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Search results for differential equations

differential-equations x
210 search results found
Differentialequations.jl ā­Ā 2,689
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.
Gosl ā­Ā 1,791
Linear algebra, eigenvalues, FFT, Bessel, elliptic, orthogonal polys, geometry, NURBS, numerical quadrature, 3D transfinite interpolation, random numbers, Mersenne twister, probability distributions, optimisation, differential equations.
Scimlbook ā­Ā 1,722
Parallel Computing and Scientific Machine Learning (SciML): Methods and Applications (MIT 18.337J/6.338J)
Torchsde ā­Ā 1,357
Differentiable SDE solvers with GPU support and efficient sensitivity analysis.
Modelingtoolkit.jl ā­Ā 1,292
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
Diffrax ā­Ā 1,131
Numerical differential equation solvers in JAX. Autodifferentiable and GPU-capable. https://docs.kidger.site/diffrax/
Neuralpde.jl ā­Ā 864
Physics-Informed Neural Networks (PINN) Solvers of (Partial) Differential Equations for Scientific Machine Learning (SciML) accelerated simulation
Brian2 ā­Ā 838
Brian is a free, open source simulator for spiking neural networks.
Diffeqflux.jl ā­Ā 810
Universal neural differential equations with O(1) backprop, GPUs, and stiff+non-stiff DE solvers, demonstrating scientific machine learning (SciML) and physics-informed machine learning methods
Scimltutorials.jl ā­Ā 698
Tutorials for doing scientific machine learning (SciML) and high-performance differential equation solving with open source software.
Neurodiffeq ā­Ā 576
A library for solving differential equations using neural networks based on PyTorch, used by multiple research groups around the world, including at Harvard IACS.
Ordinarydiffeq.jl ā­Ā 479
High performance ordinary differential equation (ODE) and differential-algebraic equation (DAE) solvers, including neural ordinary differential equations (neural ODEs) and scientific machine learning (SciML)
Diffeqpy ā­Ā 456
Solving differential equations in Python using DifferentialEquations.jl and the SciML Scientific Machine Learning organization
Brainpy ā­Ā 438
Brain Dynamics Programming in Python
Catalyst.jl ā­Ā 402
Chemical reaction network and systems biology interface for scientific machine learning (SciML). High performance, GPU-parallelized, and O(1) solvers in open source software.
Datadrivendiffeq.jl ā­Ā 393
Data driven modeling and automated discovery of dynamical systems for the SciML Scientific Machine Learning organization
Torchcde ā­Ā 361
Differentiable controlled differential equation solvers for PyTorch with GPU support and memory-efficient adjoint backpropagation.
Neuralcde ā­Ā 352
Code for "Neural Controlled Differential Equations for Irregular Time Series" (Neurips 2020 Spotlight)
Wavetorch ā­Ā 348
šŸŒŠ Numerically solving and backpropagating through the wave equation
Vsl ā­Ā 311
V library to develop Artificial Intelligence and High-Performance Scientific Computations
Surrogates.jl ā­Ā 302
Surrogate modeling and optimization for scientific machine learning (SciML)
Scimlsensitivity.jl ā­Ā 291
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.
Diffeqbase.jl ā­Ā 282
The lightweight Base library for shared types and functionality for defining differential equation and scientific machine learning (SciML) problems
Diffeqoperators.jl ā­Ā 279
Linear operators for discretizations of differential equations and scientific machine learning (SciML)
Scimlbenchmarks.jl ā­Ā 279
Scientific machine learning (SciML) benchmarks, AI for science, and (differential) equation solvers. Covers Julia, Python (PyTorch, Jax), MATLAB, R
18s096sciml ā­Ā 268
18.S096 - Applications of Scientific Machine Learning
Diffeqgpu.jl ā­Ā 261
GPU-acceleration routines for DifferentialEquations.jl and the broader SciML scientific machine learning ecosystem
Componentarrays.jl ā­Ā 258
Arrays with arbitrarily nested named components.
Diffeqdocs.jl ā­Ā 251
Documentation for the DiffEq differential equations and scientific machine learning (SciML) ecosystem
Amadia ā­Ā 245
Astus' Mathematical Display Application : A GUI for Mathematics (Calculator, LaTeX Converter, Plotter, ... )
Pydens ā­Ā 242
PyDEns is a framework for solving Ordinary and Partial Differential Equations (ODEs & PDEs) using neural networks
Scikit Fmm ā­Ā 232
scikit-fmm is a Python extension module which implements the fast marching method.
