Search Results for "equations"
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Showing 28 open source projects for "equations"
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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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LaTeXStrings.jl
convenient input and display of LaTeX equation strings for Julia
This is a small package to make it easier to type LaTeX equations in string literals in the Julia language, written by Steven G. Johnson. With ordinary strings in Julia, to enter a string literal with embedded LaTeX equations you need to manually escape all backslashes and dollar signs: for example, $\alpha^2$ is written \$\\alpha^2\$. Also, even though IJulia is capable of displaying formatted LaTeX equations (via MathJax), an ordinary string will not exploit this. -
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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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HomotopyContinuation.jl
A Julia package for solving systems of polynomials
HomotopyContinuation.jl is a Julia package for solving systems of polynomial equations by numerical homotopy continuation. Many models in the sciences and engineering are expressed as sets of real solutions to systems of polynomial equations. We can optimize any objective whose gradient is an algebraic function using homotopy methods by computing all critical points of the objective function. An important special case is when the objective function is the euclidean distance to a given point. ... -
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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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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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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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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... -
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ImplicitDifferentiation.jl
Automatic differentiation of implicit functions
...Reasons can vary depending on your backend, but the most common include calls to external solvers, mutating operations or type restrictions. Those for which automatic differentiation is very slow. A common example is iterative procedures like fixed point equations or optimization algorithms. -
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Latexify.jl
Convert julia objects to LaTeX equations, arrays or other environments
This is a package for generating LaTeX maths from Julia objects. This package utilizes Julia's homoiconicity to convert expressions to LaTeX-formatted strings. Latexify.jl supplies functionalities for converting a range of different Julia objects. -
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Clapeyron
Framework for the development and use of fluid-thermodynamic models
Welcome to Clapeyron! This module provides both a large library of thermodynamic models and a framework for one to easily implement their own models. Clapeyron provides a framework for the development and use of fluid-thermodynamic models, including SAFT, cubic, activity, multi-parameter, and COSMO-SAC. -
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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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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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Oceananigans.jl
Julia software for fast, friendly, flexible fluid dynamics on CPUs
Oceananigans is a fast, friendly, flexible software package for finite volume simulations of the nonhydrostatic and hydrostatic Boussinesq equations on CPUs and GPUs. It runs on GPUs (wow, fast!), though we believe Oceananigans makes the biggest waves with its ultra-flexible user interface that makes simple simulations easy, and complex, creative simulations possible. -
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MultivariatePolynomials.jl
Multivariate polynomials interface
MultivariatePolynomials.jl is an implementation-independent library for manipulating multivariate polynomials. It defines abstract types and an API for multivariate monomials, terms, and polynomials and gives default implementation for common operations on them using the API. On the one hand, This packages allows you to implement algorithms on multivariate polynomials that will be independant on the representation of the polynomial that will be chosen by the user. On the other hand, it... -
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JUDI.jl
Julia Devito inversion
JUDI is a framework for large-scale seismic modeling and inversion and is designed to enable rapid translations of algorithms to fast and efficient code that scales to industry-size 3D problems. The focus of the package lies on seismic modeling as well as PDE-constrained optimization such as full-waveform inversion (FWI) and imaging (LS-RTM). Wave equations in JUDI are solved with Devito, a Python domain-specific language for automated finite-difference (FD) computations. JUDI's modeling operators can also be used as layers in (convolutional) neural networks to implement physics-augmented deep learning algorithms thanks to its implementation of ChainRules's rrule for the linear operators representing the discre wave equation. -
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ComponentArrays.jl
Arrays with arbitrarily nested named components
The main export of this package is the ComponentArray type. "Components" of ComponentArrays are really just array blocks that can be accessed through a named index. This will create a new ComponentArray whose data is a view into the original, allowing for standalone models to be composed together by simple function composition. In essence, ComponentArrays allow you to do the things you would usually need a modeling language for, but without actually needing a modeling language. The main... -
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NBInclude.jl
import code from IJulia Jupyter notebooks into Julia programs
...The goal of this package is to make notebook files just as easy to incorporate into Julia programs as ordinary Julia (.jl) files, giving you the advantages of a notebook (integrated code, formatted text, equations, graphics, and other results) while retaining the modularity and re-usability of .jl files. -
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DynamicalBilliards.jl
An easy-to-use, modular, extendable and absurdly fast Julia package
A Julia package for dynamical billiard systems in two dimensions. The goals of the package is to provide a flexible and intuitive framework for fast implementation of billiard systems of arbitrary construction. -
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NeuralOperators.jl
DeepONets, Neural Operators, Physics-Informed Neural Ops in Julia
Neural operator is a novel deep learning architecture. It learns an operator, which is a mapping between infinite-dimensional function spaces. It can be used to resolve partial differential equations (PDE). Instead of solving by finite element method, a PDE problem can be resolved by training a neural network to learn an operator mapping from infinite-dimensional space (u, t) to infinite-dimensional space f(u, t). Neural operator learns a continuous function between two continuous function spaces. The kernel can be trained on different geometry, which is learned from a graph. ... -
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Reduce.jl
Symbolic parser for Julia language term rewriting using REDUCE algebra
REDUCE is a portable general-purpose computer algebra system. It is a system for doing scalar, vector and matrix algebra by computer, which also supports arbitrary precision numerical approximation and interfaces to gnuplot to provide graphics. It can be used interactively for simple calculations (as illustrated in the screenshot below) but also provides a full programming language, with a syntax similar to other modern programming languages. REDUCE supports alternative user interfaces... -
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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.
