Physics-Informed Neural networks for Advanced modeling
Physics-Informed Neural networks for Advanced modeling - Published in JOSS (2023)
GlobalSensitivity.jl
GlobalSensitivity.jl: Performant and Parallel Global Sensitivity Analysis with Julia - Published in JOSS (2022)
ProbNumDiffEq.jl
ProbNumDiffEq.jl: Probabilistic Numerical Solvers for Ordinary Differential Equations in Julia - Published in JOSS (2024)
ModeCouplingTheory.jl
ModeCouplingTheory.jl: A solver for mode-coupling-theory-like integro-differential equations - Published in JOSS (2023)
Kinetic.jl
Kinetic.jl: A portable finite volume toolbox for scientific and neural computing - Published in JOSS (2021)
(py)oscode
(py)oscode: fast solutions of oscillatory ODEs - Published in JOSS (2020)
Simframe
Simframe: A Python Framework for Scientific Simulations - Published in JOSS (2022)
OwlDE
OwlDE: making ODEs first-class Owl citizens - Published in JOSS (2019)
BracketingNonlinearSolve
High-performance and differentiation-enabled nonlinear solvers (Newton methods), bracketed rootfinding (bisection, Falsi), with sparsity and Newton-Krylov support.
`QuasinormalModes.jl`
`QuasinormalModes.jl`: A Julia package for computing discrete eigenvalues of second order ODEs - Published in JOSS (2022)
Catalyst
Chemical reaction network and systems biology interface for scientific machine learning (SciML). High performance, GPU-parallelized, and O(1) solvers in open source software.
reachabilityanalysis.jl
Computing reachable states of dynamical systems in Julia
Sundials
Julia interface to Sundials, including a nonlinear solver (KINSOL), ODE's (CVODE and ARKODE), and DAE's (IDA) in a SciML scientific machine learning enabled manner
ModelingToolkit
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
DelayDiffEq
Delay differential equation (DDE) solvers in Julia for the SciML scientific machine learning ecosystem. Covers neutral and retarded delay differential equations, and differential-algebraic equations.
NeuralPDE
Physics-Informed Neural Networks (PINN) Solvers of (Partial) Differential Equations for Scientific Machine Learning (SciML) accelerated simulation
SciMLBenchmarks
Scientific machine learning (SciML) benchmarks, AI for science, and (differential) equation solvers. Covers Julia, Python (PyTorch, Jax), MATLAB, R
ImplicitDiscreteSolve
High performance ordinary differential equation (ODE) and differential-algebraic equation (DAE) solvers, including neural ordinary differential equations (neural ODEs) and scientific machine learning (SciML)
RootedTrees
A collection of functionality around rooted trees to generate order conditions for Runge-Kutta methods in Julia for differential equations and scientific machine learning (SciML)
SBMLToolkit
SBML differential equation and chemical reaction model (Gillespie simulations) for Julia's SciML ModelingToolkit
JumpProcesses
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)
pomp
R package for statistical inference using partially observed Markov processes
scimlbook
Parallel Computing and Scientific Machine Learning (SciML): Methods and Applications (MIT 18.337J/6.338J)
NeuroDiffEq
NeuroDiffEq: A Python package for solving differential equations with neural networks - Published in JOSS (2020)
ClosedLoopReachability
Reachability analysis for closed-loop control systems in Julia
DiffEqBase
The lightweight Base library for shared types and functionality for defining differential equation and scientific machine learning (SciML) problems
https://github.com/sciml/surrogates.jl
Surrogate modeling and optimization for scientific machine learning (SciML)
StochasticDiffEq
Solvers for stochastic differential equations which connect with the scientific machine learning (SciML) ecosystem
BoundaryValueDiffEq
Boundary value problem (BVP) solvers for scientific machine learning (SciML)
SciMLSensitivity
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.
DiffEqFlux
Pre-built implicit layer architectures with O(1) backprop, GPUs, and stiff+non-stiff DE solvers, demonstrating scientific machine learning (SciML) and physics-informed machine learning methods
DifferentialEquations
Multi-language suite for high-performance solvers of differential equations and scientific machine learning (SciML) components. Ordinary differential equations (ODEs), stochastic differential equations (SDEs), delay differential equations (DDEs), differential-algebraic equations (DAEs), and more in Julia.
DiffEqNoiseProcess
A library of noise processes for stochastic systems like stochastic differential equations (SDEs) and other systems that are present in scientific machine learning (SciML)
SteadyStateDiffEq
Solvers for steady states in scientific machine learning (SciML)
SciMLTutorials
Tutorials for doing scientific machine learning (SciML) and high-performance differential equation solving with open source software.
