BioPreDyn-bench B4 (CHO Cell Metabolism) Parameter Estimation Benchmark
Parameter estimation of a Chinese Hamster Ovary (CHO) cell metabolic model
This benchmark implements problem B4 from the BioPreDyn-bench suite (Villaverde et al. 2015), addressing SciMLBenchmarks.jl#555. B4 is a log-linear kinetic model of Chinese Hamster Ovary (CHO) cell metabolism during a batch fermentation producing a recombinant protein: 35 states (34 metabolite concentrations across the fermenter, cytosol, and mitochondrial compartments, plus the fermenter volume) connected by 32 reactions, with 117 unknown kinetic (log-linear elasticity and Michaelis) parameters. Unlike B2, which fits real experimental data, B4 uses noised pseudo-data simulated from the model's own nominal parameters — 13 metabolites sampled at 12 unevenly spaced time points over a 300-hour fermentation.
The model equations, nominal parameters, parameter bounds, and simulated data below are transcribed directly from the benchmark's official MATLAB/AMIGO2 implementation, available as supplementary material to the paper (Additional files 2-3, directory BioPreDynBenchFiles/B4).
using OrdinaryDiffEq, Optimization, ForwardDiff
using OptimizationBBO, OptimizationNLopt, Plots, BenchmarkTools, DataFrames
using ParallelParticleSwarms
gr(fmt = :png)Plots.GRBackend()Model
States (in order; compartments: f fermenter, c cytosol, m mitochondria): beta-D-glucose (f), L-lactate (f), L-leucine (f), L-methionine (f), the recombinant product protein (f), L-glutamate (m), NAD (m), 2-oxoglutarate (m), NADH (m), L-glutamine (c), ADP (c), L-glutamate (c), ATP (c), L-aspartate (m), oxaloacetate (m), L-malate (m), the CoQH radical (m), extra-mitochondrial protons H_out (m), CoQ (m), intra-mitochondrial protons H_in (m), pyruvate (c), phosphoenolpyruvate (c), NADH (c), D-glycerate 3-phosphate (c), NAD (c), beta-D-glucose (c), L-malate (c), 2-oxoglutarate (c), L-aspartate (c), ATP (m), orthophosphate (m), ADP (m), L-leucine (c), L-methionine (c), and the fermenter volume.
All 32 reactions except Subset4 (protein synthesis) use a log-linear (linlog) kinetic form: rate = steady-state reference flux rss times one plus a sum of elasticity-weighted log-concentration terms. Subset4 instead uses a multi-substrate/product saturable (generalized reversible Michaelis-Menten) rate law. States are tracked already normalized by their steady-state reference concentrations css (so a value of 1.0 means "at the reference level"), which is why the elasticity terms below use log(c) directly rather than log(c / css).
const b4_css = [
100000.0, 1.0, 1000.0, 1000.0, 30.0, 1000.0, 1000.0, 1000.0, 1000.0, 1000.0,
1000.0, 1000.0, 3000.0, 1000.0, 1000.0, 1000.0, 100.0, 100.0, 100.0, 100.0,
1000.0, 1000.0, 1000.0, 1000.0, 1000.0, 1000.0, 1000.0, 1000.0, 1000.0, 3000.0,
100000.0, 1000.0, 1000.0, 1000.0]
# steady-state reference fluxes (rss); vol_1/vol_2 is the cytosol/mitochondria volume
# fraction ratio applied to reactions that straddle both compartments
const b4_vol1 = 0.9
const b4_vol2 = 0.1
const b4_rss = [
83401.9654177705, 127877.37232994902, 603.4140712332287, 603.4140712332287,
5.028450593613567, 2413.6562849217303 * b4_vol1 / b4_vol2, 603.414071180172,
40133.38664791273 * b4_vol1 / b4_vol2, 74836.04665510054 * b4_vol1 / b4_vol2,
180754.26889005644 * b4_vol1 / b4_vol2, 164390.2745505474, 36512.902220891134,
166803.93083553354, 39529.972576829896, 1810.242213701644, 127877.37232994902,
166200.51676427448, 216060.34296802033 * b4_vol1 / b4_vol2, 5.028450593613567,
35306.0740779408 * b4_vol1 / b4_vol2, 0.0, 532531.1670427525, 38926.55850561767,
40133.38664808034, 689982.1797742102, 495414.85075147304 * b4_vol1 / b4_vol2,
2413.6562849329107, 83401.9654177705, 603.4140712332287, 603.4140712332287,
2413.656284931604, 533134.5811139438]
# maps the 117 estimated parameters onto the 128-entry elasticity vector `e` used by the
# rate laws below; a handful of `e` entries are fixed constants rather than estimated
# (mirroring the AMIGO reference implementation's index bookkeeping exactly), and several
# more are the negative of an estimated (always-positive, bound-constrained) parameter,
# since AMIGO stores every parameter's magnitude but the sign is fixed by its role
# (substrate/activator elasticities are positive, product/inhibitor elasticities negative).
function b4_expand_params(p)
e = zeros(eltype(p), 128)
for i in 1:8
e[i] = p[i]
end
e[9] = 0.0
e[10] = 1.0
e[11] = 0.0
e[12] = 0.0
e[13] = 1.0
for i in 9:35
e[i + 5] = p[i]
end
e[41] = 0.0
for i in 36:41
e[i + 6] = p[i]
end
e[48] = 0.0
for i in 42:83
e[i + 7] = p[i]
end
e[91] = 0.0
e[92] = 0.0
e[93] = p[84]
e[94] = 0.7
e[95] = -0.2
for i in 85:117
e[i + 11] = p[i]
end
for (ei, pi) in (
(16, 11), (17, 12), (20, 15), (21, 16), (24, 19), (25, 20), (29, 24),
(30, 25), (34, 29), (35, 30), (36, 31), (39, 34), (40, 35), (45, 39),
(46, 40), (49, 42), (52, 45), (53, 46), (55, 48), (56, 49), (57, 50),
(61, 54), (62, 55), (63, 56), (65, 58), (69, 62), (70, 63), (71, 64),
(74, 67), (75, 68), (77, 70), (80, 73), (81, 74), (87, 80), (88, 81),
