Asynchronous, Generation-Free ABC: Streaming AMIS Reweighting for Heterogeneous Simulator Workloads on HPC

Julian Herold; Markus Götz; Alexander Schug

stat.COOct 21, 2026

Asynchronous, Generation-Free ABC: Streaming AMIS Reweighting for Heterogeneous Simulator Workloads on HPC

Authors: Julian Herold, Markus Götz, Alexander Schug

Organizations: Scientific Computing Center, Karlsruhe Institute of Technology, Karlsruhe, Germany

Abstract

Approximate Bayesian computation (ABC) enables Bayesian inference for models with intractable likelihoods by estimating parameter posterior distributions from simulated data. Sequential ABC methods improve sampling efficiency by iteratively adapting the proposal distribution toward regions of high posterior probability. However, these methods typically operate in generations, where each generation must wait for its slowest simulation before the next can begin. On a parallel machine, this synchronization barrier leaves workers idle and reduces throughput, particularly when simulation runtimes vary substantially. We introduce a generation-free ABC sampler that updates its proposal when simulation results arrive and sends a new candidate to each available worker. The proposal is based on the best particles evaluated so far. To estimate the posterior, we reuse the full history and reweight particles against a reconstructed mixture of sampling proposals. We show how errors in approximating the mixture of sampling proposals affect the estimated posterior and establish consistency for the smooth-ABC posterior when the approximation becomes asymptotically exact. In our experiments, the method achieves well-calibrated posterior estimates where a pyABC baseline with the same kernel and bandwidth schedule under-covers. From the asynchronous run's timing alone, we predict how much a synchronization barrier would slow the sampler. These predictions agree with measured synchronization penalties ranging from 1.2x to 400x. On a Cellular Potts tissue simulator, the asynchronous sampler completes 2.1-2.4x as many evaluations as pyABC in the same hour, and the discrepancy threshold for its best 100 evaluations is 4.1x smaller. With the starting bandwidth set from prior-predictive discrepancies, it also produces a more concentrated two-parameter posterior with a larger effective sample size than pyABC.

Figures & tables

Figure 1: One generation of ABC-PMC (a) beside one update of our sampler (b), step by step on a two-dimensional toy problem. ABC-PMC proposes a whole population from one mixture, simulates all of it, keeps the accepted particles and only then forms the next proposal, so a generation ends with its slowest simulation. Our sampler appends every completed evaluation to a history and rebuilds the archive, bandwidth and proposal from that history at every call. It draws one candidate for the free worker and weights that candidate against the current and stored proposals rather than against a single proposal. Row (a) is a schematic of textbook hard-threshold PMC, not the smooth-kernel pyABC baseline of § 5.2 . Appendix C explains the symbols used in the figure.

Benchmark	$d$	cost/sim	runtime spread	budget, workers	role
Gaussian mean	1	$0.1$ ms	injected: straggler $0$ – $20\times$ ; lognormal $\sigma\leq 2$	$300$ s, $48$ ( $16$ in the straggler study)	calibration; barrier cost under a known runtime distribution; the near-instantaneous end of the cost boundary
g-and-k	4	$2$ ms	none	$600$ s, $48$	4-D calibration and recovery against a reference posterior
Lotka–Volterra	4	$4$ ms	trajectory-dependent; $98\%$ extinct	$600$ s, $48$ ; scaling to $288$	strong scaling; the cost boundary
Cellular Potts $50^{3}$	2	$13$ s	CV $0.05$	$3600$ s, $48$ ; scaling to $384$	posterior recovery against a known truth; barrier cost on a real simulator
Cellular Potts $80^{3}$	2	$170$ s	CV $0.13$ – $0.23$	$3600$ s, $48$	barrier cost at realistic cost and heterogeneity

Table 1: Benchmark suite. Cost is the mean wall-clock time of one simulation in the asynchronous runs (an evaluation on Cellular Potts is four replicate simulations); runtime spread is the in-run coefficient of variation of that time, or how it is injected. Budgets are per replicate; five replicates throughout except three at

80^{3}

Figure 2: The barrier’s cost predicted from the asynchronous run’s timing alone (§ 5.3 ) against the cost measured with the synchronized variant, on every configuration the synchronized variant was run on: a persistent straggler at five slowdowns, lognormal runtime heterogeneity at five spreads, and Cellular Potts at

50^{3}

(

48

–

384

workers, earlier parameterization, utilization ratio) and

80^{3}

(

48

workers, against pyABC). Points show replicate medians and ranges. The dashed line indicates equal predicted and measured costs; open markers identify the three configurations outside the predictor’s domain.

