No clear winner. The survival gap is under 10 percentage points and the balanced-score gap is under 0.05, so neither SolvSRK nor the best baseline clears the win threshold. Either works — choose on cost, licensing, or integration effort. All verdicts →
9-species H2/O2 combustion mechanism (Mueller subset of GRI-Mech 3.0), constant-pressure 0D reactor
Mueller et al. (1999); GRI-Mech 3.0 (Smith et al.)
Canonical RHS excerpt from the registered callable used for this benchmark cell. Expand it to verify the state equations; it is not a standalone runnable fixture.
def _h2_mean_mw(Y):
"""Mean molecular weight from mass fractions (Y for 8 reactive species)."""
Y_N2 = max(1.0 - np.sum(Y), 0.0)
inv_W = np.sum(Y / _H2_MW) + Y_N2 / _MW["N2"]
return 1.0 / max(inv_W, 1e-30)
def h2_combustion_9sp_rhs(t, y):
T = max(y[0], 200.0)
Y = np.maximum(y[1:], 0.0)
W_mix = _h2_mean_mw(Y)
rho = _P_ATM * W_mix / (_R_U * T) * 1e-3 # kg/m^3 (MW in g/mol -> /1000)
# Molar concentrations [mol/cm^3] (cgs for rate constants)
rho_cgs = rho * 1e-3 # g/cm^3
C = np.empty(8)
for i in range(8):
C[i] = max(rho_cgs * Y[i] / _H2_MW[i], 0.0)
C_N2 = max(rho_cgs * max(1.0 - np.sum(Y), 0.0) / _MW["N2"], 0.0)
C_M = np.sum(C) + C_N2 # third-body concentration
inv_T = 1.0 / T
# Arrhenius rates [mol/cm^3/s]
k1 = 3.52e16 * T**(-0.7) * np.exp(-17070.0 * inv_T)
k2 = 5.06e4 * T**2.67 * np.exp(-6290.0 * inv_T)
k3 = 2.65e19 * T**(-1.3) # third-body
k4 = 1.17e9 * T**1.3 * np.exp(-3626.0 * inv_T)
k5 = 4.20e14 * np.exp(-12000.0 * inv_T)
k6 = 2.95e14 * np.exp(-24370.0 * inv_T) # unimolecular + M
# Reaction rates (indices: H2=0 O2=1 H2O=2 H=3 O=4 OH=5 HO2=6 H2O2=7)
r1 = k1 * C[3] * C[1] # H + O2 -> OH + O
r2 = k2 * C[4] * C[0] # O + H2 -> OH + H
r3 = k3 * C[3] * C[1] * C_M # H + O2 + M -> HO2 + M
r4 = k4 * C[5] * C[0] # OH + H2 -> H2O + H
r5 = k5 * C[6] * C[6] # HO2 + HO2 -> H2O2 + O2
r6 = k6 * C[7] * C_M # H2O2 + M -> 2 OH + M
# Species production rates omega_dot [mol/cm^3/s]
omega = np.zeros(8)
omega[0] += -r2 - r4 # H2
omega[1] += -r1 - r3 + r5 # O2
omega[2] += r4 # H2O
omega[3] += -r1 - r3 + r2 + r4 # H
omega[4] += r1 - r2 # O
omega[5] += r1 + r2 - r4 + 2.0 * r6 # OH
omega[6] += r3 - 2.0 * r5 # HO2
omega[7] += r5 - r6 # H2O2
# Convert to SI: omega [mol/cm^3/s] -> [mol/m^3/s] (* 1e6)
omega_si = omega * 1e6
dy = np.empty(9)
# dY_k/dt = W_k * omega_dot_k / rho (W_k in kg/mol = g/mol * 1e-3)
for i in range(8):
dy[i + 1] = (_H2_MW[i] * 1e-3) * omega_si[i] / max(rho, 1e-30)
# dT/dt = -1/(rho*cp) * sum(hf_k * omega_dot_k) [hf in J/mol, omega in mol/m^3/s]
q_dot = np.dot(_H2_HF, omega_si)
dy[0] = -q_dot / max(rho * _CP, 1e-30)
return dyCanonical RHS excerpt captured from the same registered callable used for the published benchmark. Frozen closure values are summarized below; helper imports and solver settings are intentionally omitted.
