherical harmonic expansions

FluxReconstruction.jl18Flux reconstruction method for advectiondiffusion type physics

EffectiveWaves.jl17A package to calculate ensemble averaged waves in heterogeneous materials. The focus is on wave propagation, scattering, and reflection, from particulate and porous materials.

MOSLab.jl16From Semiconductor to TransistorLevel Modeling in Julia

CompactBases.jl16Julia library for function approximation with compact basis functions

MultivariateOrthogonalPolynomials.jl15Supports approximating functions and solving differential equations on various higher dimensional domains such as disks and triangles

ApproxFunBase.jl13Core functionality of ApproxFun

SimpleDifferentialOperators.jl12Library for simple upwind finite differences

KitML.jl11Lightweight module of neural differential equations in Kinetic.jl

MRIgeneralizedBloch.jl10

AtomicLevels.jl9

Poltergeist.jl9Julia package for transfer operator spectral methods

NPCFs.jl9NPoint Correlation Functions in Julia

QuantumStateDistributions.jl7Distributions for continuous variables

KitBase.jl7Lightweight module of physical formulations in Kinetic.jl

OrthogonalPolynomialsQuasi.jl7A package for representing orthogonal polynomials as quasi arrays

OscillatoryIntegrals.jl7Calculate oscillatory integrals using Julia

QuantumStateBase.jl7Quantum states for quantum optics.

QuantumStatePlots.jl7Plot Wigner function and density matrix generated by QuantumStateBase.jl

ApproxFunFourier.jl6Support for Fourierbased spaces in ApproxFun

SemiseparableMatrices.jl5A Julia package to represent semiseparable and almost banded matrices

SingularIntegrals.jl5A Julia package for computing singular integrals

CoulombIntegrals.jl5

ApproxFunOrthogonalPolynomials.jl5Support for orthogonal polynomialbased spaces in ApproxFun
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