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

Julian Herold, Markus Götz, Alexander Schug

arXiv:2610.29506v1stat.COcs.LG

TL;DR

Generation-based ABC can leave workers idle while waiting for slow simulations, especially when runtimes vary. The paper introduces a generation-free sampler that updates from completed results and reweights the full history against reconstructed proposal mixtures. It reports improved throughput and tighter tolerance on a tissue simulator, while identifying scope conditions for its asymptotic guarantees.

  • Problem

    Generation-based sequential ABC waits for the slowest simulation in each generation before updating proposals, which can reduce throughput when runtimes vary substantially.

    Source: §1 · p. 1

  • Method

    The sampler updates proposals as simulations complete and estimates the posterior by reweighting the full history against a reconstructed mixture of sampling proposals.

    Source: §1 · p. 2, §9 · p. 18

  • Results

    On the tissue simulator, the asynchronous sampler completes more evaluations per hour and reaches a tighter tolerance than matched pyABC, while pyABC has smaller Wasserstein distance on g-and-k.

    Source: §7 · pp. 17–18

  • Takeaways & Limitations

    For the examined workloads, asynchronous execution can improve throughput and tolerance on the tissue simulator, while posterior accuracy comparisons vary by benchmark.

    Source: §7 · pp. 17–18

    The consistency results require a reporting bandwidth bounded away from zero, and the fidelity ratio is only partly measured.

    Source: §6.4 · pp. 16–17, §8 · p. 18

Abstract

from arXiv · show

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.

1 Introduction

Generation-based ABC can leave workers idle while they wait for the slowest simulation, especially when runtime varies across parameters. The paper introduces a generation-free sampler that updates on completed results and reweights the full history, then evaluates its posterior estimates and synchronization costs.

Motivation

  • Generation-based sequential ABC waits for the slowest simulation before updating its proposal and bandwidth, reducing throughput when runtimes vary substantially.This is particularly relevant to cell-based tissue models, where parameter values can produce different cell counts and runtimes.Source: §1 · pp. 1–2

Contribution

  • The sampler updates its proposal whenever a simulation finishes, sends a candidate to a free worker, and reweights the history against a mixture of sampling proposals.The proposal uses the k lowest-discrepancy particles evaluated so far.Source: §1 · p. 2

Evaluation

  • The paper compares its sampler with pyABC configured with the same kernel and bandwidth schedule, including tests of posterior quality and the simulation costs at which asynchronous updates pay off.In one experiment with a slow worker, pyABC throughput falls by more than 100-fold while the sampler loses less than half its throughput.Source: §1 · p. 2

Contribution

  • Runtime-based predictions of synchronization penalties agree with measured penalties ranging from 1.2× to 400×.The predictions are validated against a synchronized variant of the same sampler.Source: §1 · p. 2
  • The paper analyzes how proposal-mixture approximation affects posterior estimation and establishes consistency for the smooth-ABC posterior when the approximation becomes asymptotically exact.It also assesses mixture approximation, calibration, recovery, starting bandwidth, and archive size.Source: §1 · p. 2

2 Background and Related Work

ABC uses simulated data and discrepancies to infer parameters when likelihoods are intractable; smooth kernels assign continuous weights rather than making binary accept-or-reject decisions. Sequential ABC and related adaptive methods address sampling efficiency, but generation-based implementations retain a synchronization barrier.

ABC background

  • Smooth-kernel ABC gives each simulation a continuous weight, unlike the classical hard indicator that accepts or rejects at a fixed threshold.The bandwidth ϵ is the kernel bandwidth; the paper distinguishes it from the sampler's empirical tolerance.Source: §2 · p. 2

Sequential ABC and the generation

  • Sequential ABC adapts proposals across generations, but the next generation cannot begin until the slowest candidate in the current one has been simulated.Generation-based implementations including pyABC, ABCpy, and ELFI can parallelize within a generation but wait before constructing the next.Source: §2 · pp. 2–3

Reusing every draw: AMIS

  • AMIS reweights particles from different proposal distributions against a mixture of the proposals used, allowing earlier draws to contribute after the proposal changes.The paper applies this principle to individual arrivals and reconstructs posterior weights from completed simulations.Source: §2 · p. 3

Simulators with parameter-dependent cost

  • Cellular Potts runtimes can vary by orders of magnitude across the prior because the number of simulated cells depends on inferred parameters, making the model susceptible to generation barriers.The model represents cells on a lattice and is used to infer parameters by comparing simulated tissue features with microscopy data.Source: §2 · p. 3

