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Two-Layer Heat MOL dim=1000

ADVANTAGES2 · dim 1000

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 →

1D two-layer heat equation (MOL), 500 nodes per layer. Tests LRDE at large-scale discretization. At dim=1000 the N_talbot resolvent solves each require a 1000x1000 linear system — tests whether sparse factorization keeps wall time practical.

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=(1000,), min=1e-06, max=0.0001]
  • dx2 = 1e-10
  • n = 1000
Initial condition
y(0) = [400, 399.8998999, 399.7997998, 399.6996997, 399.5995996, 399.499499499, …] [shape=(1000,), 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: SolvSRK

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=1000 (two-layer-heat-mol-dim-1000)

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%
12.017,8067.50 s0.905
2SciPy RadauSciPy
100%
10.61,4994.31 s0.871
3SciPy BDFSciPy
100%
8.21,3631.35 s0.815
4CVODE BDFexternal
100%
7.84,2292.70 s0.805
-SciPy RK45SciPy
0%
----
-SciPy LSODASciPy
0%
----
-SciPy DOP853SciPy
0%
----
-SciPy RK23SciPy
0%
----
-CVODE Adamsexternal
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_1000_2026,
  title        = {Resonix Evidence Portal: Two-Layer Heat MOL dim=1000},
  author       = {{Resonix Labs (Canada) Inc.}},
  year         = {2026},
  howpublished = {\url{https://resonixusa.com/evidence/problems/two-layer-heat-mol-dim-1000}},
  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