Search Results for "differential equations"
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Showing 128 open source projects for "differential equations"
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OrdinaryDiffEq.jl
High performance ordinary differential equation (ODE)
This is a suite for numerically solving differential equations written in Julia and available for use in Julia, Python, and R. The purpose of this package is to supply efficient Julia implementations of solvers for various differential equations. The well-optimized DifferentialEquations solvers benchmark as some of the fastest implementations, using classic algorithms and ones from recent research that routinely outperform the “standard” C/Fortran methods, and include algorithms optimized for high-precision and HPC applications. ... -
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DifferentialEquations.jl
Multi-language suite for high-performance solvers of equations
This is a suite for numerically solving differential equations written in Julia and available for use in Julia, Python, and R. The purpose of this package is to supply efficient Julia implementations of solvers for various differential equations. The well-optimized DifferentialEquations solvers benchmark as some of the fastest implementations, using classic algorithms and ones from recent research which routinely outperform the “standard” C/Fortran methods, and include algorithms optimized for high-precision and HPC applications. ... -
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Sundials.jl
Julia interface to Sundials, including a nonlinear solver
This is a suite for numerically solving differential equations written in Julia and available for use in Julia, Python, and R. The purpose of this package is to supply efficient Julia implementations of solvers for various differential equations. -
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DiffEqFlux.jl
Pre-built implicit layer architectures with O(1) backprop, GPUs
DiffEqFlux.jl is a Julia library that combines differential equations with neural networks, enabling the creation of neural differential equations (neural ODEs), universal differential equations, and physics-informed learning models. It serves as a bridge between the DifferentialEquations.jl and Flux.jl libraries, allowing for end-to-end differentiable simulations and model training in scientific machine learning. -
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Diffrax
Numerical differential equation solvers in JAX
Diffrax is a numerical differential equation solving library built for the JAX ecosystem, with a strong focus on composability, differentiability, and high-performance scientific computing. The project provides tools for solving ordinary differential equations, stochastic differential equations, controlled differential equations, and related systems in a way that fits naturally into modern machine learning and differentiable programming workflows. ... -
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VoronoiFVM.jl
Solution of nonlinear multiphysics partial differential equations
Solver for coupled nonlinear partial differential equations (elliptic-parabolic conservation laws) based on the Voronoi finite volume method. It uses automatic differentiation via ForwardDiff.jl and DiffResults.jl to evaluate user functions along with their jacobians and calculate derivatives of solutions with respect to their parameters. -
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DiffEqBayes.jl
Extension functionality which uses Stan.jl, DynamicHMC.jl
This repository is a set of extension functionality for estimating the parameters of differential equations using Bayesian methods. It allows the choice of using CmdStan.jl, Turing.jl, DynamicHMC.jl and ApproxBayes.jl to perform a Bayesian estimation of a differential equation problem specified via the DifferentialEquations.jl interface. -
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MethodOfLines.jl
Automatic Finite Difference PDE solving with Julia SciML
MethodOfLines.jl is a Julia package for automated finite difference discretization of symbolically defined PDEs in N dimensions. It uses symbolic expressions for systems of partial differential equations as defined with ModelingToolkit.jl, and Interval from DomainSets.jl to define the space(time) over which the simulation runs. This project is under active development, therefore the interface is subject to change. The docs will be updated to reflect any changes, please check back for current usage information. -
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PySINDy
A package for the sparse identification of nonlinear dynamical systems
PySINDy is a Python library that implements the Sparse Identification of Nonlinear Dynamics (SINDy) method for discovering mathematical models of dynamical systems from data. The framework focuses on identifying governing equations that describe the behavior of complex physical systems by selecting sparse combinations of candidate functions. Instead of fitting a purely predictive machine learning model, PySINDy attempts to recover interpretable differential equations that explain how a system evolves over time. This approach is particularly valuable in scientific fields such as physics, engineering, and biology where researchers seek both predictive accuracy and theoretical insight. ... -
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ProbNumDiffEq.jl
Probabilistic Numerical Differential Equation solvers via Bayesian fil
ProbNumDiffEq.jl provides probabilistic numerical ODE solvers to the DifferentialEquations.jl ecosystem. The implemented ODE filters solve differential equations via Bayesian filtering and smoothing. The filters compute not just a single point estimate of the true solution, but a posterior distribution that contains an estimate of its numerical approximation error. -
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ReachabilityAnalysis.jl
Compute reachable states of dynamical systems
...In the scope of this package are systems modeled by continuous or hybrid dynamical systems, where the dynamics change with discrete events. Systems are modeled by ordinary differential equations (ODEs) or semi-discrete partial differential equations (PDEs), with uncertain initial states, uncertain parameters or non-deterministic inputs. -
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Lux.jl
Elegant and Performant Deep Learning
