Benchmarking Variable Rate Aggregator
using DiffEqBase, Catalyst, JumpProcesses, OrdinaryDiffEq, StochasticDiffEq
using Random, LinearSolve, StableRNGs, BenchmarkTools, Plots, LinearAlgebra
fmt = :png
width_px, height_px = default(:size)
rng = StableRNG(12345)StableRNGs.LehmerRNG(state=0x00000000000000000000000000006073)Introduction
This document benchmarks the performance of variable rate jumps in JumpProcesses.jl, comparing the VR_Direct, VR_DirectFW, and VR_FRM aggregators for variable rate jumps.
The test cases are:
- Scalar ODE with Variable Rate Jumps: Solved with
Tsit5andRosenbrock23(autodiff). - Complex ODE with Variable Rate Jump: Solved with
Tsit5. - DNA Gene Model: ODE with 10 variable rate jumps from the RSSA paper, solved with
Tsit5. - Negative Feedback Gene Expression: Variable rate jumps solved with
Tsit5, from Marchetti et al. (2017).
For benchmarking, we vary the number of jumps from 1 to 20 for Tests 1 and 2 and use a fixed number of jumps for Test 3 (10) and Test 4 (8), running 50 trajectories. Benchmarking saves only at the final time with save_positions=(false, false).
Benchmark and Plot Test 1
We benchmark Test 1 for 1 to 20 jumps, running 50 trajectories, and plot mean execution times as a line plot.
let
algorithms = Tuple{Any, Any, String, String}[
(VR_Direct(), Tsit5(), "VR_Direct", "Test 1 Tsit5 (VR_Direct)"),
(VR_DirectFW(), Tsit5(), "VR_DirectFW", "Test 1 Tsit5 (VR_DirectFW)"),
(VR_FRM(), Tsit5(), "VR_FRM", "Test 1 Tsit5 (VR_FRM)"),
(VR_Direct(), Rosenbrock23(), "VR_Direct", "Test 1 Rosenbrock23 (autodiff, VR_Direct)"),
(VR_DirectFW(), Rosenbrock23(), "VR_DirectFW", "Test 1 Rosenbrock23 (autodiff, VR_DirectFW)"),
(VR_FRM(), Rosenbrock23(), "VR_FRM", "Test 1 Rosenbrock23 (autodiff, VR_FRM)"),
]
function create_test1_problem(num_jumps, vr_aggregator, solver)
f = (du, u, p, t) -> (du[1] = u[1])
prob = ODEProblem(f, [0.2], (0.0, 10.0))
jumps = [VariableRateJump((u, p, t) -> u[1], (integrator) -> (integrator.u[1] = integrator.u[1] / 2.0); interp_points=20) for _ in 1:num_jumps]
jump_prob = JumpProblem(prob, Direct(), jumps...; vr_aggregator=vr_aggregator, rng=rng, save_positions=(false, false))
ensemble_prob = EnsembleProblem(jump_prob)
return ensemble_prob, jump_prob
end
num_jumps_range = append!([1], 5:5:20)
bs = Vector{Vector{BenchmarkTools.Trial}}()
errors = Dict{String, Vector{String}}()
for (algo, stepper, agg_name, label) in algorithms
@info "Benchmarking $label"
push!(bs, Vector{BenchmarkTools.Trial}())
errors[label] = String[]
_bs = bs[end]
for var in num_jumps_range
ensemble_prob, jump_prob = create_test1_problem(var, algo, stepper)
trial = try
@benchmark(
solve($jump_prob, $stepper, saveat=[$jump_prob.prob.tspan[2]]),
samples=50,
evals=1,
seconds=100
)
catch e
push!(errors[label], "Error at Num Jumps = $var: $(sprint(showerror, e))")
BenchmarkTools.Trial(BenchmarkTools.Parameters(samples=50, evals=1, seconds=100))
end
push!(_bs, trial)
mean_time = length(trial) > 0 ? "$(BenchmarkTools.prettytime(mean(trial.times)))" : "nan"
println("algo=$label, Num Jumps = $var, length = $(length(trial.times)), mean time = $mean_time")
end
end
# Log errors
for (label, err_list) in errors
if !isempty(err_list)
@warn "Errors for $label:"
for err in err_list
println(err)
end
end
end
# Plot results
fig = plot(
yscale=:log10,
xlabel="Number of Jumps",
ylabel="Time (ns)",
legend_position=:outertopright,
title="Test 1: Simulations, 50 samples"
)
for (i, (algo, stepper, agg_name, label)) in enumerate(algorithms)
_bs, _vars = [], []
for (j, b) in enumerate(bs[i])
if length(b) == 50
push!(_bs, mean(b.times))
push!(_vars, num_jumps_range[j])
end
end
if !isempty(_bs)
plot!(_vars, _bs, label=label)
else
@warn "No valid data for $label in Test 1"
end
end
display(plot(fig, layout=(1, 1), format=fmt, size=(width_px, height_px)))
endalgo=Test 1 Tsit5 (VR_Direct), Num Jumps = 1, length = 50, mean time = 137.