Figure 3: Strong scaling at a fixed wall-clock budget against pyABC with population

\max(100,W)

. Left: Lotka–Volterra (

4

ms;

180

s; medians and inter-quartile ranges over five replicates). Right: Cellular Potts

50^{3}

(earlier parameterization,

5.1

1800

s; log–log), with linear scaling dotted.

Benchmark	cost/sim	sims (async / sync)	throughput	per-simulation	equal wall clock
Gaussian mean	$0.1$ ms	$1.31$ M / $4.61$ M	$0.28\times$	$0.78\times$ ( $0.77$ – $1.12$ )	$0.24\times$ ( $0.21$ – $0.28$ )
g-and-k	$2$ ms	$1.75$ M / $3.81$ M	$0.46\times$	$1.06\times$ ( $1.02$ – $1.15$ )	$0.88\times$ ( $0.85$ – $0.92$ )
Lotka–Volterra	$4$ ms	$1.51$ M / $1.56$ M	$0.96\times$	$1.30\times$ ( $1.08$ – $1.51$ )	$1.30\times$ ( $1.02$ – $1.43$ )
Cellular Potts	$13$ s	$12{,}900$ / $5{,}400$	$2.39\times$	$1.6\times$ ( $1.14$ – $1.94$ )	$4.09\times$ ( $3.1$ – $6.6$ )

Table 2: Tolerance at a matched budget on every benchmark (

k=100

order statistic of each method’s own discrepancies; five replicates; medians, with the replicate range of each ratio in parentheses; completed simulations only). Per-simulation:

\epsilon

of pyABC over the asynchronous sampler at pyABC’s own simulation count; equal wall clock: the same ratio at the end of both runs. Bold marks the larger simulation count.

Figure 4: Throughput ratio and per-simulation efficiency of the asynchronous sampler over pyABC against the cost of one simulation, one point per benchmark (Table 2 ).

Target	Method	0.50	0.80	0.90	0.95
Gaussian mean (1-D)	asynchronous	0.51	0.80	0.90	0.94
	pyABC	0.35	0.63	0.75	0.83
Bimodal $\mathcal{N}(\theta^{2},\sigma^{2})$ (1-D)	asynchronous	0.50	0.82	0.91	0.96
	pyABC	0.45	0.82	0.90	0.95
g-and-k (4-D), $A$	asynchronous, full history	0.62	0.91	0.96	0.99
	pyABC	0.54	0.82	0.91	0.95

Table 3: Simulation-based calibration of the posterior estimate (

1000

trials; empirical coverage of central intervals at the nominal levels; Monte Carlo standard error

{\pm}0.007

–

0.016

). Nominal is best, and bold marks the method closer to it.

Figure 5: Each method’s own posterior (§ 5.3 ) scored against the analytic posterior (a) and the g-and-k reference posterior (b) over wall-clock prefixes. The upper panels show median

W_{1}

and interquartile ranges over five replicates. The lower panels show posterior effective sample size; dotted lines indicate the number of evaluated particles.

Figure 6: Cellular Potts posterior (division rate, cell volume) on the fixed production run, replicate

0

: the asynchronous AMIS estimator over the full history, pyABC’s last completed generation with its population weights, and the

100

best rejection draws, each drawn as a weighted kernel density estimate of the method’s own particles (effective sample sizes in the legend) (Table 4 ). Axes are the log-uniform prior coordinates ticked in physical units; the joint panel outlines each method’s

90\%

highest-density region, and dashed lines mark the truth.

				contraction
	sims	util.	$\epsilon_{(100)}$ , end	division rate	cell volume	ESS
Asynchronous, $\epsilon_{0}=10$	13,300	99.8%	$6.3\times 10^{-5}$	$84\pm 6\%$	$13\pm 14\%$	645
Asynchronous, $\epsilon_{0}=0.1$	12,900	99.8%	$7.6\times 10^{-5}$	$92\pm 1\%$	$81\pm 1\%$	303
pyABC, $\epsilon_{0}=0.1$	5,400	42.8%	$3.1\times 10^{-4}$	$91\pm 1\%$	$72\pm 4\%$	66
Rejection ABC, best $100$ of $13{,}000$	13,000	—	$2.9\times 10^{-3}$	$91\%$	$67\%$	100