(89, 82), (90, 83), (93, 84), (98, 87), (99, 88), (102, 91), (103, 92),
(106, 95), (107, 96), (109, 98), (113, 102), (114, 103), (117, 106),
(119, 108), (121, 110), (123, 112), (125, 114), (127, 116), (128, 117),
)
e[ei] = -p[pi]
end
return e
end
function b4_kinetics!(du, c, p, t)
e = b4_expand_params(p)
css = b4_css
clogk = ntuple(i -> c[i] < 0 ? zero(c[i]) : log(c[i]), 35)
cap = ntuple(_ -> 1.0, 32) # AMIGO's per-reaction "capacity" scaling; always 1 here
r = zeros(eltype(c), 32)
r[6] = cap[6] * (b4_rss[6] * (1.0 + (((e[14] * clogk[8]) + (e[15] * clogk[9])) +
((e[16] * clogk[6]) + (e[17] * clogk[7])))))
r[7] = cap[7] * (b4_rss[7] * (1.0 + (((e[18] * clogk[12]) + (e[19] * clogk[13])) +
((e[20] * clogk[10]) + (e[21] * clogk[11])))))
r[8] = cap[8] * (b4_rss[8] * (1.0 + ((((e[22] * clogk[15]) + (e[23] * clogk[6])) +
((e[24] * clogk[8]) + (e[25] * clogk[14]))) +
(e[26] * clogk[16]))))
r[9] = cap[9] * (b4_rss[9] * (1.0 + (((e[27] * clogk[16]) + (e[28] * clogk[7])) +
((e[29] * clogk[15]) + (e[30] * clogk[9])))))
r[10] = cap[10] * (b4_rss[10] * (1.0 + ((((e[31] * clogk[9]) + (e[32] * clogk[19])) +
(e[33] * clogk[20])) +
(((e[34] * clogk[7]) + (e[35] * clogk[17])) +
(e[36] * clogk[18])))))
r[11] = cap[11] * (b4_rss[11] * (1.0 + ((((e[37] * clogk[22]) + (e[38] * clogk[11])) +
((e[39] * clogk[21]) + (e[40] * clogk[13]))) +
(e[41] * clogk[13]))))
r[12] = cap[12] * (b4_rss[12] * (1.0 + (((((((e[42] * clogk[15]) + (e[43] * clogk[7])) +
(e[44] * clogk[21])) +
((e[45] * clogk[8]) + (e[46] * clogk[9]))) +
(e[47] * clogk[32])) + (e[48] * clogk[9])) +
(e[49] * clogk[30]))))
r[13] = cap[13] * (b4_rss[13] * (1.0 + (((((((e[50] * clogk[25]) + (e[51] * clogk[26])) +
((e[52] * clogk[23]) + (e[53] * clogk[24]))) +
(e[54] * clogk[11])) + (e[55] * clogk[11])) +
(e[56] * clogk[13])) + (e[57] * clogk[22]))))
r[14] = cap[14] * (b4_rss[14] * (1.0 + ((((((e[58] * clogk[28]) + (e[59] * clogk[29])) +
(e[60] * clogk[23])) +
(((e[61] * clogk[12]) + (e[62] * clogk[27])) +
(e[63] * clogk[25]))) + (e[64] * clogk[27])) +
(e[65] * clogk[10]))))
r[15] = cap[15] * (b4_rss[15] * (1.0 + ((((e[66] * clogk[32]) + (e[67] * clogk[22])) +
(e[68] * clogk[16])) +
(((e[69] * clogk[15]) + (e[70] * clogk[30])) +
(e[71] * clogk[27])))))
r[16] = cap[16] * (b4_rss[16] * (1.0 + (((e[72] * clogk[21]) + (e[73] * clogk[23])) +
((e[74] * clogk[2]) + (e[75] * clogk[25])))))
r[17] = cap[17] * (b4_rss[17] * (1.0 + ((e[76] * clogk[24]) + (e[77] * clogk[22]))))
r[18] = cap[18] * (b4_rss[18] * (1.0 + (((e[78] * clogk[20]) + (e[79] * clogk[17])) +
((e[80] * clogk[18]) + (e[81] * clogk[19])))))
# Subset4 (protein synthesis): a generalized reversible Michaelis-Menten rate law
# with 8 participating substrates/products, unlike every other (log-linear) reaction
# above. `e[1..8]` here are the Km_Subset4_* parameters (raw `p[1..8]`, unmodified by
# `b4_expand_params`). Written as a loop over the 8 (state, Km) pairs instead of
# AMIGO's manually unrolled product -- algebraically identical, since the terms all
# commute under multiplication.
subset4_idx = (24, 25, 12, 33, 34, 29, 10, 13)
num_ss = one(eltype(c))
den_ss = one(eltype(c))
num_c = one(eltype(c))
den_c = one(eltype(c))
for (j, idx) in enumerate(subset4_idx)
tss = css[idx] / e[j]
tc = (c[idx] * css[idx]) / e[j]
num_ss *= tss
den_ss *= (1.0 + tss)
num_c *= tc
den_c *= (1.0 + tc)
end
r[19] = cap[19] * (b4_rss[19] * den_ss / num_ss) * (num_c / den_c)
r[20] = cap[20] * (b4_rss[20] * (1.0 + (((((((( (e[82] * clogk[8]) + (e[83] * clogk[7])) +
(e[84] * clogk[19])) +
(e[85] * clogk[31])) + (e[86] * clogk[32])) +
((((e[87] * clogk[16]) + (e[88] * clogk[9])) +
(e[89] * clogk[17])) + (e[90] * clogk[30]))) +
(e[91] * clogk[31])) + (e[92] * clogk[9])) +
(e[93] * clogk[15]))))
r[21] = cap[21] * (b4_rss[21] * (1.0 + ((e[94] * clogk[18]) + (e[95] * clogk[20]))))
r[22] = cap[22] * (b4_rss[22] * (1.0 + (((e[96] * clogk[11]) + (e[97] * clogk[30])) +
((e[98] * clogk[32]) + (e[99] * clogk[13])))))
r[23] = cap[23] * (b4_rss[23] * (1.0 + (((e[100] * clogk[8]) + (e[101] * clogk[27])) +
((e[102] * clogk[28]) + (e[103] * clogk[16])))))
r[24] = cap[24] * (b4_rss[24] * (1.0 + (((e[104] * clogk[14]) + (e[105] * clogk[12])) +
((e[106] * clogk[29]) + (e[107] * clogk[6])))))
r[25] = cap[25] * (b4_rss[25] * (1.0 + ((e[108] * clogk[13]) + (e[109] * clogk[11]))))
r[26] = cap[26] * (b4_rss[26] * (1.0 + ((((e[110] * clogk[32]) + (e[111] * clogk[31])) +
(e[112] * clogk[18])) +
((e[113] * clogk[30]) + (e[114] * clogk[20])))))
r[27] = cap[27] * (b4_rss[27] * (1.0 + (((e[115] * clogk[27]) + (e[116] * clogk[31])) +
(e[117] * clogk[16]))))
r[28] = cap[28] * (b4_rss[28] * (1.0 + ((e[118] * clogk[1]) + (e[119] * clogk[26]))))
r[29] = cap[29] * (b4_rss[29] * (1.0 + ((e[120] * clogk[3]) + (e[121] * clogk[33]))))
r[30] = cap[30] * (b4_rss[30] * (1.0 + ((e[122] * clogk[4]) + (e[123] * clogk[34]))))
r[31] = cap[31] * (b4_rss[31] * (1.0 + ((e[124] * clogk[6]) + (e[125] * clogk[12]))))
r[32] = cap[32] * (b4_rss[32] * (1.0 + ((e[126] * clogk[18]) +
((e[127] * clogk[31]) + (e[128] * clogk[20])))))