Barrier-free sampling elsewhere

  • Prior barrier-free SMC and look-ahead scheduling do not combine barrier-free execution with AMIS-style reweighting for asynchronous ABC simulations.The cited parallel adaptive reweighting method assumes an evaluable target density and does not address asynchronous ABC with heterogeneous runtimes.Source: §2 · p. 3

3 Method

The sampler uses completed evaluations to update proposals without waiting for other workers, while retaining the full history for posterior reconstruction. Its archive, bandwidth schedule, proposal construction, and reweighting scheme define how it adapts and estimates the posterior.

3.1 Overview

  • The sampler updates from the history available to a worker and uses the full recorded history to reconstruct the posterior with weights against a mixture of proposals.The online buffer of previous proposals helps parent selection but is not needed for posterior reconstruction.Source: §3.1 · pp. 4–5

3.2 History and archive (steps 1 and 2)

  • Each completed evaluation enters a growing history; the k lowest-discrepancy particles form the archive used to build the next proposal.The archive, bandwidth, and proposal are recomputed from the available history at each call.Source: §3.2 · p. 5

3.3 Bandwidth (step 2)

  • The bandwidth decreases in controlled steps, retaining at least 95% of the archive's kernel-weighted effective sample size and waiting until at least 2k evaluated particles lie below it.Each decrease is limited to a factor of two; on expensive simulations, the run may end before the bandwidth moves far from its user-set starting value.Source: §3.3 · p. 5

3.4 Archive proposal (steps 3 to 5)

  • A Gaussian-mixture proposal places components at archive members, selects parents by mixture weight, and perturbs them using a scaled weighted archive covariance.Components are truncated to the prior box, and smooth kernels let an archive member's contribution shrink continuously as bandwidth tightens.Source: §3.4 · pp. 5–6

3.5 Weights and the posterior estimate (step 6)

  • Posterior estimation reweights every evaluated particle against a finite reconstructed mixture of proposal snapshots, with a prior component that keeps the denominator bounded away from zero.The full-history estimate is distinct from the parent weights used to generate new candidates.Source: §3.1 · p. 5, §3.5 · p. 6

3.6 Update loop

  • Each worker runs the update loop on its own growing history, and no step waits for another worker.A worker returning from a slow simulation sees a larger history than the one it left.Source: §3.6 · p. 6

4 Theoretical Analysis

The analysis studies how replacing the full mixture of sampling proposals with a reconstructed denominator affects the posterior estimate. Under stated assumptions, the estimate tracks a smooth-ABC target modified by a fidelity ratio, and exact fidelity yields the intended target when the reporting bandwidth stays positive.

Mixture approximation

  • Replacing the full proposal mixture with a fixed-size reconstructed mixture can introduce denominator approximation error, represented by a ratio between the actual sampling mixture and the denominator used for reweighting.Where the denominator is too small relative to the actual mixture, the reweighted sample gives a region too much mass; where it is too large, the region receives too little.Source: §4 · p. 7

Consistency

  • If the fidelity ratio converges to r, the estimate converges to a posterior tilted by r; when r is identically one, it converges to the smooth-ABC posterior at the limiting bandwidth.The analysis uses martingale arguments because proposals depend on previously observed evaluations.Source: §4 · pp. 7–8

Tracking result

  • Under Assumptions 1–4 and a positive limiting bandwidth, the weighted estimate tracks the smooth-ABC posterior at the realized bandwidth, with its remaining difference described by the fidelity ratio.The random variation vanishes under the stated assumptions; the normalized conclusion additionally requires the average unnormalized weight not to collapse.Source: §4 · p. 8

Conditions and scope

  • The asymptotic results require a reporting bandwidth bounded away from zero, and the fidelity ratio must converge to a finite, strictly positive function for the tilted-limit result.The implementation's fidelity assessment is partial: two contributions are measured and two are bounded rather than measured.Source: §4 · pp. 8–9

5 Experimental Design

The experiments separate posterior accuracy, synchronization overhead, and simulator performance across benchmarks with different runtime properties. Comparisons use distinct baselines and metrics, with a prior-predictive rule for setting the starting bandwidth.