Table 4: Cellular Potts

50^{3}

, five replicates per adaptive method and one rejection run,

3600

s on

48

workers (means

{\pm}

standard deviation for contraction, medians otherwise). The first row is the asynchronous sampler at the benchmark’s original starting bandwidth (

10

, twenty times the prior-predictive median discrepancy), the rest at the production value (

0.1

). Rejection ABC is one run of

13{,}000

prior draws on all

48

workers, keeping the best

100

. Contraction is

1-\mathrm{sd}/\mathrm{sd}_{\mathrm{prior}}

; the truth lies inside the central

90\%

interval of every run. Bold marks the best value per column.

Appendix figures & tables17 assets

Supplementary material from the paper’s appendix.

Appendix

Assumption	Status	Basis
1 kernel, Lipschitz part	by construction	Gaussian and Epanechnikov are peak-normalized and Lipschitz in $\epsilon$ on every $[a,\epsilon_{0}]$ , with $L_{K}(a)=2/ea$ and $2/a$ . The hard indicator is not, and is excluded from the theory.
1 $Z_{\epsilon_{\infty}}>0$	holds for Gaussian	The Gaussian kernel is strictly positive, so $L_{\epsilon_{\infty}}>0$ and the limiting target is non-degenerate whatever the discrepancy distribution. For a compactly supported kernel (Epanechnikov) it requires the achievable discrepancies to reach inside the support, which we do not verify.
2 denominator class	by construction	The prior support is a box and the archive lies in it, so component means do; the covariance carries an additive jitter $10^{-9}\mathrm{tr}(\widehat{\Sigma})/d+10^{-12}\bar{b}^{2}$ ( $\bar{b}^{2}$ the mean squared box width), whose second term is a run-independent floor, giving $\sigma_{-}^{2}>0$ , and $\sigma_{+}^{2}$ follows from the archive lying in a bounded box. The truncation normalizer is the product of per-axis in-box masses, so with a correlated covariance $\bar{q}_{n}$ does not integrate to one. Assumption 2 does not require that: it constrains a positive function, and the discrepancy is carried by $r$ instead (§ A.1 (c)).
4 execution model	holds; implementation property	(B1), (B2): the propagator draws from its own stream, seeded once per rank, and every simulator call receives a fresh seed derived from the run seed, the rank and a per-rank call counter, so the two streams are independent in the sense in which pseudo-random streams are, and no two calls share a seed. (B3): a worker proposes when its own simulation completes and builds the proposal from the results that have reached it; delivery is asynchronous message passing, exogenous to both streams. Lemma 5 then gives the adapted filtration with $\tilde{q}_{i}$ the emitted density. What asynchrony leaves in $r$ is the arrival-order reconstruction of the snapshots, a boundary of at most $W$ particles per snapshot (§ A.1 (d)).
3 prior floor	by construction	The retroactive denominator floors the prior component’s mass at $\delta=0.5/(m{+}1)$ (Appendix C ), so $\bar{q}_{n}\geq\delta\pi$ and Lemma 6 bounds every posterior weight by $1/\delta$ , independently of what the sampler does.
5 fidelity ( 9 )	assumed; two of its four factors measured	The one place the sampler enters for Corollary 2 ; Theorem 1 does not use it. Decomposed into four factors in § A.1 , two of them estimated from stored histories rather than bounded; since the factors multiply, the measured part is a partial accounting rather than a bound on the whole.

Appendix

Table 5: What the implementation guarantees, what it assumes, and what it violates. “By construction” means the code enforces the property for every run, not that it was checked post hoc.

Property	Classical ABC-SMC	This work
Update style	generation, barrier-synchronized	event-driven (single-arrival), no barrier
Archive	explicit, generational	reconstructed, sliding top- $k$
ABC likelihood	hard threshold	smooth kernel
Importance weight	against $q_{t-1}$ only	balance heuristic over $\mathcal{S}$
Archive state	mutable, carried	none; reconstructed per call
Posterior estimate	final population	pure function of the history

Appendix

Table 6: A typical generation-staged ABC-SMC/PMC implementation (the pyABC baseline used here) versus the proposed generation-free method. The listed properties characterize pyABC as configured, not ABC-SMC as a family. The running sampler does carry the online snapshot buffer of § 3.5 ; the posterior estimate rebuilds it from the history.