690 μs
algo=Test 1 Tsit5 (VR_Direct), Num Jumps = 5, length = 50, mean time = 152.
699 μs
algo=Test 1 Tsit5 (VR_Direct), Num Jumps = 10, length = 50, mean time = 169
.023 μs
algo=Test 1 Tsit5 (VR_Direct), Num Jumps = 15, length = 50, mean time = 170
.835 μs
algo=Test 1 Tsit5 (VR_Direct), Num Jumps = 20, length = 50, mean time = 196
.389 μs
algo=Test 1 Tsit5 (VR_DirectFW), Num Jumps = 1, length = 50, mean time = 16
3.329 μs
algo=Test 1 Tsit5 (VR_DirectFW), Num Jumps = 5, length = 50, mean time = 23
5.684 μs
algo=Test 1 Tsit5 (VR_DirectFW), Num Jumps = 10, length = 50, mean time = 3
24.002 μs
algo=Test 1 Tsit5 (VR_DirectFW), Num Jumps = 15, length = 50, mean time = 4
18.490 μs
algo=Test 1 Tsit5 (VR_DirectFW), Num Jumps = 20, length = 50, mean time = 4
99.062 μs
algo=Test 1 Tsit5 (VR_FRM), Num Jumps = 1, length = 50, mean time = 180.745
μs
algo=Test 1 Tsit5 (VR_FRM), Num Jumps = 5, length = 50, mean time = 660.600
μs
algo=Test 1 Tsit5 (VR_FRM), Num Jumps = 10, length = 50, mean time = 1.448
ms
algo=Test 1 Tsit5 (VR_FRM), Num Jumps = 15, length = 50, mean time = 2.385
ms
algo=Test 1 Tsit5 (VR_FRM), Num Jumps = 20, length = 50, mean time = 3.570
ms
algo=Test 1 Rosenbrock23 (autodiff, VR_Direct), Num Jumps = 1, length = 50,
mean time = 241.615 μs
algo=Test 1 Rosenbrock23 (autodiff, VR_Direct), Num Jumps = 5, length = 50,
mean time = 318.209 μs
algo=Test 1 Rosenbrock23 (autodiff, VR_Direct), Num Jumps = 10, length = 50
, mean time = 278.782 μs
algo=Test 1 Rosenbrock23 (autodiff, VR_Direct), Num Jumps = 15, length = 50
, mean time = 292.455 μs
algo=Test 1 Rosenbrock23 (autodiff, VR_Direct), Num Jumps = 20, length = 50
, mean time = 314.673 μs
algo=Test 1 Rosenbrock23 (autodiff, VR_DirectFW), Num Jumps = 1, length = 5
0, mean time = 298.060 μs
algo=Test 1 Rosenbrock23 (autodiff, VR_DirectFW), Num Jumps = 5, length = 5
0, mean time = 433.248 μs
algo=Test 1 Rosenbrock23 (autodiff, VR_DirectFW), Num Jumps = 10, length =
50, mean time = 621.597 μs
algo=Test 1 Rosenbrock23 (autodiff, VR_DirectFW), Num Jumps = 15, length =
50, mean time = 808.563 μs
algo=Test 1 Rosenbrock23 (autodiff, VR_DirectFW), Num Jumps = 20, length =
50, mean time = 974.370 μs
algo=Test 1 Rosenbrock23 (autodiff, VR_FRM), Num Jumps = 1, length = 50, me
an time = 379.978 μs
algo=Test 1 Rosenbrock23 (autodiff, VR_FRM), Num Jumps = 5, length = 50, me
an time = 1.011 ms
algo=Test 1 Rosenbrock23 (autodiff, VR_FRM), Num Jumps = 10, length = 50, m
ean time = 1.878 ms
algo=Test 1 Rosenbrock23 (autodiff, VR_FRM), Num Jumps = 15, length = 50, m
ean time = 2.852 ms
algo=Test 1 Rosenbrock23 (autodiff, VR_FRM), Num Jumps = 20, length = 50, m
ean time = 4.011 ms
Benchmark and Plot Test 2
We benchmark Test 2 for 1 to 20 jumps, running 50 trajectories, and plot mean execution times as a line plot.