vol_1, vol_2 = b4_vol1, b4_vol2
# fermenter feed is only active for 5 < t < 10 in the reference implementation, but at
# a feed rate of exactly 0 -- the fermenter volume (and hence the dilution terms below)
# is therefore constant. Kept for fidelity to the reference model.
du[35] = 0.0
du[1] = (-r[28] / 141.4710605 - c[1] * css[1] / c[35] * du[35]) / css[1]
du[2] = (r[16] / 141.4710605 - c[2] * css[2] / c[35] * du[35]) / css[2]
du[3] = (-r[29] / 141.4710605 - c[3] * css[3] / c[35] * du[35]) / css[3]
du[4] = (-r[30] / 141.4710605 - c[4] * css[4] / c[35] * du[35]) / css[4]
du[5] = (r[19] / 141.4710605 - c[5] * css[5] / c[35] * du[35]) / css[5]
du[6] = (r[6] - r[8] + r[24] * vol_1 / vol_2 - r[31] * vol_1 / vol_2) / css[6]
du[7] = (r[6] - r[9] + r[10] - 2.0 * r[12] * vol_1 / vol_2 - r[20]) / css[7]
du[8] = (-r[6] + r[8] + r[12] * vol_1 / vol_2 - r[20] - r[23] * vol_1 / vol_2) / css[8]
du[9] = (-r[6] + r[9] - r[10] + 2.0 * r[12] * vol_1 / vol_2 + r[20]) / css[9]
du[10] = (r[7] - 120.0 * r[19]) / css[10]
du[11] = (r[7] - r[11] + 1260.0 * r[19] - r[22] + r[25]) / css[11]
du[12] = (-r[7] + r[14] - 240.0 * r[19] - r[24] + r[31]) / css[12]
du[13] = (-r[7] + r[11] - 1260.0 * r[19] + r[22] - r[25]) / css[13]
du[14] = (r[8] - r[24] * vol_1 / vol_2) / css[14]
du[15] = (-r[8] + r[9] - r[12] * vol_1 / vol_2 + r[15] * vol_1 / vol_2) / css[15]
du[16] = (-r[9] - r[15] * vol_1 / vol_2 + r[20] + r[23] * vol_1 / vol_2 +
r[27] * vol_1 / vol_2) / css[16]
du[17] = (2.0 * r[10] - 2.0 * r[18] + 2.0 * r[20]) / css[17]
du[18] = (4.0 * r[10] + 6.0 * r[18] - r[21] - 3.0 * r[26] - r[32] * vol_1 / vol_2) /
css[18]
du[19] = (-2.0 * r[10] + 2.0 * r[18] - 2.0 * r[20]) / css[19]
du[20] = (-4.0 * r[10] - 6.0 * r[18] + r[21] + 3.0 * r[26] + r[32] * vol_1 / vol_2) /
css[20]
du[21] = (r[11] - r[12] - r[16]) / css[21]
du[22] = (-r[11] - r[15] + r[17]) / css[22]
du[23] = (r[13] - r[14] - r[16] + 120.0 * r[19]) / css[23]
du[24] = (r[13] - r[17] - 120.0 * r[19]) / css[24]
du[25] = (-r[13] + r[14] + r[16] - 120.0 * r[19]) / css[25]
du[26] = (-0.5 * r[13] + r[28]) / css[26]
du[27] = (r[14] + r[15] - r[23] - r[27]) / css[27]
du[28] = (-r[14] + 120.0 * r[19] + r[23]) / css[28]
du[29] = (-r[14] - 120.0 * r[19] + r[24]) / css[29]
du[30] = (r[15] * vol_1 / vol_2 + r[20] - r[22] * vol_1 / vol_2 + r[26]) / css[30]
du[31] = (-r[20] - r[26] - r[27] * vol_1 / vol_2 + r[32] * vol_1 / vol_2) / css[31]
du[32] = (-r[15] * vol_1 / vol_2 - r[20] + r[22] * vol_1 / vol_2 - r[26]) / css[32]
du[33] = (-120.0 * r[19] + r[29]) / css[33]
du[34] = (-120.0 * r[19] + r[30]) / css[34]
nothing
endb4_kinetics! (generic function with 1 method)Nominal parameters, bounds, and initial condition
The 117 parameters are, in order: 8 Michaelis constants for the Subset4 protein-synthesis reaction (Km_Subset4_*, for D-glycerate-3P, NAD, glutamate, leucine, methionine, aspartate, glutamine, and ATP, all in cytosol), followed by 109 log-linear elasticities for the remaining 31 reactions (each named e_substrate/e_product/e_activator/e_inhibitor by the reaction and species it belongs to in the AMIGO reference source). Bounds are a factor of 5 below/above the nominal value for every parameter.
p_nom = [
1000.0, 1000.0, 1000.0, 1000.0, 1000.0, 1000.0, 1000.0, 1000.0, 1.0, 1.0, 0.7, 0.7,
0.7, 0.7, 0.2, 0.2, 1.0, 1.0, 0.7, 0.7, 0.05, 1.0, 0.5, 0.7, 0.5, 2.0, 0.7, 0.7, 2.0,
0.2, 0.2, 1.0, 0.7, 0.2, 0.21, 1.0, 0.7, 1.0, 0.2, 0.2, 0.05, 0.01, 0.7, 1.0, 0.5, 1.0,
0.04, 0.01, 0.01, 0.01, 1.0, 1.0, 0.5, 1.0, 1.0, 0.5, 0.1, 0.1, 0.5, 1.0, 1.0, 1.0, 0.3,
1.0, 1.0, 0.7, 0.4, 0.7, 1.0, 0.7, 0.7, 2.0, 0.2, 2.0, 1.0, 0.7, 0.7, 0.2, 0.7, 0.5,
0.21, 0.2, 0.2, 0.01, 2.0, 2.0, 2.0, 2.0, 2.0, 2.0, 2.0, 2.0, 1.0, 1.0, 1.0, 1.0, 1.0,
0.5, 0.7, 0.7, 2.0, 0.2, 2.0, 1.0, 1.0, 0.7, 1.0, 0.7, 1.0, 0.7, 1.0, 0.7, 2.0, 2.0, 0.7,
0.2, 0.2]
