Lennard-Jones 38 clusters with Gaussian force noise

SystemLennard-Jones

Atoms38

Runs1000

Cap10000 force calls

The main metric is Force calls. Scoring rules.

Charts

Success rate on Lennard-Jones 38 clusters with Gaussian force noise, in rank order. The rate is the share of runs that finished. 0 ranked rows did not record a success rate and are not drawn. PDF.

$Dolan-Moré profile for Minimizers on Lennard-Jones 38 clusters with Gaussian force noise. The curve is the fraction of starts whose cost is at most tau times the best finite cost in this family. Tau is 1, 2, 4, 8, and 16. An unsolved start stays in the denominator and does not cross a finite tau. Dolan, E. D. and Moré, J. J., Math. Program. 91:201-213, 2002. Colored lines are the six largest areas. The other curves are gray.$

Dolan-Moré profile for Minimizers on Lennard-Jones 38 clusters with Gaussian force noise. The curve is the fraction of starts whose cost is at most tau times the best finite cost in this family. Tau is 1, 2, 4, 8, and 16. An unsolved start stays in the denominator and does not cross a finite tau. Dolan, E. D. and Moré, J. J., Math. Program. 91:201-213, 2002. Colored lines are the six largest areas. The other curves are gray. PDF.

Force calls on each recorded start for Lennard-Jones 38 clusters with Gaussian force noise. The box is the quartiles of those counts. A blue point is a success and a vermillion cross is a recorded failure (1758). The horizontal position is the recorded count. The vertical offset only keeps marks from covering one another. PDF.

Performance profile. Higher means more starts solved within that cost ratio. Colored lines are the six largest areas. Thin lines are the other 19.

rgmin (0.4.1) · NEWTON
rgmin (0.4.1) · DOGLEG
rgmin (0.4.1) · LBFGS
DL-FIND (0.0.3) · L-BFGS
Eon svn (r2549) · LBFGS
GMIN (df8da5992675) · LBFGS

Cost distribution of 25 ranked rows. Logarithmic bins, from 81.881 to 19975.4.

Performance profile SVG Cost and success SVG

Performance profile. Select the plot for the full SVG.

Cost and success for Lennard-Jones 38 clusters with Gaussian force noise — Cost and success. Select the plot for the full SVG.

A shorter bar is a lower cost on a log scale shared by the codes of this problem.

Leaderboard

A shorter bar is a lower cost on the log scale for that problem. Select a column heading to sort.
Rank	Code	Best	Median	Success	PAR-2
1	rgmin	81.881	197.228	100.0%	81.881
2	DL-FIND	231.908	2747.86	99.8%	231.908
3	pele	268.036	1098.85	99.9%	268.036
4	Eon svn	300.052	300.052	99.5%	300.052
5	GMIN	301.399	301.399	99.7%	301.399
6	ASE	396.55	555.614	99.4%	396.55
7	vc-SQNM	598.05	598.05	98.9%	598.05
8	Sella	729.433	729.433	99.9%	729.433
9	LAMMPS	1123.81	3138.21	99.7%	1123.81

The tables below list every ranked row, by method family and overall.

A run short of the full set, or a run that is not the stock method, stays off the ranked table.

Minimizers

Minimizers. One row is one code, one version, and one method. A lower cost is better. PAR-2 counts a finished run as the calls it used and a failed run as twice the cap. An archived row shows the average it published, and its PAR-2 applies that rule to the failures the entry records. Hessians is the mean analytic Hessian count. FD calls is that count times one force call per coordinate.
Rank	Row	Cost	Unit	Hessians	FD calls	Runs
1	rgmin (0.4.1) · DOGLEG	81.881	force calls	80.881	9220.43	1000
2	rgmin (0.4.1) · NEWTON	166.337	force calls	65.649	7483.99	1000
3	rgmin (0.4.1) · LBFGS	197.228	force calls	0	0	1000
4	DL-FIND (0.0.3) · L-BFGS	231.908	force calls	0	0	1000
5	pele (0.1.2) · MYLBFGS	268.036	force calls	0	0	1000
6	pele (0.1.2) · LBFGS	288.145	force calls	0	0	1000
7	Eon svn (r2549) · LBFGS	300.052	force calls	0	0	1000
8	GMIN (df8da5992675) · LBFGS	301.399	force calls	0	0	1000
9	ASE (3.29.0) · LBFGS	396.55	force calls	0	0	1000
10	ASE (3.29.0) · BFGS	555.614	force calls	0	0	1000
11	vc-SQNM (1.3) · ASE-SQNM	598.05	force calls	0	0	1000
12	vc-SQNM (1.3) · SQNM	598.05	force calls	0	0	1000
13	rgmin (0.4.1) · CG	669.237	force calls	0	0	1000
14	Sella (2.6.0) · Sella	729.433	force calls	0	0	1000
15	rgmin (0.4.1) · FIRE	769.36	force calls	0	0	1000
16	ASE (3.29.0) · FIRE	802.384	force calls	0	0	1000
17	LAMMPS (30 Sep 2026) · Hessian-free truncated Newton	1123.81	force calls	0	0	1000
18	pele (0.1.2) · FIRE	1909.56	force calls	0	0	1000
19	LAMMPS (30 Sep 2026) · conjugate gradient	2046.69	force calls	0	0	1000
20	DL-FIND (0.0.3) · conjugate gradient	2747.86	force calls	0	0	1000
21	DL-FIND (0.0.3) · steepest descent	2798.89	force calls	0	0	1000
22	LAMMPS (30 Sep 2026) · Quickmin	3138.21	force calls	0	0	1000
23	LAMMPS (30 Sep 2026) · FIRE	5802.74	force calls	0	0	1000
24	LAMMPS (30 Sep 2026) · steepest descent	10074.7	force calls	0	0	1000
25	pele (0.1.2) · steepest descent	19975.4	force calls	0	0	1000

