BCR Work-Precision Diagrams

The following benchmark is of 1122 ODEs with 24388 terms that describe a stiff chemical reaction network modeling the BCR signaling network from Barua et al.. We use ReactionNetworkImporters to load the BioNetGen model files as a Catalyst model, and then use ModelingToolkit to convert the Catalyst network model to ODEs.

using DiffEqBase, OrdinaryDiffEq, Catalyst, ReactionNetworkImporters,
      Sundials, Plots, DiffEqDevTools, ODEInterface, ODEInterfaceDiffEq,
      LSODA, TimerOutputs, LinearAlgebra, ModelingToolkit, BenchmarkTools

datadir  = joinpath(dirname(pathof(ReactionNetworkImporters)),"../data/bcr")
const to = TimerOutput()
tf       = 100000.0

# generate ModelingToolkit ODEs
@timeit to "Parse Network" prnbng = loadrxnetwork(BNGNetwork(), joinpath(datadir, "bcr.net"))
rn    = prnbng.rn
@timeit to "Create ODESys" osys = convert(ODESystem, rn)

tspan = (0.,tf)
@timeit to "ODEProb No Jac" oprob = ODEProblem(osys, Float64[], tspan, Float64[])
Parsing parameters...done
Creating parameters...done
Parsing species...done
Creating species...done
Creating species and parameters for evaluating expressions...done
Parsing and adding reactions...done
Parsing groups...done
ODEProblem with uType Vector{Float64} and tType Float64. In-place: true
timespan: (0.0, 100000.0)
u0: 1122-element Vector{Float64}:
@timeit to "ODEProb SparseJac" sparsejacprob = ODEProblem(osys, Float64[], tspan, Float64[], jac=true, sparse=true)
                                      Time                    Allocations  
                             ───────────────────────   ────────────────────
      Tot / % measured:            440s / 100.0%            197GiB / 100.0%

 Section             ncalls     time    %tot     avg     alloc    %tot     
 ODEProb SparseJac        1     429s   97.6%    429s    194GiB   98.2%   19
 ODEProb No Jac           1    5.68s    1.3%   5.68s   1.89GiB    1.0%  1.8
 Create ODESys            1    3.87s    0.9%   3.87s   1.48GiB    0.7%  1.4
 Parse Network            1    985ms    0.2%   985ms    193MiB    0.1%   19
@show numspecies(rn) # Number of ODEs
@show numreactions(rn) # Apprx. number of terms in the ODE
@show length(parameters(rn)) # Number of Parameters
numspecies(rn) = 1122
numreactions(rn) = 24388
length(parameters(rn)) = 128

Time ODE derivative function compilation

As compiling the ODE derivative functions has in the past taken longer than running a simulation, we first force compilation by evaluating these functions one time.

u  = ModelingToolkit.varmap_to_vars(nothing, species(rn); defaults=ModelingToolkit.defaults(rn))
du = copy(u)
p  = ModelingToolkit.varmap_to_vars(nothing, parameters(rn); defaults=ModelingToolkit.defaults(rn))
@timeit to "ODE rhs Eval1" oprob.f(du,u,p,0.)
@timeit to "ODE rhs Eval2" oprob.f(du,u,p,0.)

We also time the ODE rhs function with BenchmarkTools as it is more accurate given how fast evaluating f is:

@btime oprob.f($du,$u,$p,0.)
39.210 μs (3 allocations: 576 bytes)
Js = similar(sparsejacprob.f.jac_prototype)
@timeit to "SparseJac Eval1" sparsejacprob.f.jac(Js,u,p,0.)
@timeit to "SparseJac Eval2" sparsejacprob.f.jac(Js,u,p,0.)
                                      Time                    Allocations  
                             ───────────────────────   ────────────────────
      Tot / % measured:            457s /  96.3%            197GiB / 100.0%

 Section             ncalls     time    %tot     avg     alloc    %tot     
 ODEProb SparseJac        1     429s   97.6%    429s    194GiB   98.2%   19
 ODEProb No Jac           1    5.68s    1.3%   5.68s   1.89GiB    1.0%  1.8
 Create ODESys            1    3.87s    0.9%   3.87s   1.48GiB    0.7%  1.4
 Parse Network            1    985ms    0.2%   985ms    193MiB    0.1%   19
 SparseJac Eval1          1    546μs    0.0%   546μs      848B    0.0%     
 ODE rhs Eval1            1    364μs    0.0%   364μs      752B    0.0%     
 SparseJac Eval2          1   59.5μs    0.0%  59.5μs      848B    0.0%     
 ODE rhs Eval2            1   43.1μs    0.0%  43.1μs      752B    0.0%     

Picture of the solution

sol = solve(oprob, CVODE_BDF(), saveat=tf/1000., reltol=1e-5, abstol=1e-5)
plot(sol, legend=false, fmt=:png)

For these benchmarks we will be using the time-series error with these saving points since the final time point is not well-indicative of the solution behavior (capturing the oscillation is the key!).

Generate Test Solution

@time sol = solve(oprob, CVODE_BDF(), abstol=1/10^12, reltol=1/10^12)
test_sol  = TestSolution(sol)
651.691835 seconds (3.81 M allocations: 2.066 GiB, 0.45% gc time)
retcode: Success
Interpolation: 3rd order Hermite
t: nothing
u: nothing


abstols = 1.0 ./ 10.0 .^ (5:8)
reltols = 1.0 ./ 10.0 .^ (5:8);
setups = [

Automatic Jacobian Solves

Due to the computational cost of the problem, we are only going to focus on the methods which demonstrated computational efficiency on the smaller biochemical benchmark problems. This excludes the exponential integrator, stabilized explicit, and extrapolation classes of methods.

