Benchmarks

Timing tables of the d-SEAMS 2.0 paper and its supplement. Each table names its record, a directory or file under results/reference/ of dseams2_repro. The values below are those of seams-core v2.12.0, the release the paper describes. A rerun at a later release adds its own table under the same heading and names its record, so the paper’s values stay readable next to the current ones. Reproduce gives the commands, and Versions gives the machines and the codes.

Records

record	processor	allocation	engine	read by
elja-1788072	2 x Xeon Platinum 8358	exclusive 64cpu_256mem, load 0.95	v2.6.0 sources	neighbour-list and ring scaling, cage stages
paper_manifest-elja-1785712.json	2 x Xeon Platinum 8358	64cpu_256mem, load 4.96	13c95cec	one frame against d-SEAMS 1
elja-1798666	2 x AMD EPYC 7713	exclusive 128cpu_256mem, load 0.24	e7856408	second architecture, \(q_l\) check, walk control
terra-2026-09-01	Ryzen 9 9950X	shared workstation, load 4.32	770accf9	walk and PTM controls
sota-heldout-2026-10-31	Xeon, 8-vCPU cloud VM	labels only, no timing	v2.12.0	lattice-label retention
md-heldout-2026-10-31	Xeon, 8-vCPU cloud VM	labels only, no timing	v2.12.0	held-out mW trajectories
h2h-2026-10-31	Xeon, 8-vCPU cloud VM	pinned core 3, load 0.33	v2.12.0	head-to-head table
bench-2026-10-31	Xeon, 8-vCPU cloud VM	pinned core 3 and cores 0-7, load 0.20	v2.12.0	cage drivers, incremental and churn timings
cli-carry-2026-10-31	Xeon, 8-vCPU cloud VM	pinned core 3	v2.12.0	carried command line
hydrate-inside-2026-10-31	Xeon, 8-vCPU cloud VM	labels only	v2.12.0	ray-parity hydrate occupancy
walks-2026-10-31	Xeon, 8-vCPU cloud VM	labels only	v2.12.0	label walks of the applications
terra-2026-09-02	Ryzen 9 9950X	shared workstation	0a7fc546	OpenMP strong scaling, GenIce atlas and ions, hydrate occupancy
tip-gpu-batch-elja-1787449.txt	2 x A100-PCIE-40GB	gpu-2xA100, load 0.00	not named in the record	device-resident batch
elja-production	2 x Xeon Platinum 8358	exclusive 64cpu_256mem, one job per temperature	v2.9.2 (d1983d53)	seeding and brine campaigns

Every Elja CPU timing record built the d-SEAMS 1 baseline, seams-core commit 1c8efa38, next to the engine commit listed. The GPU job built only the engine. Load is the one-minute load average when the record started, and elja-1788072 gives it before the workflow.

One frame against d-SEAMS 1

The 4096-molecule mW cubic frame has 8192 six-rings. Both versions assign none of them to a hexagonal cage (HC) and every one to a double-diamond cage (DDC). One core, best of five calls per stage, record paper_manifest-elja-1785712.json.

stage	d-SEAMS 1 baseline	d-SEAMS 2.0
ring detection	101 ms	14 ms
HC search	3.6 s	45 ms
HC and DDC searches in one call	3.9 s	48.6 ms
DDC, the combined minimum less the HC minimum	0.30 s	3.5 ms
ring detection plus the combined call	4.0 s	63 ms

The path is 63.6 times faster. The drivers of this record time the HC call and the combined call, which builds its local ring-type and cage vectors inside the timer.

On pinned core 3 of the cloud VM, record bench-2026-10-31, the drivers time findDDC alone. The ring types and cages that findHC leaves are computed once and restored outside the timer before each call. Values are medians over three sessions.

stage	d-SEAMS 1 baseline	d-SEAMS 2.0
ring detection	89 ms	3.9 ms
findHC	2.73 s	47.5 ms
findDDC	255 ms	3.06 ms
sum of the three stages	3.0 s	54 ms
combined HC and DDC call		50.3 ms

The sum is 56 times faster. Built with the -O3 -funroll-loops of the engine’s drivers instead of -O2, the baseline drivers time each stage within 1.5% of the -O2 build, and the three cage-driver stages within 0.2%.