let
algorithms = Tuple{Any, Any, String, String}[
(VR_Direct(), Tsit5(), "VR_Direct", "Test 2 Tsit5 (VR_Direct)"),
(VR_DirectFW(), Tsit5(), "VR_DirectFW", "Test 2 Tsit5 (VR_DirectFW)"),
(VR_FRM(), Tsit5(), "VR_FRM", "Test 2 Tsit5 (VR_FRM)"),
]
function create_test2_problem(num_jumps, vr_aggregator, solver)
f4 = (dx, x, p, t) -> (dx[1] = x[1])
rate4 = (x, p, t) -> t
affect4! = (integrator) -> (integrator.u[1] = integrator.u[1] * 0.5)
prob = ODEProblem(f4, [1.0 + 0.0im], (0.0, 6.0))
jumps = [VariableRateJump(rate4, affect4!) for _ in 1:num_jumps]
jump_prob = JumpProblem(prob, Direct(), jumps...; vr_aggregator=vr_aggregator, rng=rng, save_positions=(false, false))
ensemble_prob = EnsembleProblem(jump_prob)
return ensemble_prob, jump_prob
end
num_jumps_range = append!([1], 5:5:20)
bs = Vector{Vector{BenchmarkTools.Trial}}()
errors = Dict{String, Vector{String}}()
for (algo, stepper, agg_name, label) in algorithms
@info "Benchmarking $label"
push!(bs, Vector{BenchmarkTools.Trial}())
errors[label] = String[]
_bs = bs[end]
for var in num_jumps_range
ensemble_prob, jump_prob = create_test2_problem(var, algo, stepper)
trial = try
@benchmark(
solve($jump_prob, $stepper, saveat=[$jump_prob.prob.tspan[2]]),
samples=50,
evals=1,
seconds=100
)
catch e
push!(errors[label], "Error at Num Jumps = $var: $(sprint(showerror, e))")
BenchmarkTools.Trial(BenchmarkTools.Parameters(samples=50, evals=1, seconds=100))
end
push!(_bs, trial)
mean_time = length(trial) > 0 ? "$(BenchmarkTools.prettytime(mean(trial.times)))" : "nan"
println("algo=$label, Num Jumps = $var, length = $(length(trial.times)), mean time = $mean_time")
end
end
# Log errors
for (label, err_list) in errors
if !isempty(err_list)
@warn "Errors for $label:"
for err in err_list
println(err)
end
end
end
# Plot results
fig = plot(
yscale=:log10,
xlabel="Number of Jumps",
ylabel="Time (ns)",
legend_position=:outertopright,
title="Test 2: Simulations, 50 samples"
)
for (i, (algo, stepper, agg_name, label)) in enumerate(algorithms)
_bs, _vars = [], []
for (j, b) in enumerate(bs[i])
if length(b) == 50
push!(_bs, mean(b.times))
push!(_vars, num_jumps_range[j])
end
end
if !isempty(_bs)
plot!(_vars, _bs, label=label)
else
@warn "No valid data for $label in Test 2"
end
end
display(plot(fig, layout=(1, 1), format=fmt, size=(width_px, height_px)))
endalgo=Test 2 Tsit5 (VR_Direct), Num Jumps = 1, length = 50, mean time = 132.