First we test using auto-generated Jacobians (finite difference)

wp = WorkPrecisionSet(oprob,abstols,reltols,setups;error_estimate=:l2,

Sparse Jacobian

Finally we test using the generated sparse analytic Jacobian function.

setups = [
          #Dict(:alg=>CVODE_BDF(linear_solver=:KLU)), # Fails!
wp = WorkPrecisionSet(sparsejacprob,abstols,reltols,setups;error_estimate=:l2,


These benchmarks are a part of the SciMLBenchmarks.jl repository, found at: https://github.com/SciML/SciMLBenchmarks.jl. For more information on high-performance scientific machine learning, check out the SciML Open Source Software Organization https://sciml.ai.

To locally run this benchmark, do the following commands:

using SciMLBenchmarks

Computer Information:

Julia Version 1.7.3
Commit 742b9abb4d (2022-05-06 12:58 UTC)
Platform Info:
  OS: Linux (x86_64-pc-linux-gnu)
  CPU: AMD EPYC 7502 32-Core Processor
  LIBM: libopenlibm
  LLVM: libLLVM-12.0.1 (ORCJIT, znver2)
  BUILDKITE_PLUGIN_JULIA_CACHE_DIR = /cache/julia-buildkite-plugin
  JULIA_DEPOT_PATH = /cache/julia-buildkite-plugin/depots/5b300254-1738-4989-ae0a-f4d2d937f953

Package Information:

      Status `/cache/build/exclusive-amdci1-0/julialang/scimlbenchmarks-dot-jl/benchmarks/Bio/Project.toml`
  [6e4b80f9] BenchmarkTools v1.3.1
  [479239e8] Catalyst v12.1.2
  [2b5f629d] DiffEqBase v6.94.3
  [f3b72e0c] DiffEqDevTools v2.30.0
  [033835bb] JLD2 v0.4.22
  [7f56f5a3] LSODA v0.7.0
  [961ee093] ModelingToolkit v8.17.0
  [54ca160b] ODEInterface v0.5.0
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  [1dea7af3] OrdinaryDiffEq v6.19.0
  [91a5bcdd] Plots v1.31.4
  [b4db0fb7] ReactionNetworkImporters v0.13.4
  [31c91b34] SciMLBenchmarks v0.1.0
  [c3572dad] Sundials v4.9.4
  [a759f4b9] TimerOutputs v0.5.20

And the full manifest:

      Status `/cache/build/exclusive-amdci1-0/julialang/scimlbenchmarks-dot-jl/benchmarks/Bio/Manifest.toml`
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  [975044d2] Xorg_xcb_util_keysyms_jll v0.4.0+1
  [0d47668e] Xorg_xcb_util_renderutil_jll v0.3.9+1
  [c22f9ab0] Xorg_xcb_util_wm_jll v0.4.1+1
  [35661453] Xorg_xkbcomp_jll v1.4.2+4
  [33bec58e] Xorg_xkeyboard_config_jll v2.27.0+4
  [c5fb5394] Xorg_xtrans_jll v1.4.0+3
  [8f1865be] ZeroMQ_jll v4.3.4+0
  [3161d3a3] Zstd_jll v1.5.2+0
  [a4ae2306] libaom_jll v3.4.0+0
  [0ac62f75] libass_jll v0.15.1+0
  [f638f0a6] libfdk_aac_jll v2.0.2+0
  [b53b4c65] libpng_jll v1.6.38+0
  [a9144af2] libsodium_jll v1.0.20+0
  [f27f6e37] libvorbis_jll v1.3.7+1
  [1270edf5] x264_jll v2021.5.5+0
  [dfaa095f] x265_jll v3.5.0+0
  [d8fb68d0] xkbcommon_jll v0.9.1+5
  [0dad84c5] ArgTools
  [56f22d72] Artifacts
  [2a0f44e3] Base64
  [ade2ca70] Dates
  [8bb1440f] DelimitedFiles
  [8ba89e20] Distributed
  [f43a241f] Downloads
  [7b1f6079] FileWatching
  [9fa8497b] Future
  [b77e0a4c] InteractiveUtils
  [b27032c2] LibCURL
  [76f85450] LibGit2
  [8f399da3] Libdl
  [37e2e46d] LinearAlgebra
  [56ddb016] Logging
  [d6f4376e] Markdown
  [a63ad114] Mmap
  [ca575930] NetworkOptions
  [44cfe95a] Pkg
  [de0858da] Printf
  [9abbd945] Profile
  [3fa0cd96] REPL
  [9a3f8284] Random
  [ea8e919c] SHA
  [9e88b42a] Serialization
  [1a1011a3] SharedArrays
  [6462fe0b] Sockets
  [2f01184e] SparseArrays
  [10745b16] Statistics
  [4607b0f0] SuiteSparse
  [fa267f1f] TOML
  [a4e569a6] Tar
  [8dfed614] Test
  [cf7118a7] UUIDs
  [4ec0a83e] Unicode
  [e66e0078] CompilerSupportLibraries_jll
  [deac9b47] LibCURL_jll
  [29816b5a] LibSSH2_jll
  [c8ffd9c3] MbedTLS_jll
  [14a3606d] MozillaCACerts_jll
  [4536629a] OpenBLAS_jll
  [05823500] OpenLibm_jll
  [efcefdf7] PCRE2_jll
  [bea87d4a] SuiteSparse_jll
  [83775a58] Zlib_jll
  [8e850b90] libblastrampoline_jll v3.1.0+2
  [8e850ede] nghttp2_jll
  [3f19e933] p7zip_jll