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 →
10D Single Particle Model (SPM) of lithium-ion battery - Fick diffusion + Butler-Volmer kinetics
Doyle, Fuller, Newman (1993); Marquis et al. (2019); DandeLiion (Richardson et al. 2021)
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 _spm_rhs(t, y):
"""Spherical Fick's diffusion at 5 radial nodes per electrode with flux BC."""
dy = np.zeros(10)
c_neg = y[:5]
c_pos = y[5:]
# -- Anode (indices 0..4) --
for i in range(5):
if i == 0:
# symmetry BC at center: dc/dr = 0 => use forward difference
r2_half = _R_HALF_NEG[0] ** 2
flux_right = _D_S_NEG * r2_half * (c_neg[1] - c_neg[0]) / _DR_NEG
r_i_sq = max(_R_GRID_NEG[0], _DR_NEG * 0.5) ** 2 # avoid r=0 singularity
dy[0] = (1.0 / r_i_sq) * flux_right / _DR_NEG
elif i == 4:
# surface: flux boundary from applied current
r2_left = _R_HALF_NEG[3] ** 2
flux_left = _D_S_NEG * r2_left * (c_neg[4] - c_neg[3]) / _DR_NEG
r_i_sq = _R_GRID_NEG[4] ** 2
flux_surf = _R_NEG ** 2 * _J_NEG # surface flux from current
dy[4] = (1.0 / r_i_sq) * (flux_surf - flux_left) / _DR_NEG
else:
r2_right = _R_HALF_NEG[i] ** 2
r2_left = _R_HALF_NEG[i - 1] ** 2
flux_right = _D_S_NEG * r2_right * (c_neg[i + 1] - c_neg[i]) / _DR_NEG
flux_left = _D_S_NEG * r2_left * (c_neg[i] - c_neg[i - 1]) / _DR_NEG
r_i_sq = _R_GRID_NEG[i] ** 2
dy[i] = (1.0 / r_i_sq) * (flux_right - flux_left) / _DR_NEG
# -- Cathode (indices 5..9) --
for i in range(5):
if i == 0:
r2_half = _R_HALF_POS[0] ** 2
flux_right = _D_S_POS * r2_half * (c_pos[1] - c_pos[0]) / _DR_POS
r_i_sq = max(_R_GRID_POS[0], _DR_POS * 0.5) ** 2
dy[5] = (1.0 / r_i_sq) * flux_right / _DR_POS
elif i == 4:
r2_left = _R_HALF_POS[3] ** 2
flux_left = _D_S_POS * r2_left * (c_pos[4] - c_pos[3]) / _DR_POS
r_i_sq = _R_GRID_POS[4] ** 2
flux_surf = _R_POS ** 2 * _J_POS
dy[9] = (1.0 / r_i_sq) * (flux_surf - flux_left) / _DR_POS
else:
r2_right = _R_HALF_POS[i] ** 2
r2_left = _R_HALF_POS[i - 1] ** 2
flux_right = _D_S_POS * r2_right * (c_pos[i + 1] - c_pos[i]) / _DR_POS
flux_left = _D_S_POS * r2_left * (c_pos[i] - c_pos[i - 1]) / _DR_POS
r_i_sq = _R_GRID_POS[i] ** 2
dy[5 + i] = (1.0 / r_i_sq) * (flux_right - flux_left) / _DR_POS
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: low
Default noise: none
Recommendation snapshot
Clean best: SolvSRK
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: Newman SPM 10D (Li-ion battery) (newman-spm-10d-li-ion-battery)
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 | SolvSRK | 100% | 14.8 | 21,637 | 418 ms | 0.972 |
| 2 | SciPy RadauSciPy | 100% | 10.7 | 649 | 21 ms | 0.873 |
| 3 | SciPy DOP853SciPy | 100% | 10.0 | 290 | 5 ms | 0.856 |
| 4 | CVODE Adamsexternal | 100% | 9.7 | 201 | 10 ms | 0.850 |
| 5 | Tsit5external | 100% | 9.4 | 294 | 745 ms | 0.842 |
| 6 | SciPy RK45SciPy | 100% | 9.2 | 320 | 6 ms | 0.839 |
| 7 | SciPy BDFSciPy | 100% | 9.2 | 279 | 14 ms | 0.838 |
| 8 | SciPy LSODASciPy | 100% | 9.1 | 282 | 5 ms | 0.837 |
| 9 | CVODE BDFexternal | 100% | 9.1 | 193 | 10 ms | 0.835 |
| 10 | SciPy RK23SciPy | 100% | 7.9 | 644 | 13 ms | 0.807 |
At Clean, best balanced arm is SolvSRK.
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 →
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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_newman_spm_10d_li_ion_battery_2026,
title = {Resonix Evidence Portal: Newman SPM 10D (Li-ion battery)},
author = {{Resonix Labs (Canada) Inc.}},
year = {2026},
howpublished = {\url{https://resonix.tech/evidence/problems/newman-spm-10d-li-ion-battery}},
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