579 μs
algo=Test 2 Tsit5 (VR_Direct), Num Jumps = 5, length = 50, mean time = 468.
060 μs
algo=Test 2 Tsit5 (VR_Direct), Num Jumps = 10, length = 50, mean time = 898
.817 μs
algo=Test 2 Tsit5 (VR_Direct), Num Jumps = 15, length = 50, mean time = 1.4
13 ms
algo=Test 2 Tsit5 (VR_Direct), Num Jumps = 20, length = 50, mean time = 1.8
56 ms
algo=Test 2 Tsit5 (VR_DirectFW), Num Jumps = 1, length = 50, mean time = 17
4.360 μs
algo=Test 2 Tsit5 (VR_DirectFW), Num Jumps = 5, length = 50, mean time = 79
9.879 μs
algo=Test 2 Tsit5 (VR_DirectFW), Num Jumps = 10, length = 50, mean time = 2
.051 ms
algo=Test 2 Tsit5 (VR_DirectFW), Num Jumps = 15, length = 50, mean time = 3
.959 ms
algo=Test 2 Tsit5 (VR_DirectFW), Num Jumps = 20, length = 50, mean time = 6
.155 ms
algo=Test 2 Tsit5 (VR_FRM), Num Jumps = 1, length = 50, mean time = 181.273
μs
algo=Test 2 Tsit5 (VR_FRM), Num Jumps = 5, length = 50, mean time = 1.578 m
s
algo=Test 2 Tsit5 (VR_FRM), Num Jumps = 10, length = 50, mean time = 6.093
ms
algo=Test 2 Tsit5 (VR_FRM), Num Jumps = 15, length = 50, mean time = 14.118
ms
algo=Test 2 Tsit5 (VR_FRM), Num Jumps = 20, length = 50, mean time = 27.447
ms
Benchmark and Plot Test 3
We benchmark Test 3 for fixed 10 jumps, running 50 trajectories, and plot mean execution times as a bar plot.
let
algorithms = Tuple{Any, Any, String, String}[
(VR_Direct(), Tsit5(), "VR_Direct", "Test 3 Tsit5 (VR_Direct, DNA Model)"),
(VR_DirectFW(), Tsit5(), "VR_DirectFW", "Test 3 Tsit5 (VR_DirectFW, DNA Model)"),
(VR_FRM(), Tsit5(), "VR_FRM", "Test 3 Tsit5 (VR_FRM, DNA Model)"),
]
function create_test3_problem(num_jumps, vr_aggregator, solver)
r = [0.043, 0.0007, 0.0715, 0.0039, 0.0199, 0.4791, 0.00019, 0.8765, 0.083, 0.5]
k = -log(2) / 30
u0 = [10.0, 10.0, 30.0, 0.0, 0.0, 0.0] # [DNA, M, D, RNA, DNAD, DNA2D]
tspan = (0.0, 120.0)
function f_dna(du, u, p, t)
du .= 0.0
nothing
end
function rate1(u, p, t) r[1] * u[4] end
function affect1!(integrator) integrator.u[2] += 1; nothing end
jump1 = VariableRateJump(rate1, affect1!)
function rate2(u, p, t) r[2] * u[2] end
function affect2!(integrator) integrator.u[2] -= 1; nothing end
jump2 = VariableRateJump(rate2, affect2!)
function rate3(u, p, t) r[3] * u[5] end
function affect3!(integrator) integrator.u[4] += 1; nothing end
jump3 = VariableRateJump(rate3, affect3!)
function rate4(u, p, t) r[4] * u[4] end
function affect4!(integrator) integrator.u[4] -= 1; nothing end
jump4 = VariableRateJump(rate4, affect4!)
function rate5(u, p, t) r[5] * exp(k * t) * u[1] * u[3] end
function affect5!(integrator) integrator.u[1] -= 1; integrator.u[3] -= 1; integrator.u[5] += 1; nothing end
jump5 = VariableRateJump(rate5, affect5!)
