The AutoCorrelation Integral Drill (ACID) Test Set

Validation of the STable AutoCorrelationIntegral Estimator (STACIE) Using TheAutoCorrelation Integral Drill (ACID) TestSetmodel: lorentz(0.1)Gözdenur Toraman,† Dieter Fauconnier,†‡ and Toon Verstraelen✶¶† Soete Laboratory, Ghent University, Technologiepark-Zwijnaarde 46, 9052 Ghent, Belgium‡ FlandersMake@UGent, Core Lab EEDT-MP, 3001 Leuven, Belgium¶ Center for Molecular Modeling (CMM), Ghent University, Technologiepark-Zwijnaarde 46, B-9052,Ghent, Belgium✶E-mail: [email protected]Version 2025-06-25 (bf3ff8a)Contents1.Description of Figures and Tables ............................................................................ 22.Kernel exp1p .................................................................................................. 33.Kernel exp1w ................................................................................................. 51 1.Description of Figures and TablesThe following sections contain figures and tables with the same type of results in each section, butcomputed for different kernels. All figures and tables are labeled with a letter and are explained here. For afull discussion of the results, we refer to the STACIE paper: TODO ADD CITATION.(a)Illustration of input data.•Left: an example input sequences (first 100 steps).•Center: the sampling autocorrelation function (ACF) of the input data (𝑁=1024, 𝑀=256, purpleline) and the analytical ACF (dashed line).•Right: the sampling power spectral density (PSD) of the input data (𝑁=1024, 𝑀=256, turquoiseline) and the analytical PSD (dashed line).(b)Scaling of uncertainty of the autocorrelation integral with input data.•The slope of the slanted gray lines indicates the ideal scaling of the uncertainty (proportional to1√𝑁𝑀). The spacing between the lines corresponds to a factor of 2 in the uncertainty, the ideal casewhen changing 𝑁 by a factor of 4.•A square represents the standard deviations over 64 repetitions of STACIE’s estimate of theautocorrelation integral for a specific combination of 𝑁 and 𝑀.•The dotted lines represent the corresponding predicted uncertainties.(c)Assessment of the error estimate of the autocorrelation integral.•The square blocks show the ratio of the standard deviation of the STACIE estimate and the RMSvalue of the predicted uncertainty, over 64 repetitions. This value is ideally 100%.•The dots show the ratio of the mean error and the RMS value of the predicted uncertainty, over 64repetitions. This value is ideally 0%.(d)Scaling of the uncertainty of the exponential correlation time with input data.•This figure follows the same convention as in (b), but shows results for the uncertainty of theexponential correlation time.(e)Assessment of the error estimate of the exponential correlation time.•This figure follows the same convention as in (c), but shows results for the uncertainty of theexponential correlation time.(f)Sensitivity of the autocorrelation integral to the cutoff frequency.•This plot shows how the autocorrelation integral correlates with the effective number of points usedin the fit (top) and the cutoff frequency (bottom).•Results are shown only for the 𝑀=64.•The color code for different 𝑁 corresponds to the legends shown in figures (b), (c), (d) and (e).(g)Sensitivity of the exponential correlation time to the cutoff frequency.•The same conventions as in (f) apply, but this figure shows results for the exponential correlationtime.(h)Number of successful test cases (Failures are typically due to not finding any cutoff frequency withacceptable results.)(i)Sanity check counts for the effective number of points•Number of test cases for each combination of 𝑁 and 𝑀 where the effective number of points used inthe fit is below 20𝑃=40.(j)Sanity check counts for the regression cost z-score•Number of test cases for each combination of 𝑁 and 𝑀 where the z-score of the regression costexceeds 2.(k)Sanity check counts for the cutoff criterion z-score•Number of test cases for each combination of 𝑁 and 𝑀 where the z-score of the cutoff criterionexceeds 2.2 2.Kernel exp1p(a) Illustration of input data(b) Scaling of uncertainty of the autocorrelationintegral with input data(c) Assessment of the error estimate of theautocorrelation integral(d) Scaling of uncertainty of the exponentialcorrelation time with input data(e) Assessment of the error estimate of theexponential correlation time3 (f) Sensitivity of the autocorrelation integral tothe cutoff frequency(g) Sensitivity of the exponential correlationtime to the cutoff frequency(h) Number of successful test cases𝑀=1𝑀=4𝑀=16𝑀=64𝑀=256𝑁=1024064646464𝑁=40966464646464𝑁=163846464646464𝑁=655366464646464(i) Sanity check counts for the effective number of points𝑀=1𝑀=4𝑀=16𝑀=64𝑀=256𝑁=102400000𝑁=409600000𝑁=1638400000𝑁=6553600000(j) Sanity check counts for the regression cost z-score𝑀=1𝑀=4𝑀=16𝑀=64𝑀=256𝑁=102400011𝑁=409601000𝑁=1638400021𝑁=6553600003(k) Sanity check counts for the cutoff criterion z-score𝑀=1𝑀=4𝑀=16𝑀=64𝑀=256𝑁=102401100𝑁=409610010𝑁=1638420100𝑁=65536100004 3.Kernel exp1w(a) Illustration of input data(b) Scaling of uncertainty of the autocorrelationintegral with input data(c) Assessment of the error estimate of theautocorrelation integral(d) Scaling of uncertainty of the exponentialcorrelation time with input data(e) Assessment of the error estimate of theexponential correlation time5 (f) Sensitivity of the autocorrelation integral tothe cutoff frequency(g) Sensitivity of the exponential correlationtime to the cutoff frequency(h) Number of successful test cases𝑀=1𝑀=4𝑀=16𝑀=64𝑀=256𝑁=102400646464𝑁=4096064646464𝑁=163846464646464𝑁=655366464646464(i) Sanity check counts for the effective number of points𝑀=1𝑀=4𝑀=16𝑀=64𝑀=256𝑁=102400000𝑁=409600000𝑁=1638400000𝑁=6553600000(j) Sanity check counts for the regression cost z-score𝑀=1𝑀=4𝑀=16𝑀=64𝑀=256𝑁=102400101𝑁=409600301𝑁=1638400011𝑁=6553600000(k) Sanity check counts for the cutoff criterion z-score𝑀=1𝑀=4𝑀=16𝑀=64𝑀=256𝑁=102400110𝑁=409600000𝑁=1638410001𝑁=65536031006