5.1 Benchmarks

  • The benchmark suite separates posterior-accuracy tests, injected-runtime-heterogeneity tests, Lotka–Volterra scaling and cost-boundary tests, and a Cellular Potts tissue-simulator benchmark.Cellular Potts runtime varies with cell count, which correlates 0.99 with runtime; its synthetic observations have a known truth, allowing posterior recovery to be assessed.Source: §5.1 · p. 9

5.2 Baselines and instruments

  • Three comparators address distinct questions: a synchronized variant isolates barrier costs, pyABC provides a practical baseline, and rejection ABC tests adaptive-proposal gains.The pyABC comparison uses the same smooth-kernel acceptance rule and bandwidth schedule; the synchronized variant retains the proposal mechanism while adding a collective barrier.Source: §5.2 · pp. 9–10

5.3 Metrics

  • At a matched simulation budget, ϵ(100)(n) is the 100th-smallest discrepancy among the first n completed evaluations, measuring the threshold for the best 100 draws.The equal-wall-clock comparison also reflects throughput differences, while the slope against log n indicates whether additional simulations continue to tighten tolerance.Source: §5.3 · p. 10
  • Synchronization cost is predicted by resampling worker-sized sets of recorded evaluation durations and comparing predicted synchronized throughput with measured asynchronous throughput.The prediction assumes simulation time dominates collective-barrier latency and the timing sample covers the runtime-distribution tail; the general form handles slow workers and censored durations.Source: §5.3 · pp. 10–11
  • Posterior quality is assessed through simulation-based calibration, reference-posterior distance where available, and Cellular Potts contraction, truth coverage, and effective sample size.Calibration uses 1,000 prior-generated trials and central intervals at nominal levels 0.50, 0.80, 0.90, and 0.95.Source: §5.3 · p. 11
  • For expensive simulators, the starting bandwidth is set from a few thousand prior-predictive discrepancies at about one-fifth of their median.The experiments also measure the cost of starting substantially above that value.Source: §5.3 · p. 11

6 Results

The results evaluate barrier-cost prediction, throughput and tolerance against pyABC, and posterior calibration, recovery, and limitations. The asynchronous sampler predicts synchronization penalties across the tested configurations and improves same-budget Cellular Potts results, while calibration and posterior concentration depend on reporting support and starting bandwidth.

6.1 Predicting the cost of synchronization barriers (C1)

  • Across 12 configurations within its domain, the predicted-to-measured barrier-cost ratio ranged from 0.84 to 1.19, with median 0.996, for measured penalties of 1.2×–400×.The largest prediction errors, 16% and 19%, occurred at the widest runtime spreads; three configurations were outside the predictor’s domain.Source: §6.1 · p. 11, Figure 2 · p. 12
  • On Cellular Potts, the asynchronous sampler completed 2.1–2.4× pyABC’s simulations in the same budget, while pyABC utilization was 43–49% versus 98–99.8%.At 503, the measured barrier cost was 1.2×; the larger 2.3–2.4× throughput gap against pyABC also reflects its per-generation overhead.Source: §6.1 · pp. 11–12

6.2 Throughput converts into a tighter tolerance (C2)

  • 2.4× as many simulations and 4.1× tighter tolerance at equal wall clock were achieved on the Cellular Potts production run; per-simulation efficiency was 1.6× higher.At 803, the sampler completed 2.1× as many simulations and was 2.1× more efficient per simulation.Source: §6.2 · p. 13, Table 4 · p. 16

6.3 Where the net advantage becomes positive (C3)

  • The throughput crossover was about 4 ms per simulation, with net advantage turning positive between 2 and 4 ms under the tested worker placement and time budget.Below that range, coordination costs exceeded time saved by removing barriers; one packed-node Lotka–Volterra setup had a 2.1 throughput ratio versus 0.96 across four nodes.Source: §6.3 · p. 14, Figure 4 · p. 14