function rate6(u, p, t) r[6] * u[5] end
function affect6!(integrator) integrator.u[5] -= 1; integrator.u[1] += 1; integrator.u[3] += 1; nothing end
jump6 = VariableRateJump(rate6, affect6!)
function rate7(u, p, t) r[7] * exp(k * t) * u[5] * u[3] end
function affect7!(integrator) integrator.u[5] -= 1; integrator.u[3] -= 1; integrator.u[6] += 1; nothing end
jump7 = VariableRateJump(rate7, affect7!)
function rate8(u, p, t) r[8] * u[6] end
function affect8!(integrator) integrator.u[6] -= 1; integrator.u[1] += 1; integrator.u[3] += 1; nothing end
jump8 = VariableRateJump(rate8, affect8!)
function rate9(u, p, t) r[9] * exp(k * t) * u[2] * (u[2] - 1) / 2 end
function affect9!(integrator) integrator.u[2] -= 2; integrator.u[3] += 1; nothing end
jump9 = VariableRateJump(rate9, affect9!)
function rate10(u, p, t) r[10] * u[3] end
function affect10!(integrator) integrator.u[3] -= 1; integrator.u[2] += 2; nothing end
jump10 = VariableRateJump(rate10, affect10!)
prob = ODEProblem(f_dna, u0, tspan)
jumps = (jump1, jump2, jump3, jump4, jump5, jump6, jump7, jump8, jump9, jump10)
jump_prob = JumpProblem(prob, Direct(), jumps...; vr_aggregator=vr_aggregator, rng=rng, save_positions=(false, false))
ensemble_prob = EnsembleProblem(jump_prob)
return ensemble_prob, jump_prob
end
num_jumps_range = [10]
bs = Vector{Vector{BenchmarkTools.Trial}}()
errors = Dict{String, Vector{String}}()
for (algo, stepper, agg_name, label) in algorithms
@info "Benchmarking $label"
push!(bs, Vector{BenchmarkTools.Trial}())
errors[label] = String[]
_bs = bs[end]
for var in num_jumps_range
ensemble_prob, jump_prob = create_test3_problem(var, algo, stepper)
trial = try
@benchmark(
solve($jump_prob, $stepper, saveat=[$jump_prob.prob.tspan[2]]),
samples=50,
evals=1,
seconds=100
)
catch e
push!(errors[label], "Error at Num Jumps = $var: $(sprint(showerror, e))")
BenchmarkTools.Trial(BenchmarkTools.Parameters(samples=50, evals=1, seconds=100))
end
push!(_bs, trial)
mean_time = length(trial) > 0 ? "$(BenchmarkTools.prettytime(mean(trial.times)))" : "nan"
println("algo=$label, Num Jumps = $var, length = $(length(trial.times)), mean time = $mean_time")
end
end
# Log errors
for (label, err_list) in errors
if !isempty(err_list)
@warn "Errors for $label:"
for err in err_list
println(err)
end
end
end
# Plot results
fig = plot(
yscale=:log10,
xlabel="Method",
ylabel="Time (ns)",
title="Test 3: DNA Model, 10 Jumps, 50 samples",
xticks=(1:length(algorithms), [split(a[3], " (")[1] for a in algorithms]),
xrotation=45
)
means = []
for (i, (algo, stepper, agg_name, label)) in enumerate(algorithms)
b = bs[i][1] # Single jump count (10)
if length(b) == 50
push!(means, mean(b.times))
else
push!(means, NaN)
@warn "No valid data for $label in Test 3"
end
end
bar!(1:length(algorithms), means, label="", fillalpha=0.7)
display(plot(fig, layout=(1, 1), format=fmt, size=(width_px, height_px)))
endalgo=Test 3 Tsit5 (VR_Direct, DNA Model), Num Jumps = 10, length = 50, mean
time = 20.086 ms
algo=Test 3 Tsit5 (VR_DirectFW, DNA Model), Num Jumps = 10, length = 50, me
an time = 41.157 ms
algo=Test 3 Tsit5 (VR_FRM, DNA Model), Num Jumps = 10, length = 50, mean ti
me = 132.711 ms
Benchmark and Plot Test 4
We benchmark Test 4 for fixed 8 jumps, running 50 trajectories, and plot mean execution times as a bar plot.
