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 →
1-D diffusion through two materials with distinct thermal diffusivity
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, temp: np.ndarray) -> np.ndarray:
temp = np.clip(np.asarray(temp, dtype=float), 200.0, 3500.0)
d = np.zeros(n)
for i in range(n):
t_left = 400.0 if i == 0 else temp[i - 1]
t_right = 300.0 if i == n - 1 else temp[i + 1]
d[i] = alphas[i] * (t_left - 2.0 * temp[i] + t_right) / dx2
return dCanonical 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: high
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: Two-layer heat conduction (two-layer-heat-conduction)
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% | 11.7 | 1,586 | 80 ms | 0.898 |
| 2 | SciPy RadauSciPy | 100% | 10.7 | 790 | 36 ms | 0.874 |
| 3 | SciPy RK23SciPy | 100% | 9.5 | 152,063 | 4.73 s | 0.846 |
| 4 | SciPy DOP853SciPy | 100% | 9.1 | 239,018 | 6.89 s | 0.835 |
| 5 | CVODE BDFexternal | 100% | 8.7 | 409 | 18 ms | 0.827 |
| 6 | SciPy BDFSciPy | 100% | 8.7 | 467 | 27 ms | 0.826 |
| 7 | Tsit5external | 100% | 8.7 | 277,056 | 30.32 s | 0.826 |
| 8 | SciPy LSODASciPy | 100% | 8.6 | 1,598 | 42 ms | 0.823 |
| 9 | SciPy RK45SciPy | 100% | 8.4 | 269,138 | 7.87 s | 0.819 |
| 10 | CVODE Adamsexternal | 100% | 7.9 | 1,440 | 48 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 →
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_two_layer_heat_conduction_2026,
title = {Resonix Evidence Portal: Two-layer heat conduction},
author = {{Resonix Labs (Canada) Inc.}},
year = {2026},
howpublished = {\url{https://resonix.tech/evidence/problems/two-layer-heat-conduction}},
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