Stochasticdiffeq.jl ā­Ā 229
Solvers for stochastic differential equations which connect with the scientific machine learning (SciML) ecosystem
Infiniteopt.jl ā­Ā 215
An intuitive modeling interface for infinite-dimensional optimization problems.
Linearsolve.jl ā­Ā 211
LinearSolve.jl: High-Performance Unified Interface for Linear Solvers in Julia. Easily switch between factorization and Krylov methods, add preconditioners, and all in one interface.
Neuraloperators.jl ā­Ā 206
DeepONets, (Fourier) Neural Operators, Physics-Informed Neural Operators, and more in Julia
Sundials.jl ā­Ā 200
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
Pina ā­Ā 195
Physics-Informed Neural networks for Advanced modeling
Reservoircomputing.jl ā­Ā 192
Reservoir computing utilities for scientific machine learning (SciML)
Easy Neural Ode ā­Ā 186
Code for the paper "Learning Differential Equations that are Easy to Solve"
Heyoka ā­Ā 185
C++ library for ODE integration via Taylor's method and LLVM
Reachabilityanalysis.jl ā­Ā 184
Compute reachable states of dynamical systems
Nonlinearsolve.jl ā­Ā 154
High-performance and differentiation-enabled nonlinear solvers (Newton methods), bracketed rootfinding (bisection, Falsi), with sparsity and Newton-Krylov support.
Diffeqr ā­Ā 127
Solving differential equations in R using DifferentialEquations.jl and the SciML Scientific Machine Learning ecosystem
Jumpprocesses.jl ā­Ā 127
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)
Math For Macro ā­Ā 122
Source files of the course "Mathematics for Macroeconomics"
Diffeqbayes.jl ā­Ā 119
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
Polychaos.jl ā­Ā 112
A Julia package to construct orthogonal polynomials, their quadrature rules, and use it with polynomial chaos expansions.
Scimlbase.jl ā­Ā 111
The Base interface of the SciML ecosystem
Fbpinns ā­Ā 110
Solve forward and inverse problems related to partial differential equations using finite basis physics-informed neural networks (FBPINNs)
Kinetic.jl ā­Ā 110
Universal modeling and simulation of fluid mechanics upon machine learning. From the Boltzmann equation, heading towards multiscale and multiphysics flows.
Foodie ā­Ā 108
Fortran Object-Oriented Differential-equations Integration Environment, FOODIE
Probnumdiffeq.jl ā­Ā 107
Probabilistic Numerical Differential Equation solvers via Bayesian filtering and smoothing
Ode.jl ā­Ā 106
Assorted basic Ordinary Differential Equation solvers for scientific machine learning (SciML). Deprecated: Use DifferentialEquations.jl instead.
Amici ā­Ā 105
Advanced Multilanguage Interface to CVODES and IDAS
Pomp ā­Ā 103
R package for statistical inference using partially observed Markov processes
Modelingtoolkitstandardlibrary.jl ā­Ā 89
A standard library of components to model the world and beyond
Fenics.jl ā­Ā 86
A scientific machine learning (SciML) wrapper for the FEniCS Finite Element library in the Julia programming language
Exponentialutilities.jl ā­Ā 85
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.
Diffeqcallbacks.jl ā­Ā 77
A library of useful callbacks for hybrid scientific machine learning (SciML) with augmented differential equation solvers
Parameterizedfunctions.jl ā­Ā 75
A simple domain-specific language (DSL) for defining differential equations for use in scientific machine learning (SciML) and other applications
Structuralidentifiability.jl ā­Ā 75
Fast and automatic structural identifiability software for ODE systems
Numerical Methods Python ā­Ā 72
Numerical methods implementation in Python.
Ascent ā­Ā 71
A fast and flexible C++ simulation engine and differential equation solver.
Fractionaldiffeq.jl ā­Ā 70
Solve Fractional Differential Equations using high performance numerical methods
Multiscalearrays.jl ā­Ā 69
A framework for developing multi-scale arrays for use in scientific machine learning (SciML) simulations
Pyrates ā­Ā 68
Open-source, graph-based Python code generator and analysis toolbox for dynamical systems (pre-implemented and custom models). Most pre-implemented models belong to the family of neural population models.