p_lower = p_nom ./ 5
p_upper = p_nom .* 5
# a fixed initial guess distinct from the nominal parameters, taken directly from the
# benchmark's own `b4_bounds.mat`. The reference implementation explicitly warns against
# using the nominal parameters as the optimization starting point, since recovering them
# from a different guess is the point of the exercise, so (unlike this folder's other
# BioPreDyn-bench benchmark, B2, whose reference setup has no such restriction) we start
# optimization from this point instead of from `p_nom`.
p_start = [
559.246183586727, 951.8526159783388, 1209.3926423296261, 1108.2411804507406,
1131.8844697068953, 614.8098822286546, 693.4962891662825, 756.8581555974563,
1.1618334014402798, 1.010360100180178, 0.6874899615341215, 1.0042191933785871,
0.6420942544552156, 0.7963352463317699, 0.251259801109437, 0.21169093679552325,
1.128819668117032, 1.2148062169753862, 0.5550645201598408, 0.7885095239226643,
0.0716151015376954, 0.6822024241425708, 0.4439305029548263, 0.555274158152172,
0.5422120602672525, 1.7269813402785503, 0.6442439212775087, 1.0044963464600916,
1.8310696571959042, 0.2695166078706759, 0.21912758579110164, 0.5196983631758563,
1.0173514455706194, 0.2645786406646756, 0.29513807176327145, 1.074909052745588,
0.38718147238096434, 0.7158240994061267, 0.21184210019886696, 0.15959491343921442,
0.06846293053544839, 0.007682552400632342, 0.9695076945059595, 0.7798099216337468,
0.2777873319493819, 1.122789527159203, 0.021740120977325465, 0.011341759897234783,
0.01095767461148841, 0.012242399769196301, 0.733778133275873, 0.8400273052741705,
0.28490418578462706, 1.0804765014375879, 0.5593299283267159, 0.2627912987262461,
0.07498598954796754, 0.061907330786564796, 0.26773767481968, 0.7289397586656472,
1.4019935413749123, 0.5233697368046363, 0.39393756786208023, 0.9461802947619279,
1.4361566955705485, 0.5724627510264765, 0.5766001030478425, 0.5947799645609589,
1.1145113324366538, 0.538400339185408, 0.998265898794248, 1.3488341531122623,
0.1341520669763673, 2.295993105129317, 1.1740131819235997, 0.9435308639264697,
0.3872582502696485, 0.13194624230468477, 0.6069057535685372, 0.38476369751245376,
0.2538709132488072, 0.17104939996228308, 0.250647137649718, 0.010910354043587226,
1.326619209465763, 2.0092983707023944, 1.8933925033966557, 2.144119804894699,
1.0420838393148957, 2.902406882331043, 2.1977421761971287, 1.975812719036163,
1.4586895089103473, 1.4936210103484457, 0.64402021343644, 0.634129763871874,
1.3541757134464245, 0.3388126779599871, 0.5391033859006893, 0.8575049977994068,
1.0646059748143037, 0.28664633803157213, 1.3726629930823835, 0.954835879225296,
0.9816520738173586, 0.5123831799652268, 1.4082199137925364, 0.4684683476985062,
1.3268735896615724, 0.9411624153376564, 0.961002381260504, 0.639646441106458,
1.2299527260165495, 1.9534697095422526, 0.5795627195075416, 0.17739683892594194,
0.2063468961527426]
u0 = vcat([5.0, 1.0, 5.0, 5.0], ones(30), [6.0])
tspan = (0.0, 300.0)
prob = ODEProblem(b4_kinetics!, u0, tspan, p_nom)ODEProblem with uType Vector{Float64} and tType Float64. In-place: true
Non-trivial mass matrix: false
timespan: (0.0, 300.0)
u0: 35-element Vector{Float64}:
5.0
1.0
5.0
5.0
1.0
1.0
1.0
1.0
1.0
1.0
⋮
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
6.0Simulated experimental data
13 metabolites sampled at 12 time points (plus the initial condition, not used in the objective below), as simulated and noised in the original AMIGO benchmark. Each column's associated standard deviation (used to weight the residuals) is given alongside it.
b4_state_idxs = [5, 4, 3, 2, 1, 29, 27, 21, 15, 13, 30, 32, 11]
b4_divisors = [30.0, 1000.0, 1000.0, 1.0, 100000.0, 1000.0, 1000.0, 1000.0, 1000.0,
3000.0, 3000.0, 1000.0, 1000.0]
b4_times = [0.0, 23.9759, 48.4337, 72.8916, 90.3614, 115.984, 140.442, 164.9, 210.321,
233.614, 258.072, 282.53, 300.0]
# columns: Productprotein_f, L-Methionine_f, L-Leucine_f, L-Lactate_f, beta-D-Glucose_f,
# L-Aspartate_c, L-Malate_c, Pyruvate_c, Oxaloacetate_m, ATP_c, ATP_m, ADP_m, ADP_c
b4_data = [
29.54174187 5110.119691 4999.956639 1.056682831 449958.4343 1009.945764 988.3517969 996.1405443 839.7703035 3314.558385 2968.296835 1016.447754 1029.663149
29.06135825 4427.537773 4990.471667 19033.05068 499628.9405 514.889607 1883.981851 4115.730274 443.5222307 3298.082924 3588.716676 701.1769714 841.6656476
31.56920926 4649.633023 4706.446115 29713.37459 498137.7445 614.0882509 1999.234422 5088.17481 457.2654501 3144.678363 3524.003949 534.3245626 898.4469128
32.58992629 4642.175831 4703.420191 52653.84782 469436.4399 667.144403 1977.174384 4941.17988 452.1008571 3343.981672 3274.933898 637.1604048 748.7508252
32.93492455 4581.482695 4580.779761 62491.60793 458816.0559 706.4697945 2027.556359 5561.084132 416.1288178 3305.264733 3377.224218 608.6810043 760.8237877
33.80995822 4231.998041 4576.568758 71665.49964 441725.8779 748.837145 1834.640732 4711.566421 433.6235068 2664.13707 3359.281519 608.5031107 746.0614226
34.67192676 4609.073999 4388.444795 93744.69241 371353.6441 761.4219172 1741.34438 4466.968205 471.9681186 3276.842196 3268.007202 609.2855454 770.8013591
35.64086504 4379.397091 4823.258118 96012.12538 409872.6888 913.9581526 2054.553359 4841.62543 462.4384044 3326.232934 3375.331315 657.6144762 747.1622156
35.1073701 4047.37735 4757.799632 131633.9417 429309.5792 838.4429003 2023.441102 4741.87247 463.3431076 2838.535673 3344.113884 606.0191858 696.1165299
34.78766884 4354.532227 4267.505383 139701.0391 377830.4707 864.115653 2012.727053 4982.305375 451.6411544 3445.146289 3384.49464 596.595147 747.4997328
35.10275329 3893.078648 3946.812817 156106.4324 376607.9654 1019.41341 2077.935601 4932.876021 432.2633547 3185.845081 3123.317817 606.9552722 742.2563724
39.16229127 4223.934695 4229.786474 189350.8377 350136.0051 945.7524046 2018.02482 4965.805674 459.569613 3248.126308 3303.223152 634.2843344 740.5121927
39.36873083 3819.952372 3226.591797 170253.9838 362466.0386 962.815767 2167.954632 4922.316021 461.1326466 3189.167366 3335.671338 664.509921 757.3732437]
b4_stdev = [
0.916516259 220.2393825 0.086722941 0.113365662 100083.1314 19.8915281 23.29640617 7.718911471 320.4593929 629.11677 63.40633065 32.89550786 59.32629796
3.42708349 859.4844544 266.3833335 524.0986472 27089.88103 72.52278599 1.363702921 13.17945154 67.9675385 110.2258472 512.6933529 67.11194286 169.2792952
0.072781474 197.1939541 83.56777088 13530.25082 50101.48902 8.871498249 109.6688443 1402.38962 25.79309975 208.3432738 361.1878982 244.5448747 294.6078256
0.345652583 11.22833874 111.2603823 145.6956478 17694.8798 11.00519392 1.408768357 800.1597591 29.84428584 184.2633444 149.0122046 26.80319038 1.191650429