let
algorithms = Tuple{Any, Any, String, String}[
#(Direct(), SSAStepper(), "Direct", "Test 4 SSAStepper (Direct, NegFeedback, Constant Rate)"),
(VR_Direct(), Tsit5(), "VR_Direct", "Test 4 Tsit5 (VR_Direct, NegFeedback, Variable Rate)"),
(VR_DirectFW(), Tsit5(), "VR_DirectFW", "Test 4 Tsit5 (VR_DirectFW, NegFeedback, Variable Rate)"),
(VR_FRM(), Tsit5(), "VR_FRM", "Test 4 Tsit5 (VR_FRM, NegFeedback, Variable Rate)"),
]
function create_test4_problem(num_jumps, aggregator, solver)
rn = @reaction_network begin
c1, G --> G + M
c2, M --> M + P
c3, M --> 0
c4, P --> 0
c5, 2P --> P2
c6, P2 --> 2P
c7, P2 + G --> P2G
c8, P2G --> P2 + G
end
rnpar = [:c1 => 0.09, :c2 => 0.05, :c3 => 0.001, :c4 => 0.0009, :c5 => 0.00001,
:c6 => 0.0005, :c7 => 0.005, :c8 => 0.9]
u0 = [:G => 500, :M => 0, :P => 0, :P2 => 0, :P2G => 0]
tspan = (0.0, 100.0)
if aggregator isa Direct
prob = DiscreteProblem(rn, u0, tspan, rnpar)
jump_prob = JumpProblem(rn, prob, Direct(), rng=rng, save_positions=(false, false))
ensemble_prob = EnsembleProblem(jump_prob)
else
function f_gene(du, u, p, t)
du .= 0.0
nothing
end
u0_numeric = [500.0, 0.0, 0.0, 0.0, 0.0]
p_numeric = [0.09, 0.05, 0.001, 0.0009, 0.00001, 0.0005, 0.005, 0.9]
var_rate = true
prob = ODEProblem(f_gene, u0_numeric, tspan, (p_numeric, var_rate))
function rate1(u, p, t) p[1][1] * (p[2] ? (1 + 0.1 * sin(t)) : 1.0) * u[1] end
function affect1!(integrator) integrator.u[2] += 1; nothing end
jump1 = VariableRateJump(rate1, affect1!)
function rate2(u, p, t) p[1][2] * u[2] end
function affect2!(integrator) integrator.u[3] += 1; nothing end
jump2 = VariableRateJump(rate2, affect2!)
function rate3(u, p, t) p[1][3] * u[2] end
function affect3!(integrator) integrator.u[2] -= 1; nothing end
jump3 = VariableRateJump(rate3, affect3!)
function rate4(u, p, t) p[1][4] * u[3] end
function affect4!(integrator) integrator.u[3] -= 1; nothing end
jump4 = VariableRateJump(rate4, affect4!)
function rate5(u, p, t) p[1][5] * (p[2] ? (1 + 0.1 * cos(t)) : 1.0) * u[3] * (u[3] - 1) / 2 end
function affect5!(integrator) integrator.u[3] -= 2; integrator.u[4] += 1; nothing end
jump5 = VariableRateJump(rate5, affect5!)
function rate6(u, p, t) p[1][6] * u[4] end
function affect6!(integrator) integrator.u[4] -= 1; integrator.u[3] += 2; nothing end
jump6 = VariableRateJump(rate6, affect6!)
function rate7(u, p, t) p[1][7] * u[4] * u[1] end
function affect7!(integrator) integrator.u[4] -= 1; integrator.u[1] -= 1; integrator.u[5] += 1; nothing end
jump7 = VariableRateJump(rate7, affect7!)
function rate8(u, p, t) p[1][8] * u[5] end
function affect8!(integrator) integrator.u[5] -= 1; integrator.u[4] += 1; integrator.u[1] += 1; nothing end
jump8 = VariableRateJump(rate8, affect8!)
