NBodySimulator.jl
ForwardDiff.jl
NBodySimulator.jl | ForwardDiff.jl | |
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2 | 4 | |
124 | 854 | |
0.8% | 0.6% | |
4.9 | 5.7 | |
about 7 hours ago | 24 days ago | |
Julia | Julia | |
GNU General Public License v3.0 or later | GNU General Public License v3.0 or later |
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NBodySimulator.jl
- How Good Is Julia for AI, Machine Learning, And Simulations?
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What's the best/easiest way of starting with Julia?
Ah, like the N-body problem? That certainly sounds doable, but not super in my wheelhouse. Plenty of differential equation packages, and I know there are some cool animation/visual packages. I've even seen some that are interactive, so you could possibly on a plot see what changing the parameters does in-time. Neat stuff. Have fun! Maybe start by recreating the 2- or 3-body problem, as I'm sure that's been done and probably can be found with some searching. (I just saw this too, may be relevant https://github.com/SciML/NBodySimulator.jl ) Julia is a joy to use, in my opinion.
ForwardDiff.jl
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The Elements of Differentiable Programming
You seem somewhat obsessed with the idea that reverse-mode autodiff is not the same technique as forward-mode autodiff. It makes you,,, angry? Seems like such a trivial thing to act a complete fool over.
What's up with that?
Anyway, here's a forward differentiation package with a file that might interest you
https://github.com/JuliaDiff/ForwardDiff.jl/blob/master/src/...
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Excited for Julia v1.9
Just so you know, v1.9 doesn't solve the load problems. What it does it gives package authors the tools to solve the problems, specifically precompilation as binaries and package extensions. It won't actually solve the load problems until the packages are updated to effectively make use of these features. This is already underway, https://sciml.ai/news/2022/09/21/compile_time/ with things like and https://github.com/JuliaDiff/ForwardDiff.jl/pull/625, but it is a fairly heavy lift to ensure things aren't invalidating and that everything that's necessary is precompiling.
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Looking for numerical/iterative approach for determining a value
As a quick way to do it, you can use ForwardDiff.jl to determine the partial with respect to h. Then use a Newton-Raphson algorithm to solve for the value of h. I'm not familiar with the actual problem you're solving so there may be more appropriate ways to solve this based on the shape of your function, but this is my knee-jerk reaction to a problem like this. You could also calculate the partial derivative analytically if that is something that you want.
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Question About Numerical Derivatives/Gradients: Why has no one yet implemented a gradient function in Julia that is similar to the gradient function in MATLAB and NumPy?
In these discussions, which are the only ones I could find that are the most pertinent and similar to what I'm talking about, https://github.com/JuliaDiff/ForwardDiff.jl/issues/390 and https://discourse.julialang.org/t/differentiation-without-explicit-function-np-gradient/57784 , nobody suggested or answered FiniteDiff.jl's finite differencing gradient for getting the numerical derivatives/gradients of an array of values. The answer is either the diff() function or Interpolations.jl, which I already explained in the post why I would want an alternative to those two options to exist, without having to call NumPy's gradient function.
What are some alternatives?
Enzyme.jl - Julia bindings for the Enzyme automatic differentiator
Zygote.jl - 21st century AD
Astrodynamics.jl - A Fresh Approach to Astrodynamics
FiniteDiff.jl - Fast non-allocating calculations of gradients, Jacobians, and Hessians with sparsity support
jill.py - A cross-platform installer for the Julia programming language
Molly.jl - Molecular simulation in Julia
ChainRules.jl - forward and reverse mode automatic differentiation primitives for Julia Base + StdLibs
OrbitalTrajectories.jl - OrbitalTrajectories.jl is a modern orbital trajectory design, optimisation, and analysis library for Julia, providing methods and tools for designing spacecraft orbits and transfers via high-performance simulations of astrodynamical models.
Tullio.jl - ⅀
AstroDynPropagators.jl - Trajectory Propagators for Astrodynamics.jl
Symbolics.jl - Symbolic programming for the next generation of numerical software