0.103150906 5.585389682 4.179521469 2222.584132 13862.11186 0.953588928 72.01271842 1881.128264 99.10036436 104.3694651 49.86843658 78.08799131 27.79957543
0.003516434 495.8039179 193.3375168 15030.00072 4663.755834 0.759709907 343.8585363 3.332842875 61.44498639 1179.74586 8.403037386 72.83977854 0.150845275
0.186053515 442.6879971 1.429589001 515.5848117 112764.7117 48.67616557 548.4312396 616.2835899 16.98823721 45.18439211 177.4455966 67.99290924 50.07871826
0.604730081 164.3741824 1052.096236 22589.74924 12874.62245 190.2563052 67.32671764 29.79086077 0.791191271 144.5058684 35.34263088 30.52495245 2.300431195
3.228859795 170.8252992 1250.019264 372.1165486 67335.15833 70.03419938 0.977796603 311.3950597 2.654215273 828.1886549 27.87223266 71.86362837 102.5249403
5.262062329 608.8844539 434.830766 8311.921766 14941.05855 69.51269399 20.40589406 115.4107506 20.1576913 387.132577 53.48928055 91.2997059 1.854534475
6.079093429 142.482705 35.01436682 49.13512714 3973.930766 190.684819 114.9912025 29.80795876 58.42129056 128.8298377 467.6643662 71.7674556 14.94525519
0.608382544 688.7293909 700.4329474 42607.67548 27959.98971 4.487190854 2.669639537 1.328651269 3.420773959 1.32738423 106.1736951 18.79533114 21.39761464
0.008461654 0.624744428 1186.096406 12180.03246 11498.07728 3.204466046 309.209264 110.2279582 0.074706795 116.9052678 39.83732302 40.18584194 10.01248736]13×13 Matrix{Float64}:
0.916516 220.239 0.0867229 … 63.4063 32.8955 59.3263
3.42708 859.484 266.383 512.693 67.1119 169.279
0.0727815 197.194 83.5678 361.188 244.545 294.608
0.345653 11.2283 111.26 149.012 26.8032 1.19165
0.103151 5.58539 4.17952 49.8684 78.088 27.7996
0.00351643 495.804 193.338 … 8.40304 72.8398 0.150845
0.186054 442.688 1.42959 177.446 67.9929 50.0787
0.60473 164.374 1052.1 35.3426 30.525 2.30043
3.22886 170.825 1250.02 27.8722 71.8636 102.525
5.26206 608.884 434.831 53.4893 91.2997 1.85453
6.07909 142.483 35.0144 … 467.664 71.7675 14.9453
0.608383 688.729 700.433 106.174 18.7953 21.3976
0.00846165 0.624744 1186.1 39.8373 40.1858 10.0125Objective function
The objective is a weighted least-squares cost comparing the 13 tracked states (scaled by their reference concentrations) against the simulated data above, reproduced here exactly from the AMIGO2 script b4_obj.m.
function biopredyn_b4_cost(p)
# Away from the nominal parameters, global optimizers routinely probe combinations
# that make this stiff log-linear model numerically unstable; `maxiters` bounds how
# long a single doomed integration can spend retrying ever-smaller steps before giving
# up (returning a non-`Success` retcode) rather than a full search-budget iteration
# spent uselessly on it.
sol = solve(prob, Rodas5P(), p = p, reltol = 1e-6, abstol = 1e-6, maxiters = 10_000)
sol.retcode == ReturnCode.Success || return 1e20
simvals = Array(sol(b4_times))[b4_state_idxs, 2:end]' # (12 times) x (13 observables)
data = b4_data[2:end, :] ./ b4_divisors'
err = b4_stdev[2:end, :] ./ b4_divisors'
cost = sum(((simvals .- data) ./ err) .^ 2)
return isfinite(cost) ? cost : 1e20
endbiopredyn_b4_cost (generic function with 1 method)@time cost_nominal = biopredyn_b4_cost(p_nom)
@time cost_start = biopredyn_b4_cost(p_start)4.481824 seconds (8.51 M allocations: 445.007 MiB, 5.89% gc time, 96.56%
compilation time)
0.116649 seconds (883.88 k allocations: 53.430 MiB, 28.03% gc time)
1.0213152934777013e11The original study reports reaching a cost of Jf ≈ 45.718 using the enhanced scatter search (eSS) global optimizer after ~1.6·10⁵ function evaluations (about 1 hour of CPU time), starting from a random point inside the bounds – since this benchmark's simulated data was itself generated from p_nom, recovering it (rather than merely improving on the initial guess) is the actual goal of the exercise.
Visualizing the fit at nominal and starting parameters
sol_nom = solve(prob, Rodas5P(), p = p_nom, reltol = 1e-6, abstol = 1e-6)
plot(sol_nom, idxs = b4_state_idxs, label = permutedims(string.(b4_state_idxs)),
xlabel = "time (h)", title = "B4 dynamics at nominal parameters")
Parameter estimation
We benchmark global optimizers on this 117-parameter problem, starting from p_start (not p_nom, per the reference implementation's guidance – see above) and using the bounds given above. As with B2, we include BBO_adaptive_de_rand_1_bin, GN_CRS2_LM, and ParallelPSOArray from ParallelParticleSwarms.jl. Each trackable optimizer's raw per-evaluation cost is recorded via a callback, from which we compute the running best-found cost for a convergence plot; ParallelPSOArray does not yet support the callback keyword, so only its final result is available.
optf = OptimizationFunction((p, _) -> biopredyn_b4_cost(p))
optprob = OptimizationProblem(optf, p_start, lb = p_lower, ub = p_upper)OptimizationProblem. In-place: true
u0: 117-element Vector{Float64}:
559.246183586727
951.8526159783388
1209.3926423296261
1108.2411804507406
1131.8844697068953
614.8098822286546
693.4962891662825
756.8581555974563
1.1618334014402798
1.010360100180178
⋮
1.3268735896615724
0.9411624153376564
0.961002381260504
0.639646441106458
1.2299527260165495
1.9534697095422526
0.5795627195075416
0.17739683892594194
0.2063468961527426losses_bbo = Float64[]
times_bbo = Float64[]
t0_bbo = time()
cb_bbo = (state, l) -> (push!(losses_bbo, l); push!(times_bbo, time() - t0_bbo); false)
@time res_bbo = solve(
optprob, BBO_adaptive_de_rand_1_bin(), maxiters = 20000, callback = cb_bbo)
res_bbo.objective2194.130392 seconds (14.70 G allocations: 866.028 GiB, 31.07% gc time, 0.19
% compilation time: 2% of which was recompilation)
124525.9374347846losses_nlopt = Float64[]
times_nlopt = Float64[]
t0_nlopt = time()
cb_nlopt = (state, l) -> (push!(losses_nlopt, l); push!(times_nlopt, time() - t0_nlopt); false)
opt = Opt(:GN_CRS2_LM, length(p_nom))
@time res_nlopt = solve(optprob, opt, maxiters = 20000, callback = cb_nlopt)
res_nlopt.objective2060.654299 seconds (13.83 G allocations: 814.987 GiB, 31.16% gc time, 0.04
% compilation time)
41955.65492908892n_particles = 40
@time res_pso = solve(optprob, ParallelPSOArray(n_particles), maxiters = 12000 ÷ n_particles)
res_pso.objective779.092874 seconds (7.51 G allocations: 442.803 GiB, 82.53% gc time, 7.69%
compilation time)
186837.41319842328Local refinement
Global metaheuristics are good at finding a promising basin but slow to fine-tune within it; the original study's own eSS method is itself a hybrid global+local algorithm for exactly this reason. We polish each of the three global results above with LN_BOBYQA (derivative-free).