jumps = (jump1, jump2, jump3, jump4, jump5, jump6, jump7, jump8)
jump_prob = JumpProblem(prob, Direct(), jumps...; vr_aggregator=aggregator, rng=rng, save_positions=(false, false))
ensemble_prob = EnsembleProblem(jump_prob)
end
return ensemble_prob, jump_prob
end
num_jumps_range = [8]
bs = Vector{Vector{BenchmarkTools.Trial}}()
errors = Dict{String, Vector{String}}()
for (algo, stepper, agg_name, label) in algorithms
@info "Benchmarking $label"
push!(bs, Vector{BenchmarkTools.Trial}())
errors[label] = String[]
_bs = bs[end]
for var in num_jumps_range
ensemble_prob, jump_prob = create_test4_problem(var, algo, stepper)
trial = try
@benchmark(
solve($jump_prob, $stepper, saveat=[$jump_prob.prob.tspan[2]]),
samples=50,
evals=1,
seconds=1000
)
catch e
push!(errors[label], "Error at Num Jumps = $var: $(sprint(showerror, e))")
BenchmarkTools.Trial(BenchmarkTools.Parameters(samples=10, evals=1, seconds=1000))
end
push!(_bs, trial)
mean_time = length(trial) > 0 ? "$(BenchmarkTools.prettytime(mean(trial.times)))" : "nan"
println("algo=$label, Num Jumps = $var, length = $(length(trial.times)), mean time = $mean_time")
end
end
# Log errors
for (label, err_list) in errors
if !isempty(err_list)
@warn "Errors for $label:"
for err in err_list
println(err)
end
end
end
# Plot results
fig = plot(
yscale=:log10,
xlabel="Method",
ylabel="Time (ns)",
title="Test 4: NegFeedback, 8 Jumps, 50 samples",
xticks=(1:length(algorithms), [split(a[3], " (")[1] for a in algorithms]),
xrotation=45
)
means = []
for (i, (algo, stepper, agg_name, label)) in enumerate(algorithms)
b = bs[i][1] # Single jump count (8)
if length(b) == 50
push!(means, mean(b.times))
else
push!(means, NaN)
@warn "No valid data for $label in Test 4"
end
end
bar!(1:length(algorithms), means, label="", fillalpha=0.7)
display(plot(fig, layout=(1, 1), format=fmt, size=(width_px, height_px)))
endalgo=Test 4 Tsit5 (VR_Direct, NegFeedback, Variable Rate), Num Jumps = 8, l
ength = 50, mean time = 357.787 ms
algo=Test 4 Tsit5 (VR_DirectFW, NegFeedback, Variable Rate), Num Jumps = 8,
length = 50, mean time = 638.580 ms
algo=Test 4 Tsit5 (VR_FRM, NegFeedback, Variable Rate), Num Jumps = 8, leng
th = 50, mean time = 1.579 s
Appendix
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
SciMLBenchmarks.weave_file("benchmarks/HybridJumps","VR_Aggregator_Benchmark.jmd")Computer Information:
Julia Version 1.12.7
Commit 6d172b025e4 (2026-08-15 08:05 UTC)
Build Info:
Official https://julialang.org release
Platform Info:
OS: Linux (x86_64-linux-gnu)
CPU: 128 × AMD EPYC 7502 32-Core Processor
WORD_SIZE: 64
LLVM: libLLVM-18.1.7 (ORCJIT, znver2)
GC: Built with stock GC
Threads: 128 default, 1 interactive, 128 GC (on 128 virtual cores)
Environment:
JULIA_NUM_THREADS = auto
Package Information:
Status `~/github-runners/amdci3-1/_work/SciMLBenchmarks.jl/SciMLBenchmarks.jl/benchmarks/HybridJumps/Project.toml`
[6e4b80f9] BenchmarkTools v1.8.0