Symbol	Meaning	Option	Value
$k$	archive size	k	$100$ ( $200$ in the four-dimensional calibration runs)
$\epsilon_{0}$	starting bandwidth	tol_init	$5$ (Gaussian mean), $10$ (g-and-k), $5\times 10^{5}$ (Lotka–Volterra), $0.1$ (Cellular Potts; $10$ in its earlier parameterization)
$K_{\epsilon}$	ABC kernel	kernel	Gaussian
$s$	scale of the perturbation covariance $\Sigma_{n}$	perturbation_scale	$0.8$
$S$	kept snapshots	amis_snapshots	$20$
	snapshot cadence, in calls	amis_interval	$k$

Appendix

Table 7: Settings of the asynchronous sampler. Option names are those of the implementation; values are those of the production experiments, except where a study sweeps them (Appendix F ).

Experiment	Workers	Budget (s)	Reps	$k$	Methods
Gaussian mean	48	300	5	100	A,S,R
g-and-k	48	600	5	100	A,S,R
Lotka–Volterra	48	600	5	100	A,S
Cellular Potts $50^{3}$	48	3600	5	100	A,S,R
Cellular Potts $80^{3}$	48	3600	3	100	A,S,R
Straggler	16	300	5	100	A,S

Appendix

Table 8: Resolved experiment configurations. Workers, per-run wall-clock budget, replicates (trials for SBC), archive size

k

, and methods (A: asynchronous; S: pyABC (matched kernel); R: rejection ABC; T: synchronized variant). The synchronized variant row covers the straggler, heterogeneity and Cellular Potts

50^{3}

studies at

16

48

and

48

–

384

workers. † Simulation-limited: the budget is per-trial (SBC) or per-run (kill-and-resume) simulations , not wall-clock seconds; the synchronized variant, and the asynchronous re-run matched to it, stop at a fixed simulation count per level (§ 5.2 , Table 9 ). ‡ Also run with AMIS on/off, a drain-after-deadline variant, and a steeper coupling regime (base delay

0.5

s, cap

8

s). § The Cellular Potts rows of these studies ran the benchmark’s earlier configuration (Appendix E ).

Figure 7: Inference per unit wall clock under runtime heterogeneity (Gaussian mean, analytic posterior,

48

workers,

60

s budget, five replicates; bands are inter-quartile ranges). Left: error of the archive mean (the unweighted top-

k

archive, not

\widehat{\pi}_{n}

; § 6.4 ) to the analytic posterior mean, against the runtime spread

\sigma

. Right: simulations completed within the budget. The barrier starves pyABC as

\sigma

grows; the asynchronous sampler’s error stays flat.

Straggler slowdown	$0\times$	$1\times$	$5\times$	$10\times$	$20\times$
Asynchronous, sims/s	3888	3112	3241	3218	3205
Synchronized variant, barrier every $W$	48.7	65.3	31.6	15.9	8.0
Synchronized variant, barrier every $112$	162.8	148.4	31.8	15.9	8.0
Synchronized variant, predicted	(3870)	(154)	31.8	15.9	7.98
Ratio, measured (every $W$ )	$80\times$	$48\times$	$103\times$	$202\times$	$402\times$
Ratio, predicted	—	—	$102\times$	$202\times$	$401\times$

Appendix

Table 9: Synchronized variant on the straggler benchmark (

W=16

, five replicates, medians). Throughput in simulations per second; predicted as in § 5.3 , and at

0\times

and

1\times

the collective’s latency, absent from the model, dominates. Lower block:

W_{1}

of each sampler’s posterior to the analytic posterior at the synchronized variant’s simulation count and seeds, at the bandwidth its schedule reached and, last row, re-reported at

\epsilon_{(100)}

(§ 6.4 ).

Figure 8: pyABC against the asynchronous sampler under injected runtime heterogeneity on the Gaussian mean (§ 6.1 ). (a) Throughput under a persistent straggler: one of

16

workers carries a permanent post-evaluation delay of

0.1

s scaled by the factor (

300

s; medians and inter-quartile ranges over five replicates; logarithmic axis). (b) Fraction of worker time spent idle under a lognormal runtime multiplier of spread

\sigma

(

48

workers,

60

s).

