The Jax developers optimized a differential equation benchmark in this issue which used DiffEqFlux.jl as a performance baseline. The Julia code from there was updated to include some standard performance tricks and is the benchmark code here. Thus both codes have been optimized by the library developers.
Christopher Rackauckas ChrisRackauckas
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ChrisRackauckas
/ ewing-optim-cr.jl
Created
September 27, 2020 07:22
State-dependent delay diffeq model from "Modelling the Effects of Temperature on Temperature Mosquito Seasonal Abundance"
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| # -------------------------------------------------------------------------------- | |
| # Ewing model | |
| # translation by: slwu89@berkeleu.edu (July 2020) | |
| # -------------------------------------------------------------------------------- | |
| using DifferentialEquations | |
| using Plots | |
| using LabelledArrays | |
| using StaticArrays |
ChrisRackauckas
/ lotka_volterra_neural_ode.jl
Last active
July 24, 2024 18:30
Lotka-Volterra Learned via a Neural ODE (takes about 1 minute!)
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| using OrdinaryDiffEq | |
| using Plots | |
| using Flux, DiffEqFlux, Optim | |
| function lotka_volterra(du,u,p,t) | |
| x, y = u | |
| α, β, δ, γ = p | |
| du[1] = dx = α*x - β*x*y | |
| du[2] = dy = -δ*y + γ*x*y | |
| end |
ChrisRackauckas
/ gist:c05f580c40378dd6da2274e61fca599a
Created
March 11, 2021 07:13
Symbolics.jl Lotka-Volterra Tracing result
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| retcode: Success | |
| Interpolation: 3rd order Hermite | |
| t: [0.0, 0.5, 1.0] | |
| u: Vector{Num}[[x0, y0], [x0 + 0.08333333333333333((1.5x0) + (1.5(x0 + (0.5((1.5(x0 + (0.25((1.5(x0 + (0.25((1.5x0) - (x0*y0))))) - ((x0 + (0.25((1.5x0) - (x0*y0))))*(y0 + (0.25((x0*y0) - (3y0))))))))) - ((x0 + (0.25((1.5(x0 + (0.25((1.5x0) - (x0*y0))))) - ((x0 + (0.25((1.5x0) - (x0*y0))))*(y0 + (0.25((x0*y0) - (3y0))))))))*(y0 + (0.25(((x0 + (0.25((1.5x0) - (x0*y0))))*(y0 + (0.25((x0*y0) - (3y0))))) - (3(y0 + (0.25((x0*y0) - (3y0))))))))))))) + (2((1.5(x0 + (0.25((1.5x0) - (x0*y0))))) + (1.5(x0 + (0.25((1.5(x0 + (0.25((1.5x0) - (x0*y0))))) - ((x0 + (0.25((1.5x0) - (x0*y0))))*(y0 + (0.25((x0*y0) - (3y0))))))))) - ((x0 + (0.25((1.5x0) - (x0*y0))))*(y0 + (0.25((x0*y0) - (3y0))))) - ((x0 + (0.25((1.5(x0 + (0.25((1.5x0) - (x0*y0))))) - ((x0 + (0.25((1.5x0) - (x0*y0))))*(y0 + (0.25((x0*y0) - (3y0))))))))*(y0 + (0.25(((x0 + (0.25((1.5x0) - (x0*y0))))*(y0 + (0.25((x0*y0) - (3y0))))) - (3(y0 + (0.25((x0*y0) - (3y0))))))))))) - (x0*y0) - ((x0 + (0.5( |
ChrisRackauckas
/ diffeqflux_vs_jax_results.md
Last active
April 9, 2024 00:57
DiffEqFlux.jl (Julia) vs Jax on an Epidemic Model
ChrisRackauckas
/ hasbranching.jl
Created
June 22, 2021 13:54
hasbranching for automatically specializing ReverseDiff tape compilation
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| using Cassette, DiffRules | |
| using Core: CodeInfo, SlotNumber, SSAValue, ReturnNode, GotoIfNot | |
| const printbranch = true | |
| Cassette.@context HasBranchingCtx | |
| function Cassette.overdub(ctx::HasBranchingCtx, f, args...) | |
| if Cassette.canrecurse(ctx, f, args...) | |
| return Cassette.recurse(ctx, f, args...) |
ChrisRackauckas
/ a_pde_bruss_scaling_benchmark_python_julia.md
Last active
January 11, 2022 02:19
Brusselator Stiff Partial Differential Equation Benchmark: Julia DifferentialEquations.jl vs Python SciPy. Julia 935x faster
Brusselator Stiff Partial Differential Equation Benchmark: Julia DifferentialEquations.jl vs Python SciPy
Tested is DifferentialEquations.jl vs Python's SciPy ODE solvers. Notes:
- Stiff ODE solvers are used since they are required to solve this problem effectively.