Keymaerax Release ā­Ā 65
KeYmaera X: An aXiomatic Tactical Theorem Prover for Hybrid Systems (release)
Rklib ā­Ā 65
Fixed and variable-step Runge-Kutta solvers in Modern Fortran
Highdimpde.jl ā­Ā 61
A Julia package for Deep Backwards Stochastic Differential Equation (Deep BSDE) and Feynman-Kac methods to solve high-dimensional PDEs without the curse of dimensionality
Scimlexpectations.jl ā­Ā 61
Fast uncertainty quantification for scientific machine learning (SciML) and differential equations
Diffeqnoiseprocess.jl ā­Ā 61
A library of noise processes for stochastic systems like stochastic differential equations (SDEs) and other systems that are present in scientific machine learning (SciML)
Tensordiffeq ā­Ā 60
Efficient and Scalable Physics-Informed Deep Learning and Scientific Machine Learning on top of Tensorflow for multi-worker distributed computing
Diffeqparamestim.jl ā­Ā 60
Easy scientific machine learning (SciML) parameter estimation with pre-built loss functions
Scientific Programming In Julia ā­Ā 60
Repository for B0M36SPJ
Simplenonlinearsolve.jl ā­Ā 57
Fast and simple nonlinear solvers for the SciML common interface. Newton, Broyden, Bisection, Falsi, and more rootfinders on a standard interface.
Heyoka.py ā­Ā 57
Python library for ODE integration via Taylor's method and LLVM
Brian2cuda ā­Ā 56
A brian2 extension to simulate spiking neural networks on GPUs
Delaydiffeq.jl ā­Ā 53
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.
Cellmltoolkit.jl ā­Ā 53
CellMLToolkit.jl is a Julia library that connects CellML models to the Scientific Julia ecosystem.
Sparsitydetection.jl ā­Ā 53
Automatic detection of sparsity in pure Julia functions for sparsity-enabled scientific machine learning (SciML)
Fasterneuraldiffeq ā­Ā 52
Code for "'Hey, that's not an ODE:' Faster ODE Adjoints via Seminorms" (ICML 2021)
Diffeqproblemlibrary.jl ā­Ā 51
A library of premade problems for examples and testing differential equation solvers and other SciML scientific machine learning tools
Diffyqs ā­Ā 50
Notes on Diffy Qs, a textbook for differential equations
Odinn.jl ā­Ā 49
Global glacier model using Universal Differential Equations for climate-glacier interactions
Double_pendulum ā­Ā 49
Animations of random double pendulums
Neurallaplace ā­Ā 48
Neural Laplace: Differentiable Laplace Reconstructions for modelling any time observation with O(1) complexity.
Petlion.jl ā­Ā 48
High-performance simulations of the Porous Electrode Theory for Li-ion batteries
Sciml.ai ā­Ā 48
The SciML Scientific Machine Learning Software Organization Website
Diffeqphysics.jl ā­Ā 47
A library for building differential equations arising from physical problems for physics-informed and scientific machine learning (SciML)
Epde ā­Ā 47
EPDE - partial differential equations discovery framework
Diffeqdevtools.jl ā­Ā 46
Benchmarking, testing, and development tools for differential equations and scientific machine learning (SciML)
Stg Ncde ā­Ā 45
"Graph Neural Controlled Differential Equations for Traffic Forecasting", AAAI 2022
Ukf Snmpc ā­Ā 44
This repository contains the source code for ā€œUnscented Kalman filter stochastic nonlinear model predictive controlā€ (UKF-SNMPC).
Torch_de_solver ā­Ā 42
Combines power of torch, numerical methods to conquer and solve ALL {O,P}DEs
Closedloopreachability.jl ā­Ā 42
Reachability analysis for closed-loop control systems
Flint ā­Ā 41
Fortran Library for numerical INTegration of differential equations
Scimloperators.jl ā­Ā 41
SciMLOperators.jl: Matrix-Free Operators for the SciML Scientific Machine Learning Common Interface in Julia
Globalsensitivity.jl ā­Ā 41
Robust, Fast, and Parallel Global Sensitivity Analysis (GSA) in Julia
Odeintw ā­Ā 39
odeintw provides a wrapper of scipy.integrate.odeint that allows it to handle complex and matrix differential equations.
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