differential-equations

There are 23 repositories under differential-equations topic.

SciML / DifferentialEquations.jl
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.
dae dde delay-differential-equations differential-algebraic-equations differential-equations differentialequations dynamical-systems julia neural-differential-equations ode partial-differential-equations pde python r scientific-machine-learning sciml sde spde stochastic-differential-equations stochastic-processes
Language:Julia 2756
cpmech / gosl
Linear algebra, eigenvalues, FFT, Bessel, elliptic, orthogonal polys, geometry, NURBS, numerical quadrature, 3D transfinite interpolation, random numbers, Mersenne twister, probability distributions, optimisation, differential equations.
computational-geometry differential-equations eigenvalues eigenvectors fast-fourier-transform linear-algebra linear-programming mersenne-twister optimization parallel-computations scientific-computing sparse-systems
Language:Go 1805
SciML / SciMLBook
Parallel Computing and Scientific Machine Learning (SciML): Methods and Applications (MIT 18.337J/6.338J)
differential-equations scientific-machine-learning neural-networks numerical-methods gpu-computing stiff-equations lecture-notes performance-engineering parallelism scientific-simulators neural-ode neural-sde sciml
Language:HTML 1790
google-research / torchsde
Differentiable SDE solvers with GPU support and efficient sensitivity analysis.
deep-learning deep-neural-networks differential-equations dynamical-systems neural-differential-equations pytorch stochastic-differential-equations stochastic-processes stochastic-volatility-models
Language:Python 1469
SciML / ModelingToolkit.jl
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
differential-equations ode dae ordinary-differential-equations pde sde dde stochastic-differential-equations delay-differential-equations julia symbolic symbolic-computation symbolic-numerics computer-algebra sciml scientific-machine-learning optimization nonlinear-programming acausal equation-based
Language:Julia 1334
patrick-kidger / diffrax
Numerical differential equation solvers in JAX. Autodifferentiable and GPU-capable. https://docs.kidger.site/diffrax/
deep-learning differential-equations dynamical-systems equinox jax machine-learning neural-differential-equations neural-networks
Language:Python 1230
SciML / NeuralPDE.jl
Physics-Informed Neural Networks (PINN) Solvers of (Partial) Differential Equations for Scientific Machine Learning (SciML) accelerated simulation
differential-equations differentialequations neural-differential-equations scientific-ml scientific-ai partial-differential-equations ordinary-differential-equations neural-network neural-networks ode pde sciml scientific-machine-learning pinn machine-learning
Language:Julia 903
brian2
brian-team / brian2
Brian is a free, open source simulator for spiking neural networks.
biological-simulations brian brian2 code-generation computational-neuroscience differential-equations neuroscience python science simulation-framework spiking-neural-networks
Language:Python 879
SciML / DiffEqFlux.jl
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-ode neural-sde neural-pde neural-dde neural-differential-equations stiff-ode ordinary-differential-equations stochastic-differential-equations delay-differential-equations partial-differential-equations neural-networks differentialequations differential-equations scientific-ml scientific-ai neural-jump-diffusions neural-sdes scientific-machine-learning pinn physics-informed-learning
Language:Julia 836
SciML / SciMLTutorials.jl
Tutorials for doing scientific machine learning (SciML) and high-performance differential equation solving with open source software.
differentialequations differential-equations ode sde dae dde ordinary-differential-equations neural-differential-equations neural-ode pde partial-differential-equations stochastic-differential-equations julia scientific-machine-learning sciml python r hacktoberfest
Language:CSS 708
neurodiffeq
NeuroDiffGym / neurodiffeq
A library for solving differential equations using neural networks based on PyTorch, used by multiple research groups around the world, including at Harvard IACS.
