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Wilson-Cowan E/I — noise σ=0.1 (extreme (exploratory))

PARITYS0 · dim 2

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=0.1. Noise regime: extreme (exploratory). Base problem: NMM.1. Runner injects noise via acceptance_criteria.noise_sigma.

Neuroscience

Problem definition

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.

Show canonical RHS excerpt
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])
Parameters
  • G_E = 1
  • I_ext = 1.5
  • c_EE = 16
  • c_EI = 12
  • c_IE = 15
  • mu_E = 1.3
  • mu_I = 2
  • sigma_E = 4
  • sigma_I = 3.7
  • tau_E = 0.0025
  • tau_I = 0.00375
Initial condition
y(0) = [0.100001, 0.050001]
Horizon
t ∈ [0, 2]

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

Versions & freeze

Methodology →
Freeze
2026-08-13
libsolvsrk
2.3.0
SciPy
1.14
SUNDIALS
CVODE (bundled backend)

20 seeds/cell default · 14 arms · TRL 4–5 · simulation-lab validated · this page: Wilson-Cowan E/I — noise σ=0.1 (extreme (exploratory)) (wilson-cowan-e-i-noise-0-1-extreme-exploratory)

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

Results matrix

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

#SolverSurvivalSCDnfevWallScore
1SolvSRK
100%
16.02874 ms1.000
-SciPy BDFSciPy
0%
----
-SciPy RadauSciPy
0%
----
-SciPy RK45SciPy
0%
----
-SciPy LSODASciPy
0%
----
-SciPy DOP853SciPy
0%
----
-SciPy RK23SciPy
0%
----
-CVODE BDFexternal
0%
----
-CVODE Adamsexternal
0%
----
-Tsit5external
0%
----
-Vern7external
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 →

Cite this page

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_1_extreme_exploratory_2026,
  title        = {Resonix Evidence Portal: Wilson-Cowan E/I — noise σ=0.1 (extreme (exploratory))},
  author       = {{Resonix Labs (Canada) Inc.}},
  year         = {2026},
  howpublished = {\url{https://resonixusa.com/evidence/problems/wilson-cowan-e-i-noise-0-1-extreme-exploratory}},
  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.}
}

Related

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