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
/ diffeqflux_vs_jax_results.md
Last active
April 9, 2024 00:57
DiffEqFlux.jl (Julia) vs Jax on an Epidemic Model
ChrisRackauckas
/ diffeqflux_differentialequations_vs_torchdiffeq_results.md
Last active
December 20, 2023 13:10
torchdiffeq (Python) vs DifferentialEquations.jl (Julia) ODE Benchmarks (Neural ODE Solvers)
Only non-stiff ODE solvers are tested since torchdiffeq does not have methods for stiff ODEs. The ODEs are chosen to be representative of models seen in physics and model-informed drug development (MIDD) studies (quantiative systems pharmacology) in order to capture the performance on realistic scenarios.
Below are the timings relative to the fastest method (lower is better). For approximately 1 million ODEs and less, torchdiffeq was more than an order of magnitude slower than DifferentialEquations.jl
ChrisRackauckas
/ a_stiff_ode_performance_python_julia.md
Last active
November 29, 2023 01:30
SciPy+Numba odeint vs Julia ODE vs NumbaLSODA: 50x performance difference on stiff ODE
All are solved at reltol=1e-3, abstol=1e-6 using the fastest ODE solver of the respective package for the given problem.
- SciPy LSODA through odeint takes ~489μs
- SciPy LSODA through odeint with Numba takes ~257μs
- NumbaLSODA takes ~25μs
- DifferentialEquations.jl Rosenbrock23 takes ~9.2μs
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
/ diffeq_vs_torchsde.md
Last active
September 28, 2022 20:49
torchsde vs DifferentialEquations.jl / DiffEqFlux.jl (Julia) benchmarks
This example is a 4-dimensional geometric brownian motion. The code
for the torchsde version is pulled directly from the
torchsde README
so that it would be a fair comparison against the author's own code.
The only change to that example is the addition of a dt choice so that
the simulation method and time step matches between the two different programs.
The SDE is solved 100 times. The summary of the results is as follows:
ChrisRackauckas
/ neural_ode_benchmarks.md
Last active
September 28, 2022 20:48
torchdiffeq vs Julia DiffEqflux Neural ODE Training Benchmark
The spiral neural ODE was used as the training benchmark for both torchdiffeq (Python) and DiffEqFlux (Julia) which utilized the same architecture and 500 steps of ADAM. Both achived similar objective values at the end. Results:
- DiffEqFlux defaults: 7.4 seconds
- DiffEqFlux optimized: 2.7 seconds
- torchdiffeq: 288.965871299999 seconds
ChrisRackauckas
/ sparsity_reaction_diffusion.jl
Created
February 4, 2020 07:49
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| using OrdinaryDiffEq, RecursiveArrayTools, LinearAlgebra, Test, SparseArrays, SparseDiffTools, Sundials | |
| # Define the constants for the PDE | |
| const α₂ = 1.0 | |
| const α₃ = 1.0 | |
| const β₁ = 1.0 | |
| const β₂ = 1.0 | |
| const β₃ = 1.0 | |
| const r₁ = 1.0 | |
| const r₂ = 1.0 |
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
/ 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
/ 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({ |
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