ParameterizedFunctions
A simple domain-specific language (DSL) for defining differential equations for use in scientific machine learning (SciML) and other applications
diffeqpy
Solving differential equations in Python using DifferentialEquations.jl and the SciML Scientific Machine Learning organization
ReservoirComputing
Reservoir computing utilities for scientific machine learning (SciML)
DiffEqParamEstim
Easy scientific machine learning (SciML) parameter estimation with pre-built loss functions
MultiScaleArrays
A framework for developing multi-scale arrays for use in scientific machine learning (SciML) simulations
DiffEqBayes
Extension functionality which uses Stan.jl, DynamicHMC.jl, and Turing.jl to estimate the parameters to differential equations and perform Bayesian probabilistic scientific machine learning
DiffEqPhysics
A library for building differential equations arising from physical problems for physics-informed and scientific machine learning (SciML)
DiffEqDevTools
Benchmarking, testing, and development tools for differential equations and scientific machine learning (SciML)
SimpleDiffEq
Simple differential equation solvers in native Julia for scientific machine learning (SciML)
DiffEqFinancial
Differential equation problem specifications and scientific machine learning for common financial models
FEniCS
A scientific machine learning (SciML) wrapper for the FEniCS Finite Element library in the Julia programming language
SciMLExpectations
Fast uncertainty quantification for scientific machine learning (SciML) and differential equations
https://github.com/bluescarni/heyoka.py
Python library for ODE integration via Taylor's method and LLVM
exponentialutilities.jl
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.
pydiffgame
PyDiffGame is a Python implementation of a Nash Equilibrium solution to Differential Games, based on a reduction of Game Hamilton-Bellman-Jacobi (GHJB) equations to Game Algebraic and Differential Riccati equations, associated with Multi-Objective Dynamical Control Systems
DASKR
Interface to DASKR, a differential algebraic system solver for the SciML scientific machine learning ecosystem
StochasticDelayDiffEq
Stochastic delay differential equations (SDDE) solvers for the SciML scientific machine learning ecosystem
DASSL
Solves stiff differential algebraic equations (DAE) using variable stepsize backwards finite difference formula (BDF) in the SciML scientific machine learning organization
FdeSolver
FdeSolver.jl: A Julia package for the numerical solution of fractional differential equations (FDEs) as well as systems of equations.
diffeqdevdocs.jl
Developer documentation for the SciML scientific machine learning ecosystem's differential equation solvers
geometricintegratorsdiffeq.jl
Wrappers for GeometricIntegrators.jl into the SciML common interface for scientific machine learning (SciML)
Adapode
Adaptive P/ODE numerics with Grassmann element TensorField assembly
scimlbenchmarksoutput
SciML-Bench Benchmarks for Scientific Machine Learning (SciML), Physics-Informed Machine Learning (PIML), and Scientific AI Performance
DiffEqCallbacks
A library of useful callbacks for hybrid scientific machine learning (SciML) with augmented differential equation solvers
BVProblemLibrary
A library of premade problems for examples and testing differential equation solvers and other SciML scientific machine learning tools
omfrontend.jl
Experimental implementation of NF. That is a Modelica frontend in 100% Julia
diffeqdocs.jl
Documentation for the DiffEq differential equations and scientific machine learning (SciML) ecosystem
ODEInterfaceDiffEq
Adds the common API onto ODEInterface classic Fortran methods for the SciML Scientific Machine Learning organization
https://github.com/cpmech/russell
Rust Scientific Libary. ODE and DAE (Runge-Kutta) solvers. Special functions (Bessel, Elliptic, Beta, Gamma, Erf). Linear algebra. Sparse solvers (MUMPS, UMFPACK). Probability distributions. Tensor calculus.
https://github.com/rveltz/piecewisedeterministicmarkovprocesses.jl
Piecewise Deterministic Markov Processes in Julia
ModifiedHankelFunctionsOfOrderOneThird
Solutions to Stokes' differential equation.
diffeqonline
It's Angular2 business in the front, and a Julia party in the back! It's scientific machine learning (SciML) for the web
diffeqonlineserver
Backend for DiffEqOnline, a webapp for scientific machine learning (SciML)
diffeqdevmaterials
Various developer materials, like PDFs, notes, derivations, etc. for differential equations and scientific machine learning (SciML)
coarsegrained-md-neural-ode
Thesis repository on neural ordinary differential equations used for coarse-graining molecular dynamics
https://github.com/bchao1/poissonpy
📈 poissonpy is a Python Poisson Equation library for scientific computing, image and video processing, and computer graphics.
scimltutorialsoutput
Tutorials for doing scientific machine learning (SciML) and high-performance differential equation solving with open source software.
https://github.com/avik-pal/regneuralde.jl
Official Implementation of "Opening the Blackbox: Accelerating Neural Differential Equations by Regularizing Internal Solver Heuristics" (ICML 2021)
hmde
Implementation of hierarchical Bayesian longitudinal models to estimate differential equation parameters.
NeuralFieldEq.jl
NeuralFieldEq.jl: A flexible solver to compute Neural Field Equations in several scenarios - Published in JOSS (2022)
https://github.com/chenliu-1996/imageflownet
[ICASSP 2025 Oral] ImageFlowNet: Forecasting Multiscale Image-Level Trajectories of Disease Progression with Irregularly-Sampled Longitudinal Medical Images
BridgeDiffEq
A thin wrapper over Bridge.jl for the SciML scientific machine learning common interface, enabling new methods for neural stochastic differential equations (neural SDEs)
episimulator
EpiSimulator: A Data-Driven Stochastic Hybrid Model for COVID-19 in Italy.
investigating_mitigating_failure_modes_in_pinns
This repository contains the code and models for our paper "Investigating and Mitigating Failure Modes in Physics-informed Neural Networks(PINNs)"
torchlaplace
Neural Laplace: Differentiable Laplace Reconstructions for modelling any time observation with O(1) complexity.
SciMLWorkshop
Workshop materials for training in scientific computing and scientific machine learning
moccasin
MOCCASIN translates basic ODE-based MATLAB models of biological processes into SBML format.
