SciML Open Source Scientific Machine Learning

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199 repositories

PolyChaos.jl
Public
A Julia package to construct orthogonal polynomials, their quadrature rules, and use it with polynomial chaos expansions.
julia julia-language polynomials quadrature differential-equations uncertainty-quantification uncertainty-propagation quadrature-integration quadrature-rules orthogonal-polynomials
Julia
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MIT License
•26•124•12•2•Updated Jan 4, 2026Jan 4, 2026
SciMLSensitivity.jl
Public
A component of the DiffEq ecosystem for enabling sensitivity analysis for scientific machine learning (SciML). Optimize-then-discretize, discretize-then-optimize, adjoint methods, and more for ODEs, SDEs, DDEs, DAEs, etc.
ode dde differential-equations differentialequations sde dae sensitivity-analysis hacktoberfest adjoint backpropogation
Julia
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Other
•79•373•115•14•Updated Jan 4, 2026Jan 4, 2026
SymbolicNumericIntegration.jl
Public
SymbolicNumericIntegration.jl: Symbolic-Numerics for Solving Integrals
integration julia julia-language symbolic-regression scientific-machine-learning
Julia
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MIT License
•11•130•6•3•Updated Jan 4, 2026Jan 4, 2026
ModelOrderReduction.jl
Public
High-level model-order reduction to automate the acceleration of large-scale simulations
hpc julia partial-differential-equations differential-equations model-order-reduction scientific-machine-learning sciml
Julia
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MIT License
•6•42•19•8•Updated Jan 4, 2026Jan 4, 2026
FastAlmostBandedMatrices.jl
Public
Julia
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MIT License
•4•9•1•1•Updated Jan 3, 2026Jan 3, 2026
DASKR.jl
Public
Interface to DASKR, a differential algebraic system solver for the SciML scientific machine learning ecosystem
differential-equations differentialequations dae differential-algebraic daskr differential-algebraic-equations scientific-machine-learning sciml
Julia
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Other
•15•11•3•1•Updated Jan 3, 2026Jan 3, 2026
Catalyst.jl
Public
Chemical reaction network and systems biology interface for scientific machine learning (SciML). High performance, GPU-parallelized, and O(1) solvers in open source software.
simulation biology dsl julia systems-biology ode reaction-network differential-equations sde chemical-reactions
Julia
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Other
•80•503•104•35•Updated Jan 3, 2026Jan 3, 2026
ReservoirComputing.jl
Public
Reservoir computing utilities for scientific machine learning (SciML)
machine-learning julia rnn differential-equations echo-state-networks reservoir-computing scientific-machine-learning sciml
Julia
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MIT License
•42•222•32•2•Updated Jan 3, 2026Jan 3, 2026
BoundaryValueDiffEq.jl
Public
Boundary value problem (BVP) solvers for scientific machine learning (SciML)
gpu differential-equations differentialequations bvp neural-ode scientific-machine-learning neural-differential-equations neural-bvp sciml
Julia
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Other
•40•54•27•15•Updated Jan 3, 2026Jan 3, 2026
DiffEqBase.jl
Public
The lightweight Base library for shared types and functionality for defining differential equation and scientific machine learning (SciML) problems
ode dde partial-differential-equations differential-equations ordinary-differential-equations differentialequations sde pde dae stochastic-differential-equations
Julia
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Other
•122•348•58•15•Updated Jan 3, 2026Jan 3, 2026
Static.jl
Public
Static types useful for dispatch and generated functions.