Heterogeneity $\sigma$	$0$	$0.5$	$1.0$	$1.5$	$2.0$
Asynchronous, sims/s	47.6	42.1	28.9	17.6	11.4
Synchronized variant, barrier every $W$	44.8	15.1	4.37	1.06	0.37
Synchronized variant, barrier every $96$	45.1	19.8	6.50	1.75	0.45
pyABC	23.1	18.9	9.91	4.35	2.39
Ratio, measured (every $W$ )	$1.06\times$	$2.8\times$	$6.6\times$	$16.6\times$	$29.6\times$
Ratio, predicted	$1.00\times$	$2.77\times$	$6.34\times$	$14.0\times$	$35.4\times$

Appendix

Table 10: Synchronized variant under runtime heterogeneity (

W=48

, lognormal runtime multiplier of scale

\sigma

, five replicates, medians of simulations per second of each sampler’s own elapsed wall clock). Predicted is from the injected runtime distribution and the asynchronous run’s measured overhead. The

\sigma=0

control costs almost nothing because these evaluations take

1

s and barrier latency is negligible against them; the cost is the wait for the slowest draw and grows with

\sigma

. pyABC degrades less than the synchronized variant because it discards latecomers instead of waiting for them. The lower block scores the posteriors against the analytic posterior at the bandwidth each schedule reached, then re-reported at the

100

th order statistic of the same history (§ 6.4 ); no rank made

k

calls in the asynchronous run, so its schedule never ran at

\sigma\leq 0.5

, and the synchronized variant’s ran only at

\sigma\leq 0.5

Workers ( $=$ cores)	48	96	192	384
Throughput ratio, async / synchronized variant	$1.91\times$	$1.87\times$	$1.86\times$	$2.82\times$
$=$ utilization ratio	$1.18\times$	$1.19\times$	$1.21\times$	$1.21\times$
$\times$ simulation-duration ratio	$1.63\times$	$1.59\times$	$1.52\times$	$2.33\times$
Straggler factor of the synchronized variant’s generations	1.21	1.28	1.21	1.29
Predicted from asynchronous timing	$1.26\times$	$1.30\times$	$1.32\times$	( $2.34\times$ )

Appendix

Table 11: The synchronized variant’s slowdown on Cellular Potts

50^{3}

(earlier parameterization, Appendix E ), factorized (five replicates, medians). Throughput is utilization over mean simulation time, so the ratio is the product of the two columns that follow. The utilization ratio is what the barrier costs; it agrees with the expected-maximum-to-mean runtime ratio measured within the synchronized variant’s generations and with the prediction from the asynchronous run’s runtime distribution. The duration ratio (the synchronized variant’s simulations running longer, with replicate means from

6

36

s against

5.1

s on every asynchronous replicate) is not a barrier effect and is not attributed here.

Figure 9: Tolerance against simulations spent,

\epsilon_{(100)}(n)

, asynchronous against pyABC on every benchmark (medians and replicate range over five replicates; the slope over the last decade of

n

in the legend). The vertical gap at equal

n

is the per-simulation efficiency, the horizontal extent is the extra simulations the wall clock allowed. On Lotka–Volterra

98\%

of simulations return the extinction fallback, so

\epsilon_{(100)}

sits on that plateau until about

5000

draws have produced

100

survivors; the plateau is cut off.

Figure 10: Parameter-coupled runtime on the Gaussian-mean benchmark (analytic posterior;

48

workers,

60

s budget, five replicates; bands are inter-quartile ranges). The post-evaluation delay grows with the inferred mean, so one region of parameter space is sampled far more often than its mirror image. (a) Aggregate throughput falls as the coupling steepens (monotonically for pyABC, and from a peak at

c=0.5

for the asynchronous sampler), consistent with the fast region dominating the raw sample counts. (b) Posterior-mean error to the analytic posterior nonetheless does not increase with coupling and stays comparable between the asynchronous sampler and pyABC, which discards latecomers, so the over-representation does not measurably distort the posterior estimate at these coupling levels.

Workers	1	4	16	48	144	192	240	288
Nodes	$<$ 1	$<$ 1	$<$ 1	1	3	4	5	6
Synchronous	105	96	437	2952	3757	4322	4539	6034
Asynchronous ( $k=100$ )	149	369	1983	6240	4195	2615	2088	1729
Asynchronous ( $k=1000$ )	106	133	620	3804	2804	1957	1587	1336

Appendix

Table 12: Strong scaling on Lotka–Volterra: median simulation throughput (sims/s) at a 180 s budget, over five replicates (Fig. 3 , left, shows the inter-quartile spread). Asynchronous (ours) at both archive sizes vs. pyABC. Multi-node points use fully packed nodes (worker counts that are exact multiples of

48

); at counts above

100

pyABC is given population size equal to the worker count so it can occupy every core (a population of

100

leaves the surplus idle), which is why it keeps scaling here. The asynchronous sampler peaks on one node and then declines as multi-node coordination dominates, so pyABC overtakes it beyond three nodes at

k=100

. Enlarging the archive tenfold costs throughput at every scale, because the per-arrival proposal reconstruction is

\mathcal{O}(k)

, and moves that crossover in from beyond three nodes to three.