Neighbour lists, CHILL+ and rings against system size

Single core of exclusive Elja 64cpu_256mem, record elja-1788072, milliseconds. “base” columns are baseline commit 1c8efa38, the others engine v2.6.0. Cutoff list and index-ordered builder at \(r_c=3.5\) Å; CHILL+ bond correlations (getCorrelPlus) on the cutoff list; primitive rings with \(D=6\) on the index-ordered list. The cells are synthetic cubic cells at the mW number density of 0.0332 Å^-3 with a deterministic jitter.

n	cutoff, base	cutoff	index, base	index	CHILL+, base	CHILL+	rings, base	rings
1000	1.975	1.461	6.794	1.443	3.446	1.404	116.282	8.064
2000	5.650	2.781	22.015	2.738	7.274	2.865	406.376	19.870
4000	17.793	5.305	99.424	5.291	13.915	5.648	576.520	37.208
8000	61.986	11.030	387.840	10.796	27.182	11.401	965.459	78.731
16000	225.734	22.712	1516.346	22.345	59.033	23.363	3626.729	226.554
32000	859.556	43.663	5975.106	42.700	110.161	45.881	4486.953	528.897

From 1000 to 32000 atoms the 2.0 cutoff list grows by a factor of 30, and the baseline list by a factor of 435. At 32000 atoms the index-ordered builder falls from 6.0 s to 43 ms, and the two builders together from 6.8 s to 86 ms.

OpenMP strong scaling

A fixed 65536-molecule cell, every host stage of the pipeline, best of seven runs per thread count, one thread per physical core (OMP_PLACES=cores, OMP_PROC_BIND=close). The machine is the 16-core Ryzen 9 9950X workstation, not reserved for the run, record terra-2026-09-02, engine 0a7fc546 with OpenMP and without vesin.

stage	1 thread	16 threads	speed-up
whole pipeline	906 ms	99 ms	9.1
primitive rings	802 ms	76 ms	10.6
Steinhardt kernel	12.6 ms	4.8 ms
cutoff neighbour list	46 ms	11 ms	4.3
index-ordered neighbour list	45 ms	8 ms	5.8

At sixteen threads the pipeline is 43 ms above the ideal line. The rings account for 26 ms of that and the two neighbour lists for 13 ms.

Second architecture

One core of an AMD EPYC 7713 (Elja 128cpu_256mem, load 0.2 at start), record elja-1798666, engine commit e7856408. The reference column is baseline commit 1c8efa38 in the first six rows, the full rebuild of the same engine in the two incremental rows, and one thread against 32 in the last row. Milliseconds.

stage	reference	2.0	factor
index-ordered neighbours, 32000	8689.6	59.3	147
cell-list neighbours, 32000	862.8	61.0	14
CHILL+, 32000	128.6	66.6	1.9
primitive rings, 32000	5111.5	752.9	6.8
hexagonal-cage search, mW 4096	4926.9	68.7	72
ring-and-cage path, mW 4096	5255.8	93.0	57
incremental rings, steady frame	20.5	1.0	20
incremental affiliation, steady frame	97.3	11.3	8.6
ring construction, 65536 atoms, 1 to 32 threads	1893.9	119.2	16

Incremental updates

Record bench-2026-10-31, pinned core 3 of the cloud VM unless noted. Every updated ring set and every updated cage flag equals the rebuild.

case	update	rebuild
jittered 8000-molecule cell, three perturbed sites per frame, smallest over five frames	4.4 ms	32 ms
mW cubic trajectory, mutual four-nearest graph, frames 2-11 means, rings	0.21 ms	3.7 ms
mW cubic trajectory, mutual four-nearest graph, frames 2-11 means, affiliation	0.25 ms	48.6 ms
nucleation excerpt, cutoff graph, rings, one thread	14.9 ms	14.3 ms
nucleation excerpt, cutoff graph, affiliation, one thread	18.0 ms	17.5 ms
nucleation excerpt, cutoff graph, rings, eight threads (cores 0-7)	3.07 ms	2.65 ms
nucleation excerpt, cutoff graph, affiliation, eight threads (cores 0-7)	4.26 ms	4.18 ms
Niu trajectory 3, cutoff graph, rings, one thread	11.9 ms	11.2 ms
Niu trajectory 3, cutoff graph, affiliation, one thread	11.1 ms	10.3 ms
Niu trajectory 3, cutoff graph, rings, eight threads (cores 0-7)	2.244 ms	2.184 ms
Niu trajectory 3, cutoff graph, affiliation, eight threads (cores 0-7)	2.725 ms	2.622 ms

On the last frame of the 8000-molecule cell the ring update enumerates 794 of the 8000 sources again. The 8000-molecule and mW cubic values are medians over three sessions, and the nucleation and Niu values, frames 2-11 means, come from one session. On frames 2-11 of the nucleation excerpt 2845 bonds change per frame on average, and 1948 on frames 2-11 of Niu trajectory 3 (2880 molecules), so both updaters take the batch pass there.

