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 →
11-state HEL thermal blooming model. States: [T_surface, T_sub1, T_sub2, T_sub3, T_melt, damage_integral, beam_wander_x, beam_wander_y, blooming_index, slew_x, slew_y]. 4-layer 1D thermal conduction with T^4 radiation + Arrhenius damage. Beam wander and slew jitter modeled as OU processes with deterministic sinusoidal surrogates. P_beam=30kW, range=1km, steel target. Mixed stiffness: fast OU dynamics (tau~0.01s) vs slow thermal diffusion.
Sprangle et al. (2002) 'Propagation of intense short laser pulses in the atmosphere'; Beason (2005) 'The E-Bomb'; Incropera & DeWitt Ch. 5 (1D conduction)
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 _spot_efficiency(wander_x: float, wander_y: float,
slew_x: float, slew_y: float,
blooming: float) -> float:
"""Fraction of beam power deposited on target, accounting for
wander, slew jitter, and thermal blooming defocus."""
r2 = (wander_x + slew_x) ** 2 + (wander_y + slew_y) ** 2
gauss_loss = np.exp(-2.0 * r2 / (_W0 ** 2))
bloom_loss = 1.0 / (1.0 + blooming ** 2)
return gauss_loss * bloom_loss
def rhs_hel_thermal(t: float, y: np.ndarray) -> np.ndarray:
T_s = max(y[0], 1.0)
T_1 = max(y[1], 1.0)
T_2 = max(y[2], 1.0)
T_3 = max(y[3], 1.0)
T_melt = y[4]
bw_x, bw_y = y[6], y[7]
bloom = y[8]
slw_x, slw_y = y[9], y[10]
eff = _spot_efficiency(bw_x, bw_y, slw_x, slw_y, bloom)
P_abs = _P_BEAM * np.exp(-_ALPHA_ATM * _RANGE) * eff
rho_cp_dx = _RHO * _CP * _DX
k_dx2 = _K_COND / (_DX ** 2)
k_dx = _K_COND / _DX
d = np.empty(11)
# Thermal layers (1D finite difference, 4 layers)
irradiance = P_abs / (np.pi * _W0 ** 2)
d[0] = (irradiance
- _SIGMA * _EPS * (T_s ** 4 - _T_AMB ** 4)
- k_dx * (T_s - T_1)) / rho_cp_dx
d[1] = k_dx2 * (T_s - 2.0 * T_1 + T_2) / (_RHO * _CP)
d[2] = k_dx2 * (T_1 - 2.0 * T_2 + T_3) / (_RHO * _CP)
d[3] = k_dx2 * (T_2 - 2.0 * T_3 + _T_AMB) / (_RHO * _CP)
# Melt tracking
d[4] = 0.0 if T_s < _T_MELT_THRESH else (T_s - _T_MELT_THRESH) / _TAU_MELT
# Arrhenius damage integral
d[5] = _A_ARR * np.exp(-_E_A / (_R_GAS * T_s))
# OU surrogates for beam wander
d[6] = -bw_x / _TAU_TURB + _SIGMA_TURB * np.sin(_FREQ_WX * t)
d[7] = -bw_y / _TAU_TURB + _SIGMA_TURB * np.sin(_FREQ_WY * t)
# Thermal blooming index
d[8] = (_N2 * _P_BEAM / (np.pi * _W0 ** 2) - bloom) / _TAU_BLOOM
# OU surrogates for slew jitter
d[9] = -slw_x / _TAU_SLEW + _SIGMA_SLEW * np.sin(_FREQ_SX * t)
d[10] = -slw_y / _TAU_SLEW + _SIGMA_SLEW * np.sin(_FREQ_SY * t)
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: 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: HEL Thermal Kill with Stochastic Atmosphere (dim=11) (hel-thermal-kill-with-stochastic-atmosphere-dim-11)
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% | 13.1 | 3,551 | 41 ms | 0.930 |
| 2 | SciPy DOP853SciPy | 100% | 11.7 | 2,702 | 31 ms | 0.897 |
| 3 | SciPy RadauSciPy | 100% | 11.4 | 2,658 | 67 ms | 0.890 |
| 4 | SciPy LSODASciPy | 100% | 10.0 | 1,869 | 17 ms | 0.857 |
| 5 | Tsit5external | 100% | 9.9 | 2,418 | 959 ms | 0.856 |
| 6 | SciPy BDFSciPy | 100% | 9.7 | 1,704 | 63 ms | 0.849 |
| 7 | CVODE Adamsexternal | 100% | 9.6 | 745 | 15 ms | 0.848 |
| 8 | SciPy RK45SciPy | 100% | 9.6 | 2,654 | 32 ms | 0.847 |
| 9 | CVODE BDFexternal | 100% | 9.5 | 860 | 17 ms | 0.846 |
| 10 | SciPy RK23SciPy | 100% | 9.4 | 2,453 | 34 ms | 0.843 |
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 →
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SolvSRK · 30-day trial
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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_hel_thermal_kill_with_stochastic_atmosphere_dim_11_2026,
title = {Resonix Evidence Portal: HEL Thermal Kill with Stochastic Atmosphere (dim=11)},
author = {{Resonix Labs (Canada) Inc.}},
year = {2026},
howpublished = {\url{https://resonix.tech/evidence/problems/hel-thermal-kill-with-stochastic-atmosphere-dim-11}},
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