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 →
2D Wilson-Cowan E/I model with additive noise σ=0.0001. Noise regime: sub-clinical. Base problem: NMM.1. Runner injects noise via acceptance_criteria.noise_sigma.
Wilson & Cowan (1972); Ableidinger et al. (2017)
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 _stable_expit(x):
"""Numerically stable sigmoid 1/(1+exp(-x)), scalar or array."""
x = np.asarray(x, dtype=float)
return np.where(
x >= 0,
1.0 / (1.0 + np.exp(-x)),
np.exp(x) / (1.0 + np.exp(x)),
)
def rhs(t: float, y: np.ndarray) -> np.ndarray:
r_E, r_I = y[0], y[1]
input_E = c_EE * G_E * r_E - c_EI * r_I + I_ext * G_E
input_I = c_IE * r_E
F_E = float(_stable_expit(sigma_E * (input_E - mu_E)))
F_I = float(_stable_expit(sigma_I * (input_I - mu_I)))
dr_E = (-r_E + F_E) / tau_E
dr_I = (-r_I + F_I) / tau_I
return np.array([dr_E, dr_I])Canonical 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: SciPy BDF
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: Wilson-Cowan E/I — noise σ=0.0001 (sub-clinical) (wilson-cowan-e-i-noise-0-0001-sub-clinical)
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% | 16.0 | 287 | 5 ms | 1.000 |
| 2 | Vern7external | 100% | 7.6 | 359,762 | 8.11 s | 0.801 |
| 3 | SciPy RK23SciPy | 100% | 7.3 | 10,952 | 126 ms | 0.792 |
| 4 | SciPy LSODASciPy | 100% | 7.0 | 160,199 | 1.47 s | 0.786 |
| 5 | CVODE BDFexternal | 100% | 7.0 | 23,602 | 252 ms | 0.784 |
| 6 | SciPy RK45SciPy | 100% | 6.8 | 8,534 | 88 ms | 0.782 |
| 7 | CVODE Adamsexternal | 100% | 6.8 | 19,467 | 224 ms | 0.781 |
| 8 | Tsit5external | 100% | 6.7 | 73,620 | 5.43 s | 0.779 |
| 9 | SciPy DOP853SciPy | 100% | 6.6 | 419,018 | 4.93 s | 0.776 |
| — | SciPy BDFSciPy | 0% | — | — | — | — |
| — | SciPy RadauSciPy | 0% | — | — | — | — |
| — | Vern9external | 0% | — | — | — | — |
| — | TRBDF2external | 0% | — | — | — | — |
| — | FBDFexternal | 0% | — | — | — | — |
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 →
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_wilson_cowan_e_i_noise_0_0001_sub_clinical_2026,
title = {Resonix Evidence Portal: Wilson-Cowan E/I — noise σ=0.0001 (sub-clinical)},
author = {{Resonix Labs (Canada) Inc.}},
year = {2026},
howpublished = {\url{https://resonix.tech/evidence/problems/wilson-cowan-e-i-noise-0-0001-sub-clinical}},
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