6.4 The posterior: calibration, recovery, and what limits it (C4)

  • Calibration was near nominal on the one-dimensional Gaussian and bimodal targets, but conservative on two parameters of the four-dimensional g-and-k model.The full-history estimator tracked nominal Gaussian coverage while pyABC’s nominal 0.90 interval covered 0.75; the top-k archive retained both bimodal modes in 86% of trials.Source: §6.4 · pp. 14–15, Table 3 · p. 15
  • On the Gaussian mean, the asynchronous estimate was closer to the analytic posterior than pyABC at every checkpoint; on four-dimensional g-and-k, pyABC ended closer (W1 0.029 versus 0.069).The Gaussian posterior effective sample size stayed at 238–296 as history grew from 105 to 1.3 × 10^6 particles; in four dimensions it varied from 7 to 2987.Source: §6.4 · p. 15, Figure 5 · p. 16
  • On the two-parameter Cellular Potts setup, all methods recovered the truth, while the asynchronous estimate had the tightest posterior and largest effective sample size: 303 versus pyABC’s 66.Cell-volume contraction was 81%±1% for the asynchronous estimator, 72%±4% for pyABC, and 67% for the best 100 rejection draws.Source: §6.4 · p. 15, Table 4 · p. 16, Figure 6 · p. 17
  • With the original starting bandwidth ϵ0 = 10, cell-volume contraction was 13% ± 14%; the schedule remained at ϵ0, 321× above the tolerance the draws supported.The production ϵ0 = 0.1 was about a fifth of the prior-predictive median discrepancy; the archive size is benchmark-dependent and should be checked against calibration and reached bandwidth.Source: §6.4 · pp. 16–17, Table 4 · p. 16

7 Discussion

Across the tested workloads, asynchronous sampling improves Cellular Potts throughput and posterior outcomes, while its advantage depends on simulation cost and reporting choices. The paper offers workload-specific guidance for estimating synchronization costs, setting the starting bandwidth, and choosing archive size.

7 Discussion

  • On Cellular Potts, asynchronous sampling completes more evaluations per hour and improves tolerance, weak-parameter contraction, and posterior effective sample size; it is calibrated where pyABC under-covers on Gaussian but loses on g-and-k Wasserstein distance.Asynchronous execution is less effective for very low-cost evaluations.Source: §7 · pp. 17–18
  • For the tested settings, consider asynchronous sampling when evaluations take at least a few milliseconds; below that, per-arrival coordination can outweigh barrier costs.The observed crossover is tied to the studied worker placement and time budget.Source: §7 · p. 18
  • Synchronization cost can be estimated from per-evaluation timing in the asynchronous run, within the stated domain.Source: §7 · p. 18
  • For expensive simulations, set the starting bandwidth from prior-predictive discrepancies and check the posterior by recomputing it at the completed evaluations’ k-th smallest discrepancy.The initial bandwidth may otherwise remain too large throughout the run.Source: §7 · p. 18
  • Archive size is a benchmark-dependent choice; assess calibration and the bandwidth reached rather than assuming a larger archive is better.Enlarging the archive can loosen the final bandwidth and lengthen the transient.Source: §7 · p. 18
  • More completed simulations do not automatically raise posterior effective sample size, which stayed within a few multiples of archive size in these experiments.Evaluating the posterior at the scheduler’s tightest bandwidth leaves only a restricted part of the history with appreciable weight.Source: §7 · p. 18

8 Limitations

The consistency result is qualified by the fidelity ratio and a reporting bandwidth bounded away from zero. Deadline-limited runs may also over-represent parameter regions with shorter runtimes.

8 Limitations

  • The estimator converges to the intended smooth-ABC posterior when the fidelity ratio approaches one, under the stated assumptions.Two factors in the ratio are measured and two are bounded.Source: §8 · p. 18
  • The asymptotic statements require reporting bandwidth to remain bounded away from zero; the proposed 10^-4ϵ0 floor would have clipped Gaussian-mean and Lotka–Volterra runs, but not g-and-k or Cellular Potts.No reported run reached its floor, so the limits describe continuation of the runs.Source: §8 · p. 18
  • At a fixed deadline, completed evaluations may over-represent parameter regions with short runtimes, while the direct effect of unfinished candidates is at most O(W/n).The remaining deadline effect operates through the adaptive proposal sequence and is covered by the fidelity ratio.Source: §8 · p. 18

9 Conclusion

The conclusion presents a generation-free ABC sampler that removes synchronization idle time and uses runtime data to predict the cost of a barrier. It also states that posterior quality is bounded by starting bandwidth and archive size, while the fidelity-ratio analysis characterizes estimator deviation.