Churn sweep

tests/bench_churn_sweep.cpp starts from frame 147 of the figshare mW nucleation excerpt (4096 molecules, cutoff graph) and moves the molecules within a radius of the box centre to their frame-148 positions. Median of seven repetitions, one thread, one session.

changed bonds	ring update	ring rebuild	affiliation update	affiliation rebuild
0	0.21 ms		0.26 ms
3	1.52 ms	14.6 ms	8.0 ms	22.5 ms
17	2.70 ms	17.8 ms	11.3 ms	25.2 ms
340	8.1 ms	13.1 to 19.0 ms over the sweep	batch pass

From 57 changed bonds the affiliation update runs the batch pass.

Carried command line

seams cages over a frame range on pinned core 3 of the cloud VM, OMP_NUM_THREADS=1, record cli-carry-2026-10-31. Milliseconds per frame, whole process. The ratio is rebuild over carry, so a value above 1 means the carried walk is faster. The last column is the same ratio for the build without the back-off. The carried and rebuilt JSON outputs are identical byte for byte in every case.

trajectory	graph	frames	rebuild	carried	ratio	no back-off
mW cubic, 4096	seeded	11	127.13	20.60	6.171	6.281
mW cubic, 4096	cutoff	11	48.90	9.10	5.374	5.453
nucleation excerpt, 4096	seeded	148	51.50	51.98	0.991	0.961
nucleation excerpt, 4096	cutoff	148	35.19	34.54	1.019	0.954
Niu trajectory 3, 2880	seeded	148	32.51	32.94	0.987	0.961
Niu trajectory 3, 2880	cutoff	148	20.13	20.54	0.980	0.958

These values are medians over three alternating sessions of the record’s run.sh. The record itself runs five.

Comparison with other codes

Single-core timings in milliseconds on the same frames, record h2h-2026-10-31. Outside the R.I.N.G.S. rows each entry times the analysis call with the frame in memory, as the best of seven runs after one warm-up, and each timer holds the neighbour search of its code. The R.I.N.G.S. rows time one whole process on each side, input included, and their d-SEAMS side is seams fingerprint, which also finds the seven-rings, so the rings of size six and below are compared. The mW R.I.N.G.S. entry is one timed run after one warm-up. The last row times the completed seeded cage rule against PTM on the 512-molecule jittered lattice at \(\sigma=0.3\) Å, generator seed 5; PTM has no d-SEAMS counterpart, so that row is not the same computation.

computation	frame	other code	d-SEAMS 2.0	other	agreement
CHILL+ labels	mW cubic, 4096	OVITO	6.09	22.7	4096 of 4096
CHILL+ labels	Niu final frame, 2880	OVITO	5.28	21.3	2610 of 2880
\(q_6\), \(\bar q_6\), four nearest	mW cubic, 4096	freud	3.50	31.9	2.2e-7
\(q_6\), \(\bar q_6\), four nearest	Niu final frame, 2880	freud	2.58	26.4	0.32; 3.0e-5 on one graph
primitive rings, \(D=6\), whole workflow	mW cubic, 4096	R.I.N.G.S.	31.0	2070379	same census, 8192 rings
primitive rings, \(D=6\), whole workflow	CRN1, 1000	R.I.N.G.S.	13.5	137797	same census, 1238 rings
shortcut-free rings, \(D=6\)	mW cubic, 4096	GenIce2	6.44	10666	same 8192 rings
shortcut-free rings, \(D=6\)	CRN1, 1000	GenIce2	2.64	1773	same 1238 rings
5^12 and 5^12 6^2 cages	sI, 368	GenIce2	28.1	436	16 and 48 in both
Ic/Ih labels	jittered Ic, 512	OVITO PTM	15.6	16.4	512 and 502 Ic

The frames are the 4096-molecule mW cubic frame, the final frame of the 2880-water Niu dump, the 1000-molecule continuous random network CRN1 and the 2 x 2 x 2 GenIce sI framework of 368 waters. Every code gets the same oxygen coordinates and orthorhombic cell, and every library runs on one thread.

