SolvSRK wins. At the comparison noise level, SolvSRK beats the best baseline by at least 10 percentage points of survival, or by at least 0.05 balanced score when survival is tied. Use SolvSRK for this class of problem. All verdicts →
Closed-loop WK3 with sigmoid valve; stiffness from fast valve time-constant vs. cardiac cycle
Canonical benchmark implementation
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 rhs(t: float, y: np.ndarray) -> np.ndarray:
P_c, Q_v, y_valve = float(y[0]), float(y[1]), float(y[2])
# Driving pressure (simplified piston model)
phase = (t % T_cycle) / T_cycle
P_lv = P_drive_amp * max(0.0, np.sin(np.pi * phase / 0.35)) if phase < 0.35 else 0.0
# Valve state (sigmoid, fast-slow separation)
v_inf = 1.0 / (1.0 + np.exp(-20.0 * (P_lv - P_c - 5.0)))
dy_valve = (v_inf - y_valve) / tau_v
# Flow through valve
Q_in = y_valve * max(P_lv - P_c, 0.0) / R1
# Windkessel ODE
dP_c = (Q_in - P_c / R2) / C
dQ_v = (P_lv - Q_v * R1 - P_c) / L
return np.array([dP_c, dQ_v, dy_valve])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: 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: 3-element Windkessel cardiac model (3-element-windkessel-cardiac-model)
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% | 11.2 | 16,028 | 46 ms | 0.886 |
| 2 | SciPy RadauSciPy | 100% | 9.7 | 21,610 | 460 ms | 0.849 |
| 3 | SciPy RK45SciPy | 100% | 8.8 | 7,754 | 60 ms | 0.829 |
| 4 | Tsit5external | 100% | 8.6 | 8,628 | 1.55 s | 0.823 |
| 5 | SciPy LSODASciPy | 100% | 8.1 | 6,514 | 31 ms | 0.812 |
| 6 | CVODE Adamsexternal | 100% | 8.0 | 3,913 | 40 ms | 0.809 |
| 7 | SciPy RK23SciPy | 100% | 7.3 | 25,142 | 241 ms | 0.793 |
| 8 | SciPy BDFSciPy | 100% | 7.2 | 7,996 | 281 ms | 0.791 |
| 9 | CVODE BDFexternal | 100% | 7.0 | 4,841 | 45 ms | 0.785 |
| 10 | SciPy DOP853SciPy | 100% | 6.6 | 9,806 | 69 ms | 0.776 |
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_3_element_windkessel_cardiac_model_2026,
title = {Resonix Evidence Portal: 3-element Windkessel cardiac model},
author = {{Resonix Labs (Canada) Inc.}},
year = {2026},
howpublished = {\url{https://resonix.tech/evidence/problems/3-element-windkessel-cardiac-model}},
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