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Showing 7 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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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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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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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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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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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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