Overall

One row is one code, one version, and one method. A lower cost is better. PAR-2 counts a finished run as the calls it used and a failed run as twice the cap. An archived row shows the average it published, and its PAR-2 applies that rule to the failures the entry records. Hessians is the mean analytic Hessian count. FD calls is that count times one force call per coordinate.
Row	Family	Family rank	Unit	PAR-2	Median calls	Mean calls	Hessians	FD calls	Failures	Runs
rgmin (0.4.1) · DOGLEG	Minimizers	1	force calls	81.881	79	81.881	80.881	9220.43	crash 0, divergence 0, cap 0, wrong_stationary 0	1000
rgmin (0.4.1) · NEWTON	Minimizers	2	force calls	166.337	64	66.649	65.649	7483.99	crash 0, divergence 0, cap 0, wrong_stationary 5	1000
rgmin (0.4.1) · LBFGS	Minimizers	3	force calls	197.228	170	177.367	0	0	crash 0, divergence 0, cap 0, wrong_stationary 1	1000
DL-FIND (0.0.3) · L-BFGS	Minimizers	4	force calls	231.908	184	202.105	0	0	crash 0, divergence 0, cap 1, wrong_stationary 1	1000
pele (0.1.2) · MYLBFGS	Minimizers	5	force calls	268.036	235	248.224	0	0	crash 0, divergence 0, cap 0, wrong_stationary 1	1000
pele (0.1.2) · LBFGS	Minimizers	6	force calls	288.145	235	248.601	0	0	crash 0, divergence 0, cap 0, wrong_stationary 2	1000
Eon svn (r2549) · LBFGS	Minimizers	7	force calls	300.052	189	200.9	0	0	crash 0, divergence 0, cap 0, wrong_stationary 5	1000
GMIN (df8da5992675) · LBFGS	Minimizers	8	force calls	301.399	223	242.093	0	0	crash 0, divergence 0, cap 0, wrong_stationary 3	1000
ASE (3.29.0) · LBFGS	Minimizers	9	force calls	396.55	256.5	326.761	0	0	crash 0, divergence 0, cap 5, wrong_stationary 1	1000
ASE (3.29.0) · BFGS	Minimizers	10	force calls	555.614	417	496.044	0	0	crash 0, divergence 0, cap 4, wrong_stationary 1	1000
vc-SQNM (1.3) · ASE-SQNM	Minimizers	11	force calls	598.05	365.5	382.068	0	0	crash 0, divergence 0, cap 0, wrong_stationary 11	1000
vc-SQNM (1.3) · SQNM	Minimizers	12	force calls	598.05	365.5	382.068	0	0	crash 0, divergence 0, cap 0, wrong_stationary 11	1000
rgmin (0.4.1) · CG	Minimizers	13	force calls	669.237	538	591.346	0	0	crash 0, divergence 0, cap 0, wrong_stationary 4	1000
Sella (2.6.0) · Sella	Minimizers	14	force calls	729.433	691.5	710.211	0	0	crash 0, divergence 0, cap 0, wrong_stationary 1	1000
rgmin (0.4.1) · FIRE	Minimizers	15	force calls	769.36	625.5	711.609	0	0	crash 0, divergence 0, cap 0, wrong_stationary 3	1000
ASE (3.29.0) · FIRE	Minimizers	16	force calls	802.384	604	706.021	0	0	crash 0, divergence 0, cap 0, wrong_stationary 5	1000
LAMMPS (30 Sep 2026) · Hessian-free truncated Newton	Minimizers	17	force calls	1123.81	974	1066.61	0	0	crash 0, divergence 0, cap 0, wrong_stationary 3	1000
pele (0.1.2) · FIRE	Minimizers	18	force calls	1909.56	614.5	776.029	0	0	crash 0, divergence 16, cap 0, wrong_stationary 43	1000
LAMMPS (30 Sep 2026) · conjugate gradient	Minimizers	19	force calls	2046.69	1776.5	1993.39	0	0	crash 0, divergence 3, cap 0, wrong_stationary 0	1000
DL-FIND (0.0.3) · conjugate gradient	Minimizers	20	force calls	2747.86	1711.5	1941.79	0	0	crash 0, divergence 0, cap 0, wrong_stationary 44	1000
DL-FIND (0.0.3) · steepest descent	Minimizers	21	force calls	2798.89	2371.5	2752.2	0	0	crash 0, divergence 0, cap 3, wrong_stationary 1	1000
LAMMPS (30 Sep 2026) · Quickmin	Minimizers	22	force calls	3138.21	2545	3020.94	0	0	crash 0, divergence 5, cap 0, wrong_stationary 4	1000
LAMMPS (30 Sep 2026) · FIRE	Minimizers	23	force calls	5802.74	411.5	417.719	0	0	crash 0, divergence 224, cap 0, wrong_stationary 47	1000
LAMMPS (30 Sep 2026) · steepest descent	Minimizers	24	force calls	10074.7	6420.5	6693.33	0	0	crash 0, divergence 0, cap 227, wrong_stationary 75	1000
pele (0.1.2) · steepest descent	Minimizers	25	force calls	19975.4	10000	9923.97	0	0	crash 0, divergence 5, cap 980, wrong_stationary 13	1000

Success on this problem: harness force calls under the cap, the noisy force at the noise-aware stop, and when sigma is positive a clean-energy window whose span is at most max(energy_tol, kappa * sigma).

The Hessian is the clean force.

The index is vibrational: the six rigid modes are removed, and a curvature is negative only below -max(force_norm, 1e-8*||H||_F, 1e-6), with that force_norm the noise-aware stop.

Energy and Kabsch RMSD are not applied: this file has no per-start reference.