OVITO CHILL+ and the d-SEAMS CHILL+:math:(r_c) both run at \(r_c=3.5\) Å. d-SEAMS clathrate, interfacial clathrate and water match OVITO hydrate, interfacial hydrate and other. The CHILL+ labels agree on every mW molecule and differ at 270 Niu molecules, 109 of which d-SEAMS labels interfacial clathrate and OVITO other. freud’s timer holds two neighbour searches, since the plain and averaged parameters are two objects, and freud stores coordinates in single precision. d-SEAMS evaluates \(q_6\) on the mutual four-nearest graph and freud on the four nearest neighbours; the two graphs differ at 175 of the 2880 Niu molecules. Given freud’s neighbour rows, the engine returns freud’s values to 3.0e-5. R.I.N.G.S. puts 97% of each run in the distance matrix of the 5 x 5 x 5 superlattice it builds for a periodic cell.

The calls on each side are these.

• d-SEAMS CHILL+:math:(r_c): neighListO, getCorrelPlus and getIceTypePlusNoPrint through PydSEAMSlib on the 3.5 Å cutoff list

• d-SEAMS \(q_6\) and \(\bar q_6\): kNearestNeighbourList and steinhardtQl

• d-SEAMS rings: neighListO, neighbourListByIndex and ringNetwork, with findBySignature added for the sI cages

• d-SEAMS against PTM: the completed seeded rule of scripts/sota_compare.py

• d-SEAMS against R.I.N.G.S.: seams fingerprint crn.lammpstrj --cutoff 3.5 --type 1

• OVITO CHILL+: ChillPlusModifier(cutoff=3.5) on a DataCollection

• OVITO PTM: PolyhedralTemplateMatchingModifier

• freud: freud.order.Steinhardt(l=6) with average=False and with average=True, each over four nearest neighbours

• GenIce2 rings: pairlist.pairs_iter at 3.5 Å into a networkx graph, then cycles_iter(graph, 6, pos) of cycless.cycles

• GenIce2 cages: those rings, then polyhedra_iter(rings, 14) of cycless.polyhed, keeping the cages of 12 and 14 five- and six-rings, as the genice2-cage formatter does

• R.I.N.G.S.: rings input on the same coordinates with one species, periodic boundaries, primitive rings only, search depth 3 (rings of up to six members) and the O-O bond at 3.5 Å

The genice2-cage formatter run from the command line first replicates the sI unit cell and builds a hydrogen-bond graph, so the record runs it once, untimed, and it returns the same 16 and 48 cages.

Steinhardt parameters across codes

The rules ql_compare_dseams and ql_compare_python evaluate Steinhardt \(q_4\), \(q_6\) and \(q_8\) with the engine, freud and pyscal3 on an ideal fcc cell (108 atoms in a 12 Å box, cutoff 3.2 Å) and an ideal bcc cell (54 atoms, same box, cutoff 4.0 Å). Record elja-1798666, files ql-dseams.txt and ql-python.txt.

cell	\(q_4\)	\(q_6\)	\(q_8\)
fcc	0.190941	0.574524	0.403915
bcc	0.509175	0.628539	0.212762

The three codes print the same six decimals.

Device-resident batch

One process of bench_gpu_batch under nsys on the eleven stored frames of the 4096-molecule mW cubic dump, one NVIDIA A100-PCIE-40GB of an Elja gpu-2xA100 node, CUDA 12.2, record tip-gpu-batch-elja-1787449.txt.

quantity	value
working set of one frame \(W\)	2867712 bytes
frames that fit, \(\lfloor A/W\rfloor\)	11672
cold call, compute, NVRTC compile included	6394 ms
best of five warm calls, compute, eleven frames	21.986 ms
upload	0.120 ms
download	0.176 ms
molecules labelled Ic	45056 of 45056
six-rings	90112
kernel time in the \(k\)-nearest walk	69.9%
kernel time in primitive hexagons	17.9%
kernel time in basal emission	7.2%