function polish(start_u, label)
prob = OptimizationProblem(optf, start_u, lb = p_lower, ub = p_upper)
losses = Float64[]
times = Float64[]
t0 = time()
cb = (state, l) -> (push!(losses, l); push!(times, time() - t0); false)
t = @elapsed res = solve(
prob, Opt(:LN_BOBYQA, length(p_nom)), maxiters = 5000, callback = cb)
println(label, ": ", res.objective, " (", t, "s)")
return res, losses, times
end
res_bbo_polish, losses_bbo_polish, times_bbo_polish = polish(res_bbo.u, "BBO -> LN_BOBYQA")
res_nlopt_polish, losses_nlopt_polish, times_nlopt_polish = polish(
res_nlopt.u, "GN_CRS2_LM -> LN_BOBYQA")
res_pso_polish, losses_pso_polish, times_pso_polish = polish(
res_pso.u, "ParallelPSOArray -> LN_BOBYQA")BBO -> LN_BOBYQA: 10301.503185220978 (413.629028475s)
GN_CRS2_LM -> LN_BOBYQA: 20580.80066763163 (476.470871553s)
ParallelPSOArray -> LN_BOBYQA: 18512.299814061877 (433.030706792s)
(retcode: MaxIters
u: [2076.5886379011627, 3015.8860909025793, 201.45628316848436, 292.0196970
1784486, 243.116873574594, 804.5835920125427, 4185.032329542567, 624.788322
6808742, 4.984184892557448, 4.013195774957875 … 0.4114165980962092, 0.212
1341905820356, 0.18970539729079933, 0.20167656418067784, 2.3316899384372523
, 0.6181521169126012, 3.546100305319167, 3.4110303470698686, 0.937166321951
3118, 0.17158601488876454]
Final objective value: 18512.299814061877
, [186837.413198329, 177475.05014608652, 160033.32471855124, 187000.6857946
16, 206225.24963917249, 197727.7658584077, 170638.4308345303, 219322.956366
66156, 189327.35938378258, 184039.16005845548 … 18517.717453439414, 18517
.690229428106, 18516.486234334727, 18515.817430177674, 18515.439177586366,
18514.731477746933, 18514.036619624087, 18513.54724383885, 18513.2327526083
46, 18512.299814061877], [0.05199289321899414, 0.11403703689575195, 0.25628
39984893799, 0.3081789016723633, 0.3703129291534424, 0.48830389976501465, 0
.5403289794921875, 0.6619210243225098, 0.7135510444641113, 0.77004098892211
91 … 432.25626397132874, 432.31095004081726, 432.368124961853, 432.514177
0839691, 432.56809186935425, 432.62765192985535, 432.77205300331116, 432.82
542085647583, 432.8865878582001, 433.02934193611145])df = DataFrame(
method = ["Nominal (true params)", "Starting guess (no fit)",
"BBO_adaptive_de_rand_1_bin", "GN_CRS2_LM", "ParallelPSOArray",
"LN_BOBYQA polish (from BBO)", "LN_BOBYQA polish (from GN_CRS2_LM)",
"LN_BOBYQA polish (from ParallelPSOArray)"],
cost = [cost_nominal, cost_start, res_bbo.objective, res_nlopt.objective,
res_pso.objective, res_bbo_polish.objective, res_nlopt_polish.objective,
res_pso_polish.objective])8×2 DataFrame
Row │ method cost
│ String Float64
─────┼───────────────────────────────────────────────────
1 │ Nominal (true params) 39.0675
2 │ Starting guess (no fit) 1.02132e11
3 │ BBO_adaptive_de_rand_1_bin 1.24526e5
4 │ GN_CRS2_LM 41955.7
5 │ ParallelPSOArray 1.86837e5
6 │ LN_BOBYQA polish (from BBO) 10301.5
7 │ LN_BOBYQA polish (from GN_CRS2_L… 20580.8
8 │ LN_BOBYQA polish (from ParallelP… 18512.3Convergence
bestcost_bbo = accumulate(min, losses_bbo)
bestcost_nlopt = accumulate(min, losses_nlopt)
bestcost_bbo_polish = accumulate(min, losses_bbo_polish)
bestcost_nlopt_polish = accumulate(min, losses_nlopt_polish)
bestcost_pso_polish = accumulate(min, losses_pso_polish)
bbo_polish_iters = length(losses_bbo) .+ (1:length(losses_bbo_polish))
nlopt_polish_iters = length(losses_bbo) .+ (1:length(losses_nlopt_polish))
pso_polish_iters = length(losses_bbo) .+ (1:length(losses_pso_polish))
plot(bestcost_bbo, label = "BBO_adaptive_de_rand_1_bin", yscale = :log10,
xlabel = "iteration", ylabel = "best cost so far (log scale)",
title = "B4 parameter estimation convergence", legend = :outertopright,
size = (900, 500))
plot!(bestcost_nlopt, label = "GN_CRS2_LM")
plot!(bbo_polish_iters, bestcost_bbo_polish, label = "LN_BOBYQA polish (from BBO)")
plot!(nlopt_polish_iters, bestcost_nlopt_polish, label = "LN_BOBYQA polish (from GN_CRS2_LM)")
plot!(pso_polish_iters, bestcost_pso_polish, label = "LN_BOBYQA polish (from PSO)")
hline!([45.718], label = "paper reference (eSS, ~1.6x10^5 evals)", linestyle = :dash)
Iteration count alone hides that these optimizers have very different per-iteration costs, so we also plot the same running-best costs against wall-clock seconds, with each curve measured from its own start:
plot(times_bbo, bestcost_bbo, label = "BBO_adaptive_de_rand_1_bin", yscale = :log10,
xlabel = "wall-clock time (s)", ylabel = "best cost so far (log scale)",
title = "B4 parameter estimation convergence (wall time)", legend = :outertopright,
size = (900, 500))
plot!(times_nlopt, bestcost_nlopt, label = "GN_CRS2_LM")
plot!(times_bbo_polish, bestcost_bbo_polish, label = "LN_BOBYQA polish (from BBO)")
plot!(times_nlopt_polish, bestcost_nlopt_polish, label = "LN_BOBYQA polish (from GN_CRS2_LM)")
plot!(times_pso_polish, bestcost_pso_polish, label = "LN_BOBYQA polish (from PSO)")
hline!([45.718], label = "paper reference (eSS, ~1.6x10^5 evals)", linestyle = :dash)
ParallelPSOArray's own result isn't shown as a curve (no per-iteration history is available, as noted above), but its polish curve starts from wherever res_pso.objective landed, plotted alongside the other two polish curves for direct comparison.