9 Conclusion

  • The sampler removes generation-barrier idle time, and runtime-based predictions let practitioners estimate the compute saving before an allocation.The conclusion also says the estimator is well calibrated in one-dimensional tests but conservative for some parameters of the four-dimensional benchmark.Source: §9 · p. 18, Broader Impact Statement · p. 19

Broader Impact Statement

  • The method's direct effect is on compute: it removes idle time imposed by generation barriers on heterogeneous simulator workloads.The synchronization-penalty prediction can estimate those savings from a practitioner's own timing data.Source: Broader Impact Statement · p. 19

Reproducibility

  • The repository includes code, run configurations, launchers, tests, figure and table data, regeneration scripts, and diagnostic outputs.Raw particle records and per-worker timing logs are slated for public release upon publication.Source: Reproducibility · p. 19

Declaration of AI Assistance

  • The authors used AI tools for manuscript editing and checking derivations and proofs, and say they reviewed suggestions and retain responsibility for the work.Source: Declaration of AI Assistance · p. 19

A The fidelity ratio

  • The fidelity-ratio analysis connects estimator deviation to approximation of the proposal mixture and relates the adaptive argument to existing AMIS theory.The cited AMIS results do not cover this every-draw adaptive scheme; the prior floor bounds weights without a moment or density-ratio condition.Source: A The fidelity ratio · p. 22

A.1 What r is for this implementation

The implementation's fidelity ratio is decomposed into contributions from the prior floor, snapshot quadrature, normalization, and capped rejection, redraws, and asynchronous reconstruction. The appendix measures some contributions and reports close agreement with reference posterior estimates, while the setting establishes assumptions used in the analysis.

A.1 What r is for this implementation

  • The fidelity ratio is decomposed into four implementation factors, and changing the intermediate mixtures changes attribution but not their telescoping product.The factors are prior floor, snapshot quadrature, normalizer, and cap, redraws, and asynchrony.Source: §A.1 · p. 23
  • Snapshot quadrature error is bounded by Vn/m, where Vn is the total variation of the reconstructed proposal path.In the five Cellular Potts runs, proposal drift decays as τ^-0.7 to τ^-0.95, and measured total variation grows sublinearly, though the measurement is diagnostic rather than asymptotic.Source: §A.1 · pp. 23–24
  • The five Cellular Potts replicates yield 0.2–0.5% total-variation distance from the reference, with posterior means within 0.012 standard deviations and marginal widths within 1%.The bound exceeds direct measurements by about an order of magnitude; neither rejection fallback nor exhausted redraw occurred in the recorded runs.Source: §A.1 · pp. 23–24
  • With fixed m, tracking the n-point mixture depends on the proposal path settling; growing m can remove this quadrature contribution if Vn/mn tends to zero.The implementation ties the prior floor δ to m, so a growing snapshot count requires decoupling them to retain the uniform weight bound.Source: §A.1 · p. 24

B.1 Setting

  • Asynchronous arrival-order reconstruction differs from proposal-order history by at most W in-flight candidates, and the lemma requires uncoupled simulator outputs and runtimes.The setting treats completion-time steering as choosing a predictable proposal, while fresh randomness determines the candidate conditional on that proposal.Source: §B.1 · pp. 24–25
  • The denominator's prior floor bounds every importance weight by 1/δ, without requiring a density-ratio or moment condition.This follows because the denominator is at least δπ pointwise and the ABC kernel is bounded by one.Source: §B.1 · p. 25

B.2 Proof of Theorem 1 and Corollaries 2–3

The proof uses bounded weights and uniform convergence over bandwidths and denominators to establish convergence to the tilted integral, with the intended smooth-ABC posterior as the exact-approximation case. It also bounds deadline censoring and the target shift induced by the fidelity ratio.

B.2 Proof of Theorem 1 and Corollaries 2–3

  • Bounded martingale differences converge uniformly over the bandwidth and denominator class, allowing the run-dependent pair to be substituted and its compensator identified as the tilted integral.When the proposal-mixture approximation becomes exact, the resulting conclusion is consistency for the smooth-ABC posterior.Source: §B.2 · pp. 26–27

B.3 Deadline censoring

  • Deadline censoring is negligible when W/n tends to zero and average weight stays bounded below, and is o(n^-1/2) when W=o(√n).For the Cellular Potts runs, W=48 and n≈12,900; a drain-after-deadline experiment measures posterior-mean effects of 0.013 or less.Source: §B.3 · p. 27

B.4 Proof of Proposition 4

  • The target's total-variation shift under the fidelity-ratio tilt is controlled by ζ0/(1−ζ0), where ζ0 is the posterior expectation of |r−1|.A set-based bound can replace ζ0 when it is less than one.Source: §B.4 · p. 28

C Implementation Details

The implementation compares the configured pyABC baseline with a history-driven, generation-free sampler, whose posterior estimator reconstructs a bounded-memory mixture after the run. Its bandwidth schedule, archive covariance, and restart state are specified alongside that estimator.