differential-equations neural-networks pytorch pde-solver odes artificial-intelligence deep-learning physics-informed-neural-networks pypi time-series mathematical-modelling scientific-computing ode pinn boundary-value-problem initial-value-problem
Language:Python 631
patrick-kidger / NeuralCDE
Code for "Neural Controlled Differential Equations for Irregular Time Series" (Neurips 2020 Spotlight)
machine-learning rough-paths neural-differential-equations time-series controlled-differential-equations deep-learning deep-neural-networks pytorch dynamical-systems differential-equations neural-networks
Language:Python 581
wavetorch
fancompute / wavetorch
🌊 Numerically solving and backpropagating through the wave equation
wave-equation differential-equations time-series vowel-recognition recurrent-neural-network rnn pytorch
Language:Python 501
SciML / OrdinaryDiffEq.jl
High performance ordinary differential equation (ODE) and differential-algebraic equation (DAE) solvers, including neural ordinary differential equations (neural ODEs) and scientific machine learning (SciML)
ordinary-differential-equations differentialequations ode event-handling adaptive high-performance differential-equations scientific-machine-learning hacktoberfest julia sciml
Language:Julia 498
SciML / diffeqpy
Solving differential equations in Python using DifferentialEquations.jl and the SciML Scientific Machine Learning organization
differential-equations differentialequations sde sdes ode numba dae ordinary-differential-equations differential-algebraic-equations stochastic-differential-equations dde delay-differential-equations sciml scientific-machine-learning
Language:Python 495
SciML / Catalyst.jl
Chemical reaction network and systems biology interface for scientific machine learning (SciML). High performance, GPU-parallelized, and O(1) solvers in open source software.
biology chemical-reactions differential-equations dsl gillespie-algorithm julia ode rate-laws reaction-network scientific-machine-learning sciml sde simulation systems-biology systems-biology-simulation
Language:Julia 419
SciML / DataDrivenDiffEq.jl
Data driven modeling and automated discovery of dynamical systems for the SciML Scientific Machine Learning organization
differential-equations julia ode scientific-machine-learning sciml
Language:Julia 398
patrick-kidger / torchcde
Differentiable controlled differential equation solvers for PyTorch with GPU support and memory-efficient adjoint backpropagation.
time-series machine-learning neural-differential-equations controlled-differential-equations deep-learning deep-neural-networks pytorch dynamical-systems differential-equations neural-networks
Language:Python 392
vlang / vsl
V library to develop Artificial Intelligence and High-Performance Scientific Computations
computational-geometry differential-equations eigenvalues eigenvectors hacktoberfest linear-algebra openblas opencl optimization parallel-computations scientific-computing sparse-systems v
Language:V 328
SciML / Surrogates.jl
Surrogate modeling and optimization for scientific machine learning (SciML)
automatic-differentiation differential-equations high-performance-computing julia optimization scientific-machine-learning sciml surrogate surrogate-based-optimization surrogate-models surrogates
Language:Julia 313
SciML / SciMLSensitivity.jl
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.
differentialequations sensitivity-analysis neural-ode adjoint backpropogation neural-sde ode sde dae dde sciml scientific-machine-learning hacktoberfest differential-equations
Language:Julia 308
mitmath / 18S096SciML
18.S096 - Applications of Scientific Machine Learning
scientific-machine-learning differential-equations neural-networks neural-ode partial-differential-equations sciml lecture-notes
Language:HTML 303
SciML / DiffEqBase.jl
The lightweight Base library for shared types and functionality for defining differential equation and scientific machine learning (SciML) problems
differentialequations differential-equations ode sde dae dde ordinary-differential-equations neural-differential-equations neural-ode stochastic-differential-equations delay-differential-equations differential-algebraic-equations pde partial-differential-equations sciml scientific-machine-learning hacktoberfest
Language:Julia 297
SciML / SciMLBenchmarks.jl
Scientific machine learning (SciML) benchmarks, AI for science, and (differential) equation solvers. Covers Julia, Python (PyTorch, Jax), MATLAB, R
differential-equations differentialequations ode sde dae neural-ode nerual-differential-equations benchmark pde partial-differential-equations sciml scientific-machine-learning ai julia ai-for-science jax matlab python pytorch
Language:MATLAB 289
SciML / DiffEqOperators.jl
Linear operators for discretizations of differential equations and scientific machine learning (SciML)
differential-equations differentialequations partial-differential-equations pde sde stochastic-differential-equations finite-difference-method fdm matrix-free julia neural-differential-equations neural-ode sciml scientific-machine-learning
Language:Julia 283
ComponentArrays.jl
jonniedie / ComponentArrays.jl
Arrays with arbitrarily nested named components.