Conclusion
This benchmark demonstrates SciML's parameter estimation stack (OrdinaryDiffEq + Optimization.jl) on BioPreDyn-bench B4, a 117-parameter, 35-state log-linear kinetic model of CHO cell metabolism – comparable in scale to B2 but built from simulated rather than real data, and with a different (log-linear/generalized-Michaelis-Menten) kinetic structure. Unlike B2, recovering the exact nominal parameters (not just a low cost) is the benchmark's actual goal, since the pseudo-data was generated from them; the runs here are best read as relative comparisons between optimizers given a fixed, modest evaluation budget rather than as fully converged fits to the literature reference of Jf ≈ 45.718.
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/ParameterEstimation","BioPreDynB4ParameterEstimation.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/ParameterEstimation/Project.toml`
[6e4b80f9] BenchmarkTools v1.8.0
[a134a8b2] BlackBoxOptim v0.6.12
[a93c6f00] DataFrames v1.8.2
⌃ [1130ab10] DiffEqParamEstim v2.6.1
[31c24e10] Distributions v0.25.131
[f6369f11] ForwardDiff v1.4.6
⌃ [961ee093] ModelingToolkit v11.43.0
⌃ [7771a370] ModelingToolkitBase v1.70.0
[76087f3c] NLopt v1.2.1
⌃ [7f7a1694] Optimization v5.9.0
[3e6eede4] OptimizationBBO v0.4.12
[4e6fcdb7] OptimizationNLopt v0.3.18
[1dea7af3] OrdinaryDiffEq v7.8.1
[ab63da0c] ParallelParticleSwarms v1.6.2
[65888b18] ParameterizedFunctions v5.27.0
[91a5bcdd] Plots v1.41.7
[731186ca] RecursiveArrayTools v4.5.1
⌃ [91a8cdf1] SciCompDSL v1.0.3
[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)]
Info Packages marked with ⌃ have new versions available and may be upgradable.And the full manifest:
Status `~/github-runners/amdci3-1/_work/SciMLBenchmarks.jl/SciMLBenchmarks.jl/benchmarks/ParameterEstimation/Manifest.toml`
[47edcb42] ADTypes v1.24.0
[14f7f29c] AMD v0.5.4
[6e696c72] AbstractPlutoDingetjes v1.4.1
[1520ce14] AbstractTrees v0.4.5
[7d9f7c33] Accessors v0.1.45
⌃ [79e6a3ab] Adapt v4.7.0
[66dad0bd] AliasTables v1.1.3
[ec485272] ArnoldiMethod v0.4.0
⌃ [4fba245c] ArrayInterface v7.30.1
[4c555306] ArrayLayouts v1.12.2
[a9b6321e] Atomix v1.2.1
[aae01518] BandedMatrices v1.12.0
[6e4b80f9] BenchmarkTools v1.8.0
[e2ed5e7c] Bijections v0.2.2
[b2a6c25c] BinaryHeaps v1.1.0
[caf10ac8] BipartiteGraphs v0.1.14
[a134a8b2] BlackBoxOptim v0.6.12
[8e7c35d0] BlockArrays v1.10.0
[70df07ce] BracketingNonlinearSolve v1.12.7
[fa961155] CEnum v0.5.0
[d360d2e6] ChainRulesCore v1.26.1
[35d6a980] ColorSchemes v3.31.0
[3da002f7] ColorTypes v0.12.1
[c3611d14] ColorVectorSpace v0.11.0
[5ae59095] Colors v0.13.1
⌅ [861a8166] Combinatorics v1.0.2
[38540f10] CommonSolve v0.2.14
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⌃ [071ae1c0] DiffEqGPU v3.21.0
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⌃ [5b8099bc] DomainSets v0.8.1
[7c1d4256] DynamicPolynomials v0.6.8
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⌃ [7da242da] Enzyme v0.13.203
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⌃ [64ca27bc] FindFirstFunctions v3.2.1
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⌅ [53c48c17] FixedPointNumbers v0.8.6
[1fa38f19] Format v1.3.7
[f6369f11] ForwardDiff v1.4.6
[a85aefff] FunctionMaps v0.1.2
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[77dc65aa] FunctionWrappersWrappers v1.13.0
[46192b85] GPUArraysCore v0.2.0
⌅ [61eb1bfa] GPUCompiler v1.23.0
[28b8d3ca] GR v0.73.27
⌃ [a0844989] Gamma v1.1.0
[86223c79] Graphs v1.15.0
[076d061b] HashArrayMappedTries v0.2.0
⌅ [eafb193a] Highlights v0.5.3
[34004b35] HypergeometricFunctions v0.3.30
[3263718b] ImplicitDiscreteSolve v2.3.0
[d25df0c9] Inflate v0.1.5
⌅ [842dd82b] InlineStrings v1.4.6
[18e54dd8] IntegerMathUtils v0.1.4
[8197267c] IntervalSets v0.7.14
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[41ab1584] InvertedIndices v1.3.1
[92d709cd] IrrationalConstants v0.2.6
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[1019f520] JLFzf v0.1.11
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⌅ [682c06a0] JSON v0.21.4
[ae98c720] Jieko v0.2.1
⌃ [ccbc3e58] JumpProcesses v9.32.3
[63c18a36] KernelAbstractions v0.9.42
⌃ [ba0b0d4f] Krylov v0.10.9
[2faa5264] LHLFactorization v2.2.2
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⌃ [87fe0de2] LineSearch v0.1.17
⌃ [7ed4a6bd] LinearSolve v5.17.2
⌃ [2ab3a3ac] LogExpFunctions v0.3.29
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⌃ [961ee093] ModelingToolkit v11.43.0
⌃ [7771a370] ModelingToolkitBase v1.70.0
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⌅ [2e0e35c7] Moshi v0.3.9
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⌃ [8913a72c] NonlinearSolve v4.30.0
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⌃ [5959db7a] NonlinearSolveFirstOrder v2.6.1
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⌃ [7f7a1694] Optimization v5.9.0
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⌃ [bca83a33] OptimizationBase v5.5.3
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⌅ [bac558e1] OrderedCollections v1.8.2 [loaded: v2.0.1]
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⌃ [bbf590c4] OrdinaryDiffEqCore v4.17.1
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⌃ [4302a76b] OrdinaryDiffEqDifferentiation v3.11.5
⌃ [127b3ac7] OrdinaryDiffEqNonlinearSolve v2.9.6
⌃ [43230ef6] OrdinaryDiffEqRosenbrock v2.7.3
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⌃ [2d112036] OrdinaryDiffEqSDIRK v2.9.2
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[ab63da0c] ParallelParticleSwarms v1.6.2
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[d96e819e] Parameters v0.13.1
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[06bb1623] PenaltyFunctions v0.3.0
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⌃ [995b91a9] PlotUtils v1.4.4