Figure 11: Measured decomposition of asynchronous worker wall-time on Lotka–Volterra (

k=100

;

180

s budget) from a dedicated instrumented run. The productive simulation fraction (blue, annotated), the share of worker wall-clock spent inside the simulator, collapses from

55\%

16

workers to

2\%

256

, while coordination and idle (MPI exchange, per-arrival proposal reconstruction, serialization, waiting) dominate as the job spreads beyond one node (16/48 = 1 node; 128 = 3 nodes; 256 = 6 nodes). The strong-scaling decline of Fig. 3 is therefore a measured property of coordinating low-cost evaluations.

	archive size $k$ (at $S=20$ )
	50	100	200	400	800
$d=1$	-0.014	-0.003	+0.006	+0.006	+0.074
$d=2$	-0.020	-0.006	+0.009	+0.030	+0.072
$d=4$	+0.025	+0.064	+0.094	+0.133	+0.063
$d=8$	-0.250	+0.055	+0.180	+0.195	+0.061
$d=16$	-0.047	+0.028	+0.049	+0.053	+0.055

Appendix

Table 13: Calibration sensitivity to the archive size

k

and the AMIS snapshot buffer

S

on the

d

-dimensional Gaussian-mean target (

1000

trials per cell; entries are the mean signed deviation of empirical from nominal coverage over the

0.50/0.80/0.90/0.95

levels and the

d

parameters). Negative is over-confident, positive is conservative;

0.000

is exactly calibrated. Left: varying

k

S=20

. Right: varying

S

k=100

$k$	sims/s at $W{=}48$	vs. $k{=}100$	worst $\|\Delta\text{cov}\|$	at	pyABC overtakes
50	6684	$+7\%$	0.250	$d{=}8$	beyond 3 nodes
100	6240	—	0.064	$d{=}4$	beyond 3 nodes
200	5904	$-5\%$	0.180	$d{=}8$	beyond 3 nodes
400	5393	$-14\%$	0.195	$d{=}8$	3 nodes
800	4331	$-31\%$	0.074	$d{=}1$	3 nodes
1000	3804	$-39\%$	—	—	3 nodes

Appendix

Table 14: The archive size on both of its axes at once. Throughput : median asynchronous throughput at the single-node peak (

48

workers) on Lotka–Volterra,

180

s wall cap, five replicates (

k\in\{100,1000\}

from the main scaling run,

k\in\{50,200,400,800\}

from the matched

k

-frontier run), and its change relative to the

k{=}100

we use throughout. Calibration : worst absolute deviation of empirical from nominal coverage over the dimensions of the

d

-dimensional Gaussian-mean sweep at

S{=}20

(Table 13 ), with the dimension attaining it. Crossover : fully packed nodes at which pyABC (population

=

worker count) overtakes the asynchronous sampler. The sweep did not include

k{=}1000

. Bold marks the best value per column.

Figure 12: Simulation-based calibration on Gaussian-mean inference (1000 trials; the full-history AMIS posterior): empirical coverage versus nominal level (left) and rank histogram (right). The asynchronous estimator is close to calibrated.

Figure 13: Cellular Potts

50^{3}

worker utilization, earlier parameterization (fraction of worker wall-clock spent inside the simulator) versus worker count (

1800

s budget; error bars are

\pm 1

standard deviation); pyABC uses a population equal to the worker count (Fig. 3 , right). The asynchronous sampler stays

{\approx}98.9

–

99.8\%

utilized at every scale. pyABC fills every core within a generation but then idles at the barrier waiting for the slowest simulation, so its utilization falls to

{\approx}24

–

29\%

(

41\%\to 24\%\to 26\%\to 29\%

48/96/192/384

workers, i.e.

{\approx}70

–

76\%

idle at every multi-node scale). The figure is the measured utilization behind pyABC’s sub-linear scaling in Fig. 3 (right).

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