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Hénon-Heiles Hamiltonian

BOUNDARYS0 · dim 4

Partial / unstable. SolvSRK survives more than 0% but less than 90% of runs at the comparison noise level, without being beaten by a baseline there. Usable with margin and monitoring; validate on your own configuration. All verdicts →

Chaotic Hamiltonian system; energy conservation benchmark

Oscillators & nonlinear dynamics

Problem definition

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.

Show canonical RHS excerpt
def _henon_heiles_rhs(t, y):
    q1, q2, p1, p2 = y
    return np.array([
        p1,
        p2,
        -q1 - 2 * q1 * q2,
        -q2 - q1**2 + q2**2,
    ])
Parameters
  • No captured parameters; constants are explicit in the RHS excerpt.
Initial condition
y(0) = [0, 0.1, 0.5, 0]
Horizon
t ∈ [0, 1000]

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: medium

Recommendation snapshot

Clean best: Vern9

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: Hénon-Heiles Hamiltonian (henon-heiles-hamiltonian)

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
1Vern9external
100%
5.436,7542.84 s0.747
2SolvSRK
100%
5.3126,384316 ms0.746
3SciPy RadauSciPy
100%
5.1217,4882.29 s0.740
4Vern7external
100%
5.046,8822.93 s0.739
5SciPy DOP853SciPy
100%
3.327,25497 ms0.698
6Tsit5external
100%
3.349,1942.80 s0.696
7SciPy RK45SciPy
100%
2.857,650225 ms0.685
8FBDFexternal
100%
2.797,7064.02 s0.683
9SciPy LSODASciPy
100%
2.719,53748 ms0.683
10CVODE Adamsexternal
100%
2.014,53969 ms0.666
11CVODE BDFexternal
100%
2.027,042124 ms0.666
12SciPy RK23SciPy
100%
1.9302,1951.49 s0.665
13SciPy BDFSciPy
100%
1.851,462975 ms0.662
14TRBDF2external
100%
1.2205,4465.00 s0.648

At Clean, best balanced arm is Vern9 · SolvSRK survival 100%, SCD 5.3.

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_henon_heiles_hamiltonian_2026,
  title        = {Resonix Evidence Portal: Hénon-Heiles Hamiltonian},
  author       = {{Resonix Labs (Canada) Inc.}},
  year         = {2026},
  howpublished = {\url{https://resonixusa.com/evidence/problems/henon-heiles-hamiltonian}},
  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