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[d236fae5] PreallocationTools v1.7.1
[aea7be01] PrecompileTools v1.3.4
⌃ [21216c6a] Preferences v1.5.2 [loaded: v1.6.0]
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⌃ [0c0d3e7f] PureKLU v1.4.2
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[05181044] RelocatableFolders v1.0.1
[ae029012] Requires v1.3.1
[9fe22ead] RespecializeParams v1.3.0
[79098fc4] Rmath v0.9.0
[f2b01f46] Roots v3.0.8
[7e49a35a] RuntimeGeneratedFunctions v0.5.26
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⌃ [91a8cdf1] SciCompDSL v1.0.3
⌃ [0bca4576] SciMLBase v3.53.3
[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)]
[19f34311] SciMLJacobianOperators v0.1.19
[a6db7da4] SciMLLogging v2.1.0
⌃ [c0aeaf25] SciMLOperators v1.30.0
[431bcebd] SciMLPublic v1.3.0
[53ae85a6] SciMLStructures v1.10.5
[7e506255] ScopedValues v1.6.2
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[91c51154] SentinelArrays v1.4.10
[efcf1570] Setfield v1.1.2
[992d4aef] Showoff v1.1.1
[05bca326] SimpleDiffEq v1.18.0
⌃ [727e6d20] SimpleNonlinearSolve v2.14.3
[510db2f7] SimpleOptimization v2.0.1
[699a6c99] SimpleTraits v0.9.6
[ed01d8cd] Sobol v1.5.0
[a2af1166] SortingAlgorithms v1.2.3
[a57abbd0] SparseColumnPivotedQR v2.1.8
[9f842d2f] SparseConnectivityTracer v1.2.3
[0a514795] SparseMatrixColorings v0.4.28
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[0c0c59c1] StarAlgebras v0.3.0
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⌃ [90137ffa] StaticArrays v1.9.20
[1e83bf80] StaticArraysCore v1.4.4
[10745b16] Statistics v1.11.5
[82ae8749] StatsAPI v1.8.0
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[69024149] StringEncodings v0.3.7
⌅ [892a3eda] StringManipulation v0.5.0
[53d494c1] StructIO v0.3.1
[2efcf032] SymbolicIndexingInterface v0.3.55
[19f23fe9] SymbolicLimits v1.2.1
⌃ [d1185830] SymbolicUtils v4.46.5
⌃ [0c5d862f] Symbolics v7.39.2
[3783bdb8] TableTraits v1.0.1
[bd369af6] Tables v1.14.0
[ed4db957] TaskLocalValues v0.1.3
[62fd8b95] TensorCore v0.1.1
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[5d786b92] TerminalLoggers v0.1.8
⌃ [a759f4b9] TimerOutputs v1.2.1
[e689c965] Tracy v0.1.6
[781d530d] TruncatedStacktraces v1.4.0
[5c2747f8] URIs v1.7.0
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[41fe7b60] Unzip v0.2.0
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[44d3d7a6] Weave v0.10.12
⌃ [ddb6d928] YAML v0.4.16 [loaded: v0.4.17]
[700de1a5] ZygoteRules v0.2.8
[6e34b625] Bzip2_jll v1.0.9+0
[83423d85] Cairo_jll v1.18.7+0
[ee1fde0b] Dbus_jll v1.16.2+0
[cd4c43a9] Dierckx_jll v0.2.0+0
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[2702e6a9] EpollShim_jll v0.0.20230411+1
[2e619515] Expat_jll v2.8.4+0
⌅ [b22a6f82] FFMPEG_jll v8.1.2+0
[a3f928ae] Fontconfig_jll v2.17.1+0
[d7e528f0] FreeType2_jll v2.14.3+1
[559328eb] FriBidi_jll v1.0.17+0
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[d2c73de3] GR_jll v0.73.27+0
⌅ [b0724c58] GettextRuntime_jll v0.22.4+0
[61579ee1] Ghostscript_jll v9.55.1+0
[7746bdde] Glib_jll v2.88.3+0
[3b182d85] Graphite2_jll v1.3.16+0
[2e76f6c2] HarfBuzz_jll v100.14004.0+0
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[1d63c593] LLVMOpenMP_jll v23.1.1+0
[ad6e5548] LibTracyClient_jll v0.13.1+0
⌅ [e9f186c6] Libffi_jll v3.4.7+0
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[94ce4f54] Libiconv_jll v1.18.0+0
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[30392449] Pixman_jll v0.46.4+0
[c0090381] Qt6Base_jll v6.10.2+2
[629bc702] Qt6Declarative_jll v6.10.2+2
[ce943373] Qt6ShaderTools_jll v6.10.2+1
[6de9746b] Qt6Svg_jll v6.10.2+0
[e99dba38] Qt6Wayland_jll v6.10.2+1
[f50d1b31] Rmath_jll v0.5.2+0
[a44049a8] Vulkan_Loader_jll v1.3.243+0
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[ffd25f8a] XZ_jll v5.8.4+0
[f67eecfb] Xorg_libICE_jll v1.1.2+0
[c834827a] Xorg_libSM_jll v1.2.6+0
[4f6342f7] Xorg_libX11_jll v1.8.13+0
[0c0b7dd1] Xorg_libXau_jll v1.0.13+0
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[a3789734] Xorg_libXdmcp_jll v1.1.6+0
[1082639a] Xorg_libXext_jll v1.3.8+0
[d091e8ba] Xorg_libXfixes_jll v6.0.2+0
[a51aa0fd] Xorg_libXi_jll v1.8.4+0
[d1454406] Xorg_libXinerama_jll v1.1.7+0
[ec84b674] Xorg_libXrandr_jll v1.5.6+0
[ea2f1a96] Xorg_libXrender_jll v0.9.12+0
[a65dc6b1] Xorg_libpciaccess_jll v0.19.0+0
[c7cfdc94] Xorg_libxcb_jll v1.17.1+0
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[e920d4aa] Xorg_xcb_util_cursor_jll v0.1.6+0
[12413925] Xorg_xcb_util_image_jll v0.4.1+0
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[975044d2] Xorg_xcb_util_keysyms_jll v0.4.1+0
[0d47668e] Xorg_xcb_util_renderutil_jll v0.3.10+0
[c22f9ab0] Xorg_xcb_util_wm_jll v0.4.2+0
[35661453] Xorg_xkbcomp_jll v1.4.7+0
[33bec58e] Xorg_xkeyboard_config_jll v2.47.0+2
[c5fb5394] Xorg_xtrans_jll v1.6.0+0
[3161d3a3] Zstd_jll v1.5.7+1
[35ca27e7] eudev_jll v3.2.14+0
⌅ [214eeab7] fzf_jll v0.61.1+0
[a4ae2306] libaom_jll v3.14.1+0
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[dfaa095f] x265_jll v4.1.0+0
[d8fb68d0] xkbcommon_jll v1.13.0+0
[0dad84c5] ArgTools v1.1.2
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[b27032c2] LibCURL v0.6.4
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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
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[3fa0cd96] REPL v1.11.0
[9a3f8284] Random v1.11.0
[ea8e919c] SHA v0.7.0
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[6462fe0b] Sockets v1.11.0
[2f01184e] SparseArrays v1.12.0
[f489334b] StyledStrings v1.11.0
[4607b0f0] SuiteSparse
[fa267f1f] TOML v1.0.3
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[e66e0078] CompilerSupportLibraries_jll v1.3.1+2
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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`