Fingerprint
Spread: extreme
Default noise: high
Recommendation snapshot
Clean best: SciPy Radau
Noisy best: SolvSRK
Coverage
14 solver arms · clean + 5 noise levels
Ranked on survival, precision, and speed
20 seeds/cell default · 14 arms · TRL 4–5 · simulation-lab validated · this page: H2/O2 combustion 9-species (Mueller subset) (h2-o2-combustion-9-species-mueller-subset)
Governed SolvTune benchmark freeze; per-arm medians only. RHS definitions and raw trial rows are not published.
Self-reported by Resonix Labs · not independently verified
Pick an objective and a noise level to rank all arms on survival, median SCD, median nfev, and median wall time. Medians across seeds.
Objective
Best overall trade-off of survival, precision, and speed.
Noise level
| # | Solver | Survival | SCD | nfev | Wall | Score |
|---|---|---|---|---|---|---|
| 1 | SciPy RadauSciPy | 100% | 9.8 | 463 | 20 ms | 0.852 |
| 2 | SciPy BDFSciPy | 100% | 9.6 | 354 | 17 ms | 0.849 |
| 3 | SolvSRK | 100% | 9.2 | 176 | 3 ms | 0.837 |
| 4 | SciPy LSODASciPy | 100% | 8.5 | 124 | 3 ms | 0.822 |
| 5 | SciPy RK45SciPy | 100% | 7.7 | 44 | 1 ms | 0.802 |
| 6 | Tsit5external | 100% | 7.1 | 42 | 750 ms | 0.787 |
| 7 | CVODE Adamsexternal | 100% | 7.0 | 33 | 10 ms | 0.786 |
| 8 | CVODE BDFexternal | 100% | 6.8 | 32 | 11 ms | 0.782 |
| 9 | SciPy DOP853SciPy | 100% | 6.4 | 146 | 4 ms | 0.772 |
| 10 | SciPy RK23SciPy | 100% | 6.2 | 14 | <1 ms | 0.768 |
At Clean, best balanced arm is SciPy Radau · SolvSRK survival 100%, SCD 9.2.
Values are medians across seeds, measured by Resonix Labs on Resonix hardware and not independently verified; nfev and wall are on reference lab hardware (indicative). Under injected noise only SolvSRK and the SciPy arms are run. How we measure accuracy → · Verification status →
SolvScout · free
This page shows one published benchmark cell. SolvScout fingerprints your ODE, compares it to the full corpus, and recommends a solver with the same survival / precision / speed ranking you see here — including when a SciPy arm wins.
SolvSRK · 30-day trial
SolvSRK is the stiffness-adaptive integrator behind the SolvSRK column in these tables. Create an account, activate a machine, and take a 30-day trial — same binary you'd ship after purchase.
Replace the access date. Pin the freeze ID and library versions when comparing against a later export. Cite it as what it is — a self-reported vendor benchmark, not an independently verified result. The note field says so; please keep it.
@misc{resonix_evidence_h2_o2_combustion_9_species_mueller_subset_2026,
title = {Resonix Evidence Portal: H2/O2 combustion 9-species (Mueller subset)},
author = {{Resonix Labs (Canada) Inc.}},
year = {2026},
howpublished = {\url{https://resonix.tech/evidence/problems/h2-o2-combustion-9-species-mueller-subset}},
note = {Self-reported vendor benchmark; internally generated by Resonix Labs and not independently verified. Accessed YYYY-MM-DD. Freeze 2026-08-13; libsolvsrk 2.3.0; SciPy 1.14.}
}TRL 4–5 · simulation-lab validated · 398 problems · 14 solver arms · clean + 5 noise levels
Freeze: 2026-08-13 · scipy 1.14 · libsolvsrk 2.3.0 · Methodology
Self-reported by Resonix Labs · not independently verified · Verification status