differential-equations differentialequations control-systems controls-and-dynamics controls scientific-machine-learning modeling simulation simulation-modeling dynamical-systems array named-tuples arrays machine-learning julia neural-ode neural-networks optimization modeling-language
Language:Julia 276
analysiscenter / pydens
PyDEns is a framework for solving Ordinary and Partial Differential Equations (ODEs & PDEs) using neural networks
deep-learning neural-networks partial-differential-equations numerical-methods differential-equations solving-pdes ode ode-solver pde-solver
Language:Jupyter Notebook 273
SciML / DiffEqGPU.jl
GPU-acceleration routines for DifferentialEquations.jl and the broader SciML scientific machine learning ecosystem
gpu gpu-parallelism differentialequations differential-equations ode sde dae dde neural-ode neural-differential-equations sciml scientific-machine-learning
Language:Julia 267
easy-neural-ode
jacobjinkelly / easy-neural-ode
Code for the paper "Learning Differential Equations that are Easy to Solve"
deep-learning deep-neural-networks differential-equations dynamical-systems jax machine-learning neural-differential-equations neural-ode numerical-integration ode ode-solver
Language:Python 262
AMaDiA
AstusRush / AMaDiA
Astus' Mathematical Display Application : A GUI for Mathematics (Calculator, LaTeX Converter, Plotter, ... )
calculator plotter latex pyqt5 sympy numpy gui-application python scientific-calculator pyplot python-calculator equation differential-equations keyboard-layout chat-application function-plotter window-frame control-systems
Language:Python 260
SciML / DiffEqDocs.jl
Documentation for the DiffEq differential equations and scientific machine learning (SciML) ecosystem
differential-equations sciml scientific-machine-learning physics-informed-learning ode sde dae dde neural-ode hacktoberfest
Language:Julia 260
scikit-fmm / scikit-fmm
scikit-fmm is a Python extension module which implements the fast marching method.
python python-extension numpy-arrays boundaries differential-equations surface-modeling surface-reconstruction scikit-fmm
Language:Python 256
mathLab / PINA
Physics-Informed Neural networks for Advanced modeling
physics-informed-neural-networks modeling machine-learning deep-learning python pytorch differential-equations neural-network ode pde physics-informed hacktoberfest lightining pinn equation-learning
Language:Python 244
SciML / StochasticDiffEq.jl
Solvers for stochastic differential equations which connect with the scientific machine learning (SciML) ecosystem
stochastic-differential-equations stochastic sde sode adaptive ito stratonovich stochastic-processes noise random random-differential-equations rode rde differentialequations differential-equations solvers sciml scientific-machine-learning hacktoberfest
Language:Julia 234
SciML / NeuralOperators.jl
DeepONets, (Fourier) Neural Operators, Physics-Informed Neural Operators, and more in Julia
automatic-differentiation deep-learning deeponet differential-equations fourier-neural-operator fourier-transform gnn julia operator partial-differential-equations pde scientific-machine-learning
Language:Julia 227
infiniteopt / InfiniteOpt.jl
An intuitive modeling interface for infinite-dimensional optimization problems.
optimization julia modeling-language dynamic-programming stochastic-optimization optimal-control pde-constrained-optimization nonlinear-optimization differential-equations measure-theory
Language:Julia 225