⌃ [479239e8] Catalyst v16.4.3
[8f4d0f93] Conda v1.10.3
[864edb3b] DataStructures v0.19.6
⌃ [2b5f629d] DiffEqBase v7.21.2
[459566f4] DiffEqCallbacks v4.19.4
[31c24e10] Distributions v0.25.131
[86223c79] Graphs v1.15.0
[ccbc3e58] JumpProcesses v9.33.1
⌅ [b4f0291d] LazySets v5.3.0
⌃ [7ed4a6bd] LinearSolve v5.18.1
[1dea7af3] OrdinaryDiffEq v7.8.1
⌅ [d96e819e] Parameters v0.12.3
[86206cdf] PiecewiseDeterministicMarkovProcesses v0.0.12
[91a5bcdd] Plots v1.41.7
[438e738f] PyCall v1.96.4
⌃ [731186ca] RecursiveArrayTools v4.5.2
[31c91b34] SciMLBenchmarks v0.2.1 [loaded: `/home/crackauc/github-runners/amdci3-1/_work/SciMLBenchmarks.jl/SciMLBenchmarks.jl/src/SciMLBenchmarks.jl` (v0.2.1) expected `/home/crackauc/.julia/packages/SciMLBenchmarks/ceJyd/src/SciMLBenchmarks.jl` (v0.2.1)]
[a6db7da4] SciMLLogging v2.1.0
⌃ [860ef19b] StableRNGs v1.0.4
⌃ [90137ffa] StaticArrays v1.9.22
[789caeaf] StochasticDiffEq v7.2.0
[37e2e46d] LinearAlgebra v1.12.0
[2f01184e] SparseArrays v1.12.0
Info Packages marked with ⌃ and ⌅ have new versions available. Those with ⌃ may be upgradable, but those with ⌅ are restricted by compatibility constraints from upgrading. To see why use `status --outdated`And the full manifest:
Status `~/github-runners/amdci3-1/_work/SciMLBenchmarks.jl/SciMLBenchmarks.jl/benchmarks/HybridJumps/Manifest.toml`
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[19f34311] SciMLJacobianOperators v0.1.19
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⌃ [c0aeaf25] SciMLOperators v1.30.1
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[8f399da3] Libdl v1.11.0
[37e2e46d] LinearAlgebra v1.12.0
[56ddb016] Logging v1.11.0
[d6f4376e] Markdown v1.11.0
[a63ad114] Mmap v1.11.0
[ca575930] NetworkOptions v1.3.0
[44cfe95a] Pkg v1.12.1
[de0858da] Printf v1.11.0
[9abbd945] Profile v1.11.0
[3fa0cd96] REPL v1.11.0
[9a3f8284] Random v1.11.0
[ea8e919c] SHA v0.7.0
[9e88b42a] Serialization v1.11.0
[1a1011a3] SharedArrays v1.11.0
[6462fe0b] Sockets v1.11.0
[2f01184e] SparseArrays v1.12.0
[f489334b] StyledStrings v1.11.0
[4607b0f0] SuiteSparse
[fa267f1f] TOML v1.0.3
[a4e569a6] Tar v1.10.0
[8dfed614] Test v1.11.0
[cf7118a7] UUIDs v1.11.0
[4ec0a83e] Unicode v1.11.0
[e66e0078] CompilerSupportLibraries_jll v1.3.1+2
[781609d7] GMP_jll v6.3.0+2
[deac9b47] LibCURL_jll v8.15.0+0
[e37daf67] LibGit2_jll v1.9.0+0
[29816b5a] LibSSH2_jll v1.11.3+1
[14a3606d] MozillaCACerts_jll v2025.11.4
[4536629a] OpenBLAS_jll v0.3.29+0
[05823500] OpenLibm_jll v0.8.7+0
[458c3c95] OpenSSL_jll v3.5.6+0
[efcefdf7] PCRE2_jll v10.44.0+1
[bea87d4a] SuiteSparse_jll v7.8.3+2
[83775a58] Zlib_jll v1.3.1+2
[8e850b90] libblastrampoline_jll v5.15.0+0
[8e850ede] nghttp2_jll v1.64.0+1
[3f19e933] p7zip_jll v17.7.0+0
Info Packages marked with ⌃ and ⌅ have new versions available. Those with ⌃ may be upgradable, but those with ⌅ are restricted by compatibility constraints from upgrading. To see why use `status --outdated -m`