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Showing 13 open source projects for "equation"
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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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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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Symbolics.jl
Symbolic programming for the next generation of numerical software
Symbolics.jl is a high-performance symbolic computation library for the Julia programming language. It enables users to define, manipulate, and analyze mathematical expressions symbolically, with strong support for symbolic differentiation, simplification, equation solving, and code generation. Designed for use in scientific computing, machine learning, and engineering, Symbolics.jl integrates smoothly with Julia’s numerical ecosystem, allowing symbolic expressions to be compiled and optimized for high-speed evaluation. -
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ModelingToolkit.jl
Modeling framework for automatically parallelized scientific ML
...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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StructuralEquationModels.jl
A fast and flexible Structural Equation Modelling Framework
This is a package for Structural Equation Modeling in development. It is written for extensibility, that is, you can easily define your own objective functions and other parts of the model. At the same time, it is (very) fast. We provide fast objective functions, gradients, and for some cases hessians as well as approximations thereof. As a user, you can easily define custom loss functions. -
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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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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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IntervalRootFinding.jl
Find all roots of a function in a guaranteed way with Julia
This package provides guaranteed methods for finding roots of functions, i.e. solutions to the equation f(x) == 0 for a function f. To do so, it uses methods from interval analysis, using interval arithmetic from the IntervalArithmetic.jl package by the same authors. The basic function is roots. A standard Julia function and an interval is provided and the roots function return a list of intervals containing all roots of the function located in the starting interval. -
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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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JUDI.jl
Julia Devito inversion
...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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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... -
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FEniCS.jl
A scientific machine learning (SciML) wrapper for the FEniCS
...Interfaces have been provided for the main functions and their attributes, and instructions to add further ones can be found here. A high-level API for usage with DifferentialEquations. An example can be seen in solving the heat equation with high-order adaptive time-stepping. Various gists/jupyter notebooks have been created to provide a brief overview of the overall functionality and of any differences between the pythonic FEniCS and the Julian wrapper. DifferentialEquations.jl ecosystem. Paraview can also be used to visualize various results just like in FEniCS. -
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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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