neural-ode

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

neural-networks partial-differential-equations differential-equations ordinary-differential-equations differentialequations stochastic-differential-equations delay-differential-equations pinn neural-ode scientific-machine-learning neural-sde neural-pde neural-dde neural-differential-equations stiff-ode scientific-ml scientific-ai neural-jump-diffusions neural-sdes physics-informed-learning

UpdatedOct 5, 2025
Julia

msurtsukov /neural-ode

Star780

Jupyter notebook with Pytorch implementation of Neural Ordinary Differential Equations

jupyter-notebook pytorch vae neural-ode

UpdatedFeb 27, 2024
Jupyter Notebook

SciML /SciMLTutorials.jl

Sponsor

Star736

Tutorials for doing scientific machine learning (SciML) and high-performance differential equation solving with open source software.

python r julia ode dde partial-differential-equations differential-equations ordinary-differential-equations differentialequations sde pde dae stochastic-differential-equations hacktoberfest neural-ode scientific-machine-learning neural-differential-equations sciml

UpdatedAug 12, 2025
CSS

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 neural-ode scientific-machine-learning neural-sde sciml

UpdatedOct 1, 2025
Julia

SciML /DiffEqBase.jl

Sponsor

Star347

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 delay-differential-equations hacktoberfest differential-algebraic-equations neural-ode scientific-machine-learning neural-differential-equations sciml

UpdatedSep 17, 2025
Julia

SciML /ComponentArrays.jl

Sponsor

Star333

Arrays with arbitrarily nested named components.

machine-learning simulation optimization julia modeling array controls neural-networks arrays dynamical-systems control-systems differential-equations modeling-language differentialequations simulation-modeling named-tuples controls-and-dynamics neural-ode scientific-machine-learning

UpdatedAug 25, 2025
Julia

SciML /SciMLBenchmarks.jl

Sponsor

Star330

Scientific machine learning (SciML) benchmarks, AI for science, and (differential) equation solvers. Covers Julia, Python (PyTorch, Jax), MATLAB, R

python benchmark ai julia matlab pytorch ode partial-differential-equations differential-equations differentialequations sde pde dae jax neural-ode scientific-machine-learning nerual-differential-equations sciml ai-for-science

UpdatedOct 7, 2025
MATLAB

SciML /DiffEqDocs.jl

Sponsor

Star314

Documentation for the DiffEq differential equations and scientific machine learning (SciML) ecosystem

ode dde differential-equations sde dae hacktoberfest neural-ode scientific-machine-learning sciml physics-informed-learning

UpdatedSep 17, 2025
Julia

mitmath /18S096SciML

Star311

18.S096 - Applications of Scientific Machine Learning

neural-networks partial-differential-equations differential-equations lecture-notes neural-ode scientific-machine-learning sciml

UpdatedApr 26, 2022
HTML

SciML /DiffEqGPU.jl

Sponsor

Star308

GPU-acceleration routines for DifferentialEquations.jl and the broader SciML scientific machine learning ecosystem

gpu ode dde differential-equations differentialequations sde dae neural-ode scientific-machine-learning neural-differential-equations gpu-parallelism sciml

UpdatedAug 11, 2025
Julia

jacobjinkelly /easy-neural-ode

Star284

Code for the paper "Learning Differential Equations that are Easy to Solve"

machine-learning deep-neural-networks deep-learning ode dynamical-systems differential-equations numerical-integration ode-solver jax neural-ode neural-differential-equations

UpdatedNov 25, 2021
Python

SciML /DiffEqOperators.jl

Sponsor

Star284

Linear operators for discretizations of differential equations and scientific machine learning (SciML)

julia partial-differential-equations differential-equations fdm differentialequations sde pde stochastic-differential-equations matrix-free finite-difference-method neural-ode scientific-machine-learning neural-differential-equations sciml

UpdatedJun 15, 2023
Julia

martenlienen /torchode

Star268

A parallel ODE solver for PyTorch

deep-learning pytorch neural-ode

UpdatedOct 3, 2024
Python

ChrisRackauckas /universal_differential_equations

Sponsor

Star233

Repository for the Universal Differential Equations for Scientific Machine Learning paper, describing a computational basis for high performance SciML

neural-ode scientific-machine-learning sciml universal-differential-equations