...Unlike traditional machine learning libraries that bundle training logic and models, Lux separates model definitions from training routines, encouraging modularity and ease of experimentation. It integrates seamlessly with SciML and other Julia packages, supporting neural differential equations and scientific machine learning workflows. -
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FourierFlows.jl
Tools for building fast, hackable, pseudospectral equation solvers
This software provides tools for partial differential equations on periodic domains using Fourier-based pseudospectral methods. A central intent of the software's design is also to provide a framework for writing new, fast solvers for new physical problems. The code is written in Julia. -
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Gridap.jl
Grid-based approximation of partial differential equations in Julia
Gridap provides a set of tools for the grid-based approximation of partial differential equations (PDEs) written in the Julia programming language. The library currently supports linear and nonlinear PDE systems for scalar and vector fields, single and multi-field problems, conforming and nonconforming finite element (FE) discretizations, on structured and unstructured meshes of simplices and n-cubes. It also provides methods for time integration. -
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DataDrivenDiffEq.jl
Data driven modeling and automated discovery of dynamical systems
DataDrivenDiffEq.jl is a package for finding systems of equations automatically from a dataset. The methods in this package take in data and return the model which generated the data. A known model is not required as input. These methods can estimate equation-free and equation-based models for discrete, continuous differential equations or direct mappings. -
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ModelingToolkit.jl
Modeling framework for automatically parallelized scientific ML
...It allows for users to give a high-level description of a model for symbolic preprocessing to analyze and enhance the model. Automatic symbolic transformations, such as index reduction of differential-algebraic equations, make it possible to solve equations that are impossible to solve with a purely numeric-based technique. ModelingToolkit.jl is a symbolic-numeric modeling package. Thus it combines some of the features from symbolic computing packages like SymPy or Mathematica with the ideas of equation-based modeling systems like the causal Simulink and the acausal Modelica. -
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DeepXDE
A library for scientific machine learning & physics-informed learning
DeepXDE is a library for scientific machine learning and physics-informed learning. DeepXDE includes the following algorithms. Physics-informed neural network (PINN). Solving different problems. Solving forward/inverse ordinary/partial differential equations (ODEs/PDEs) [SIAM Rev.] Solving forward/inverse integro-differential equations (IDEs) [SIAM Rev.] fPINN: solving forward/inverse fractional PDEs (fPDEs) [SIAM J. Sci. Comput.] NN-arbitrary polynomial chaos (NN-aPC): solving forward/inverse stochastic PDEs (sPDEs) [J. Comput. Phys.] PINN with hard constraints (hPINN): solving inverse design/topology optimization [SIAM J. ... -
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ShinyItemAnalysis
Test and Item Analysis via Shiny
...ShinyItemAnalysis provides model equations, parameter estimates and their interpretation. -
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SciMLBenchmarks.jl
Benchmarks for scientific machine learning (SciML) software
SciMLBenchmarks.jl holds webpages, pdfs, and notebooks showing the benchmarks for the SciML Scientific Machine Learning Software ecosystem. -
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PowerSimulationsDynamics.jl
Julia package to run Dynamic Power System simulations
PowerSimulationsDynamics.jl is a Julia package for power system modeling and simulation of Power Systems dynamics. -
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101-0250-00
ETH course - Solving PDEs in parallel on GPUs
This course aims to cover state-of-the-art methods in modern parallel Graphical Processing Unit (GPU) computing, supercomputing and code development with applications to natural sciences and engineering. -
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ApproxFun.jl
Julia package for function approximation
...The ApproxFun Documentation contains detailed information, or read on for a brief overview of the package. The documentation contains examples of usage, such as solving ordinary and partial differential equations. The ApproxFun Examples repo contains many examples of using this package, in Jupyter notebooks and Julia scripts. Note that this is independently maintained, so it might not always be in sync with the latest version of ApproxFun. We recommend checking the examples in the documentation first, as these will always be compatible with the latest version of the package. -
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CasADi
CasADi is a symbolic framework for numeric optimization
...These expression graphs, encapsulated in Function objects, can be evaluated in a virtual machine or exported to stand-alone C code. Initial value problems in ordinary or differential-algebraic equations (ODE/DAE) can be calculated using explicit or implicit Runge-Kutta methods or interfaces to IDAS/CVODES from the SUNDIALS suite. Derivatives are calculated using sensitivity equations, up to arbitrary order. -
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Xournal++
A handwriting notetaking software with PDF annotation support
...Keep track of the notes by using page previews. Add images and create various shapes, from circles to splines to axis. Snap objects to rectangular grid or degrees of rotation. Create anything from differential equations to electrical circuits or the structural formula of molecules using our built-in LaTeX editor. Customize your toolbar to create a new layout, tailor-made for you. -
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Catalyst.jl
Chemical reaction network and systems biology interface
Catalyst.jl is a symbolic modeling package for analysis and high-performance simulation of chemical reaction networks. Catalyst defines symbolic ReactionSystems, which can be created programmatically or easily specified using Catalyst's domain-specific language (DSL). Leveraging ModelingToolkit and Symbolics.jl, Catalyst enables large-scale simulations through auto-vectorization and parallelism. Symbolic ReactionSystems can be used to generate ModelingToolkit-based models, allowing the easy...