Julia
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MIT License
•18•62•17•5•Updated Jan 3, 2026Jan 3, 2026
ADTypes.jl
Public
Repository for automatic differentiation backend types
julia automatic-differentiation autodiff
Julia
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MIT License
•15•60•10•5•Updated Jan 3, 2026Jan 3, 2026
RuntimeGeneratedFunctions.jl
Public
Functions generated at runtime without world-age issues or overhead
julia
Julia
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MIT License
•15•108•14•0•Updated Jan 3, 2026Jan 3, 2026
SimpleNorm.jl
Public
Implementation of a norm function without LinearAlgebra.jl / BLAS / LAPACK
Julia
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MIT License
•1•1•0•0•Updated Jan 3, 2026Jan 3, 2026
ModelingToolkit.jl
Public
An acausal modeling framework for automatically parallelized scientific machine learning (SciML) in Julia. A computer algebra system for integrated symbolics for physics-informed machine learning and automated transformations of differential equations
computer-algebra optimization julia ode symbolic dde differential-equations ordinary-differential-equations sde pde
Julia
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Other
•238•1.6k•446•101•Updated Jan 3, 2026Jan 3, 2026
RecursiveArrayTools.jl
Public
Tools for easily handling objects like arrays of arrays and deeper nestings in scientific machine learning (SciML) and other applications
vector array recursion scientific-machine-learning sciml
Julia
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Other
•70•224•33•6•Updated Jan 3, 2026Jan 3, 2026
DiffEqCallbacks.jl
Public
A library of useful callbacks for hybrid scientific machine learning (SciML) with augmented differential equation solvers
julia callback ode dde differential-equations sde dae neural-ode scientific-machine-learning sciml
Julia
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Other
•53•100•22•4•Updated Jan 3, 2026Jan 3, 2026
GeometricIntegratorsDiffEq.jl
Public
Wrappers for GeometricIntegrators.jl into the SciML common interface for scientific machine learning (SciML)
differential-equations geometric-algorithms scientific-machine-learning sciml geometricintegrators
Julia
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Other
•13•8•1•0•Updated Jan 3, 2026Jan 3, 2026
DiffEqDevTools.jl
Public
Benchmarking, testing, and development tools for differential equations and scientific machine learning (SciML)
ode developer-tools dde differential-equations sde dae scientific-machine-learning sciml
Julia
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Other
•36•52•3•2•Updated Jan 3, 2026Jan 3, 2026
PoissonRandom.jl
Public
Fast Poisson Random Numbers in pure Julia for scientific machine learning (SciML)
julia high-performance-computing poisson poisson-distribution poisson-processes scientific-machine-learning sciml tau-leaping
Julia
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Other
•6•20•1•1•Updated Jan 3, 2026Jan 3, 2026
EllipsisNotation.jl
Public
Julia-based implementation of ellipsis array indexing notation `..`
julia julia-language arrays julialang
Julia
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Other
•14•97•2•1•Updated Jan 3, 2026Jan 3, 2026
JumpProcesses.jl
Public
Build and simulate jump equations like Gillespie simulations and jump diffusions with constant and state-dependent rates and mix with differential equations and scientific machine learning (SciML)
ssa ode stochastic differential-equations sde gillespie jump-diffusion neural-ode scientific-machine-learning neural-differential-equations
Julia
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Other
•38•147•71•9•Updated Jan 3, 2026Jan 3, 2026
SymbolicLimits.jl
Public
Julia
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MIT License
•5•5•1•1•Updated Jan 3, 2026Jan 3, 2026
BipartiteGraphs.jl
Public
Julia
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MIT License
•1•1•0•0•Updated Jan 3, 2026Jan 3, 2026
MaybeInplace.jl
Public
Rewrite Inplace Operations to be OOP if needed
Julia
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MIT License
•3•8•1•2•Updated Jan 3, 2026Jan 3, 2026
DataCollocations.jl
Public
Non-parametric data collocation functionality for smoothing timeseries data and estimating derivatives.
Julia
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MIT License
•0•0•0•5•Updated Jan 3, 2026Jan 3, 2026
IRKGaussLegendre.jl
Public
Implicit Runge-Kutta Gauss-Legendre 16th order (Julia)
Julia
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MIT License
•10•28•3•1•Updated Jan 3, 2026Jan 3, 2026
SimpleBoundaryValueDiffEq.jl
Public
Julia
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MIT License
•5•3•0•1•Updated Jan 3, 2026Jan 3, 2026
ExponentialUtilities.jl
Public
Fast and differentiable implementations of matrix exponentials, Krylov exponential matrix-vector multiplications ("expmv"), KIOPS, ExpoKit functions, and more. All your exponential needs in SciML form.
gpu high-performance julia exponential differential-equations krylov krylov-methods krylov-subspace-methods matrix-exponential expokit
Julia
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Other
•31•105•26•1•Updated Jan 3, 2026Jan 3, 2026
SimpleDiffEq.jl
Public
Simple differential equation solvers in native Julia for scientific machine learning (SciML)
differential-equations scientific-machine-learning sciml
Julia
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Other
•13•24•2•2•Updated Jan 3, 2026Jan 3, 2026