C Implementation Details

  • A restart reproduces the estimator over evaluated history, not the trajectory the run would otherwise have taken.Between calls, the sampler carries kept snapshots and two scheduler controls.Source: C Implementation Details · p. 28
  • The bandwidth schedule is monotone, holding until k+µ particles lie within the bandwidth and then searching for a tighter value that retains a target fraction of kernel-weighted effective sample size.The search runs on a rank's first call, at intervals, and after out-of-order arrivals rebuild cached history.Source: C Implementation Details · pp. 29–30
  • The posterior estimator rebuilds its snapshot mixture from history, while the running sampler carries an online snapshot buffer; the comparison characterizes pyABC as configured, not ABC-SMC generally.For fixed m, the post-hoc pass costs O(nk), uses chunking for flat-in-n peak memory, and is excluded from throughput measurements.Source: C Implementation Details · pp. 28, 31, Table 6 · p. 30
  • The archive is the top-k particles by discrepancy, and its perturbation covariance combines a scale-aware covariance term with jitter and box-truncated mixture components.The product of per-axis in-box masses is exact for diagonal covariance but only an approximation for correlated covariance.Source: C Implementation Details · pp. 30–31
  • The matched pyABC baseline uses a probabilistic-rejection acceptor with the same smooth kernel as the asynchronous sampler.Each replicate's rejection step uses an independently seeded random-number generator.Source: C Implementation Details · p. 31

D Additional Experimental Protocol

The experiments use fixed, reproducible seeds and consistent wall-clock deadlines, with simulation-limited exceptions for calibration and recovery runs. Benchmark settings and cluster placement vary by study, including a four-replicate Cellular Potts production setup and packed-node scaling runs.

Seeding and crash recovery

  • Replicate and derived seeds were deterministic, while a resumed run recovered the analytic posterior mean without reproducing the uninterrupted proposal trajectory exactly.The restarted run's posterior-mean absolute error was 7.6 × 10−3 versus 7.5 × 10−4 uninterrupted; re-seeding, nondeterministic MPI arrival order, and rebuilding the snapshot buffer changed adaptation.Source: D Additional Experimental Protocol · p. 31

Cluster and wall-clock control

  • Wall-clock studies used a uniform monotonic-clock deadline and recorded partial final generations rather than discarding them.Simulation-based calibration and kill-and-resume studies instead stopped at fixed simulation counts.Source: D Additional Experimental Protocol · pp. 31–32

Benchmark configurations

  • Benchmark configurations varied worker counts and archive sizes, with scaling sweeps reaching 288 workers for Lotka–Volterra and 384 for Cellular Potts.Studies generally used archive sizes k ∈{100, 1000}; budgets were specified per method run.Source: D Additional Experimental Protocol · p. 32

Benchmark-specific notes

  • The benchmark suite used fixed observed datasets, uniform priors, and simulator-specific summary discrepancies; Cellular Potts used the longest budget because evaluations were costly.The Gaussian-mean benchmark additionally supplied a closed-form posterior for calibration and recovery checks.Source: D Additional Experimental Protocol · p. 32

Computing environment

  • Experiments ran on JUWELS with ParaStation MPI, generally placing one rank per physical core on fully reserved nodes.The inexpensive-simulator production runs instead placed 48 ranks as 12 per node on four nodes; this explains lower throughput than packed single-node scaling runs.Source: D Additional Experimental Protocol · p. 33

E The Cellular Potts inference setup

The Cellular Potts production inference problem is deliberately restricted to division rate and target cell volume, selected from screening because the two retained summaries resolve those directions. Under runtime heterogeneity, the asynchronous archive also retains lower posterior-mean error than pyABC as runtime spread increases.

