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Two-Layer Heat MOL dim=100

PARITYS2 · dim 100

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 →

1D two-layer heat equation (MOL), 50 nodes per layer. Same physics as ir_two_layer_heat (alpha1=100e-6, alpha2=1e-6) with finer spatial discretization. Tests LRDE matrix-solve cost scaling.

Thermal & heat transfer

Problem definition

Incropera & DeWitt, Fundamentals of Heat Transfer; IR domain qualification spec

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 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 d
Parameters
  • alphas = [0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, …] [shape=(100,), min=1e-06, max=0.0001]
  • dx2 = 1e-08
  • n = 100
Initial condition
y(0) = [400, 398.98989899, 397.97979798, 396.96969697, 395.95959596, 394.949494949, …] [shape=(100,), min=300, max=400]
Horizon
t ∈ [0, 20]

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: high

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: Two-Layer Heat MOL dim=100 (two-layer-heat-mol-dim-100)

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%
11.72,702132 ms0.898
2SciPy RadauSciPy
100%
10.689376 ms0.870
3CVODE Adamsexternal
100%
9.22,682178 ms0.837
4SciPy LSODASciPy
100%
8.62,624151 ms0.823
5CVODE BDFexternal
100%
8.465655 ms0.820
6SciPy BDFSciPy
100%
8.152448 ms0.811
-SciPy RK45SciPy
0%
----
-SciPy DOP853SciPy
0%
----
-SciPy RK23SciPy
0%
----
-Tsit5external
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_two_layer_heat_mol_dim_100_2026,
  title        = {Resonix Evidence Portal: Two-Layer Heat MOL dim=100},
  author       = {{Resonix Labs (Canada) Inc.}},
  year         = {2026},
  howpublished = {\url{https://resonixusa.com/evidence/problems/two-layer-heat-mol-dim-100}},
  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