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TPS Thermal Transient 1D (dim=10)

ADVANTAGES2 · dim 10

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 →

10-node 1D finite-difference through a 4-layer TPS stack (ablator/insulation/adhesive/structure). Gaussian heating pulse (peak 5 MW/m^2 at t=100s) with radiative surface cooling. Harmonic-mean conductivities at interfaces. Insulated back face. Stiff from k/rho*Cp ratios spanning 3 orders of magnitude across layer boundaries.

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Problem definition

MIL-HDBK-5; NASA TPS Design Handbook (2003); Duffa, Ablative Thermal Protection Systems Modeling (2013)

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 tps_thermal_transient_rhs(t, y):
    T = np.maximum(y, 200.0)

    dy = np.empty(_N_NODES)

    # Surface node (i=0): prescribed Gaussian heat flux minus radiation
    dt_peak = t - _T_PEAK
    q_in = _Q_PEAK * np.exp(-(dt_peak * dt_peak) / (_SIGMA_T * _SIGMA_T))
    q_rad = _TPS_EPSILON * _SIGMA_SB * T[0]**4
    q_net = q_in - q_rad

    # Surface: half-cell energy balance
    # Flux from heating on left, conduction to interior on right
    q_cond_right = _K_HALF[0] * (T[1] - T[0]) * _DX2_INV
    dy[0] = (q_net / (_DX * 0.5) + q_cond_right) / _NODE_RHOC[0]

    # Interior nodes
    for i in range(1, _N_NODES - 1):
        flux_left = _K_HALF[i - 1] * (T[i - 1] - T[i])
        flux_right = _K_HALF[i] * (T[i + 1] - T[i])
        dy[i] = (flux_left + flux_right) * _DX2_INV / _NODE_RHOC[i]

    # Back face (i=N-1): insulated (zero flux on right)
    flux_left = _K_HALF[_N_NODES - 2] * (T[_N_NODES - 2] - T[_N_NODES - 1])
    dy[_N_NODES - 1] = flux_left * _DX2_INV / _NODE_RHOC[_N_NODES - 1]

    return dy

Parameters: _DX = 0.00422222222222
_DX2_INV = 56094.1828255
_K_HALF = [2, 0.190476190476, 0.1, 0.166666666667, 0.975609756098, 20, 20, 20, 20]
_NODE_RHOC = [1.8e+06, 1.8e+06, 160000, 160000, 1.44e+06, 1.35e+06, 1.35e+06, 1.35e+06, 1.35e+06, 1.35e+06]
_N_NODES = 10
_Q_PEAK = 5e+06
_SIGMA_SB = 5.67037e-08
_SIGMA_T = 80
_TPS_EPSILON = 0.85
_T_PEAK = 100
Initial condition: y(0) = [300, 300, 300, 300, 300, 300, 300, 300, 300, 300]
Horizon: t ∈ [0, 1200]

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: TPS Thermal Transient 1D (dim=10) (tps-thermal-transient-1d-dim-10)

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

#	Solver	Survival	SCD	nfev	Wall	Score
1	SolvSRK	100%	10.7	1,851	33 ms	0.873
2	SciPy RadauSciPy	100%	10.5	3,148	51 ms	0.868
3	Tsit5external	100%	8.6	8,094	1.27 s	0.823
4	SciPy DOP853SciPy	100%	8.3	7,298	57 ms	0.816
5	SciPy RK45SciPy	100%	8.3	8,030	70 ms	0.815
6	SciPy RK23SciPy	100%	7.5	5,969	58 ms	0.798
7	CVODE Adamsexternal	100%	7.5	1,231	23 ms	0.796
8	CVODE BDFexternal	100%	7.4	577	16 ms	0.794
9	SciPy BDFSciPy	100%	7.3	1,237	28 ms	0.792
10	SciPy LSODASciPy	100%	7.3	1,900	13 ms	0.792

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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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_tps_thermal_transient_1d_dim_10_2026,
  title        = {Resonix Evidence Portal: TPS Thermal Transient 1D (dim=10)},
  author       = {{Resonix Labs (Canada) Inc.}},
  year         = {2026},
  howpublished = {\url{https://resonix.tech/evidence/problems/tps-thermal-transient-1d-dim-10}},
  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