E The Cellular Potts inference setup

  • Two scalar summaries—log cell count and log 95th-percentile radius—carry nearly all measured signal, motivating inference on division rate and target cell volume.Each evaluation averages four simulations because one realization is too noisy to order nearby parameters; the retained parameter responses are near-orthogonal (| cos | = 0.07).Source: E The Cellular Potts inference setup · p. 33
  • The earlier Cellular Potts scaling setup inferred division rate and motility, which screening found confounded, so the production configuration replaced it.The earlier setup used one simulation per evaluation and a whitened distance over morphological features.Source: E The Cellular Potts inference setup · p. 33

F.1 Runtime heterogeneity: archive quality

  • As runtime spread σ grows, pyABC’s archive-mean error rises from ≈0.05 to ≈0.28, while the asynchronous archive holds ≈0.007–0.011.At the fixed 60 s Gaussian-mean budget, pyABC completes fewer simulations as σ increases, while the asynchronous sampler completes several-fold more.Source: §F.1 · p. 34
  • The runtime-heterogeneity figure compares archive-mean error to the analytic posterior mean and completed simulations against runtime spread σ.Its error measure concerns the unweighted top-k archive, not the AMIS-reweighted posterior.Source: Figure 7 · p. 34

F.2 The synchronized variant on the straggler benchmark, and pyABC under injected heterogeneity

The experiments test when asynchronous execution offsets coordination costs, how runtime-dependent sampling affects posterior estimates, and how archive settings affect calibration and scaling. Results show that synchronization predictions are accurate once stragglers dominate, while calibration and throughput trade-offs depend on runtime, archive size, and simulator behavior.

F.2 The synchronized variant on the straggler benchmark, and pyABC under injected heterogeneity

  • At a 20× persistent straggler, predicted synchronized throughput is 401× below the measured asynchronous rate, versus a measured 402× ratio.From 5× onward, predictions agree with measured penalties within 0.5%; at 0× and 1× they fail because the model omits collective cost on the 4 ms workload.Source: §F.2 · p. 34, Table 9 · p. 35

F.3 The synchronized variant under runtime heterogeneity and on Cellular Potts

  • The synchronized Cellular Potts slowdown separates barrier-related utilization loss from longer simulation durations, which the analysis does not attribute to the barrier.Table 11 compares throughput, utilization ratio, and duration ratio; the latter reflects synchronized-variant simulations running 6 to 36 s versus 5.1 s asynchronously.Source: Table 11 · p. 36

F.4 Tolerance curves

  • The tolerance plot compares tolerance against simulations spent; on Lotka–Volterra, 98% extinction fallbacks keep ϵ(100) on a plateau until about 5000 draws produce 100 survivors.At equal simulation counts, the vertical gap indicates per-simulation efficiency; the horizontal extent reflects extra simulations allowed by wall-clock time.Source: §F.4 · p. 36, Figure 9 · p. 37

F.5 Parameter-coupled runtime

  • As parameter-dependent delay steepens, aggregate throughput falls by ≈43% for the asynchronous sampler, while its posterior-mean error does not increase measurably.The delay makes one parameter region faster than its mirror image; at these coupling levels the asynchronous mean error remains comparable to pyABC’s.Source: §F.5 · p. 37, Figure 10 · p. 38
  • Across runtime coupling levels, asynchronous posterior-mean error stays ≈0.01 and comparable to pyABC, despite faster sampling of one mirrored parameter region.Reweighting lowers the effective-sample-size fraction from ≈0.99 to ≈0.88 and widens the central 90% interval by ≈15%; draining in-flight simulations changes the weighted mean by at most 0.013.Source: §F.5 · p. 37, Figure 10 · p. 38

F.6 Strong scaling on an inexpensive simulator

  • On inexpensive Lotka–Volterra, asynchronous throughput peaks on one node and declines across multi-node jobs, while pyABC overtakes beyond three nodes at k = 100.Per-arrival proposal reconstruction is O(k); increasing k to 1000 costs 39% of the single-node peak throughput and moves the crossover to three nodes.Source: §F.6 · p. 38, Table 12 · p. 39, Figure 11 · p. 39

F.7 Calibration against the archive size and the snapshot buffer

  • With k = 100, the worst calibration deviation is 0.064 at d = 4 and throughput is 6240 versus 6684 simulations/s, while k = 50 fails calibration at 0.250.The calibration and throughput axes use different benchmarks by design; k = 100 is within 7% of the fastest setting, while larger archives add no calibration and reduce throughput.Source: §F.7 · pp. 39–40, Table 14 · p. 41

F.9 Lotka–Volterra extinction

  • Lotka–Volterra posterior curves are diagnostics rather than accuracy comparisons because only ≈2% of nominal simulations are informative survivors.The observed dataset is redrawn until a trajectory survives, making the target conditional on survival; throughput and scaling are unaffected because extinct runs cost about as much as surviving ones.Source: §F.9 · p. 40

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