- The Python code is vectorized with for maximum performance
- All of the performance features are tried: automatic sparsity detection, preconditioners, etc.
ChrisRackauckas
/ automatic_differentiation_done_quick.html
Created
March 27, 2022 15:28
Automatic Differentiation Done Quick: Forward and Reverse Mode Differentiable Programming
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| <!DOCTYPE html> | |
| <HTML lang = "en"> | |
| <HEAD> | |
| <meta charset="UTF-8"/> | |
| <meta name="viewport" content="width=device-width, initial-scale=1.0, user-scalable=yes"> | |
| <title>Forward and Reverse Automatic Differentiation In A Nutshell</title> | |
| <script type="text/x-mathjax-config"> | |
| MathJax.Hub.Config({ |
ChrisRackauckas
/ gist:d0d0324c5c7bcef6012ed12a03e35859
Created
April 28, 2022 12:11
Wild function generation
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| function (ˍ₋out, ˍ₋arg1, ˍ₋arg2, t) | |
| #= C:\Users\accou\.julia\packages\SymbolicUtils\v2ZkM\src\code.jl:349 =# | |
| #= C:\Users\accou\.julia\packages\SymbolicUtils\v2ZkM\src\code.jl:350 =# | |
| #= C:\Users\accou\.julia\packages\SymbolicUtils\v2ZkM\src\code.jl:351 =# | |
| begin | |
| begin | |
| #= C:\Users\accou\.julia\packages\Symbolics\vQXbU\src\build_function.jl:452 =# | |
| #= C:\Users\accou\.julia\packages\SymbolicUtils\v2ZkM\src\code.jl:398 =# @inbounds begin | |
| #= C:\Users\accou\.julia\packages\SymbolicUtils\v2ZkM\src\code.jl:394 =# | |
| ˍ₋out[1] = (/)((*)((*)((*)((*)((*)((*)(2, ˍ₋arg2[4]), ˍ₋arg2[2]), ˍ₋arg1[1]), (+)(0.5, (*)(0.5, (tanh)((/)((+)(ˍ₋arg1[14], (/)((*)((*)(ˍ₋arg2[4], ˍ₋arg2[1]), (sqrt)((+)((+)((^)((+)((*)((*)(ˍ₋arg1[9], (sin)(ˍ₋arg1[6])), (sqrt)(ˍ₋arg1[1])), (*)((*)((*)(-1, ˍ₋arg1[10]), (cos)(ˍ₋arg1[6])), (sqrt)(ˍ₋arg1[1]))), 2), (^)((+)((+)((/)((*)((*)(ˍ₋arg1[9], (+)(ˍ₋arg1[2], (*)((+)((+)(2, (*)(ˍ₋arg1[2], (cos)(ˍ₋arg1[6]))), (*)(ˍ₋arg1[3], ( |
ChrisRackauckas
/ stacktrace_after.jl
Created
June 15, 2022 01:24
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| ERROR: MethodError: Cannot `convert` an object of type Float32 to an object of type Vector{Float32} | |
| Closest candidates are: | |
| convert(::Type{Array{T, N}}, ::SizedArray{S, T, N, N, Array{T, N}}) where {S, T, N} at C:\Users\accou\.julia\packages\StaticArrays\0T5rI\src\SizedArray.jl:121 | |
| convert(::Type{Array{T, N}}, ::SizedArray{S, T, N, M, TData} where {M, TData<:AbstractArray{T, M}}) where {T, S, N} at C:\Users\accou\.julia\packages\StaticArrays\0T5rI\src\SizedArray.jl:115 | |
| convert(::Type{<:Array}, ::LabelledArrays.LArray) at C:\Users\accou\.julia\packages\LabelledArrays\lfn1b\src\larray.jl:133 | |
| ... | |
| Stacktrace: | |
| [1] setproperty!(x::OrdinaryDiffEq.ODEIntegrator{Tsit5, false, Vector{Float32}, Float32}, f::Symbol, v::Float32) | |
| @ Base .\Base.jl:43 | |
| [2] initialize!(integrator::OrdinaryDiffEq.ODEIntegrator{Tsit5, false, Vector{Float32}, Float32}) |
ChrisRackauckas
/ README.md
Created
July 26, 2025 14:48
Julia @ccallable C Header Generator - Automatically generate C header files from Julia functions marked with @ccallable
This collection of Julia scripts automatically generates C header files from Julia functions marked with the @ccallable macro. This is useful when creating Julia libraries that need to be called from C/C++ code.
The main generator script that provides a simple and robust approach to generating C headers. It uses a manual definition approach where you explicitly define function signatures, avoiding complex AST parsing.
Features:
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