Fig. 5: Analysis of the transition rates estimation for COCOC and CCCOO models.

A, B Summarizes the prediction of all rates for the test datasets of the COCOC and CCCOO topologies (Table 1 dataset No. 2 and 3). The cumulative distributions of the error scores (RAE, Eq. 3) illustrate the predictive performance of individual rates. Rates connecting the same states are visually coupled together. For comparison, the dashed pink line shows the cumulative distribution error scores (RAE) of randomly predicted rates. The test dataset consists of 10,000 samples (2D-histograms), and the parameter space for the rates k_ij was 100 s⁻¹ to 100 ks⁻¹. C, D To investigate the impact of the stochastic simulation process, the predictions on the COCOC and CCCOO models were ranked according to the error score (RAE) and five models were selected from each topology at the percentile indicated on the horizontal axes. Each model was then simulated 1000 times using its ground truth and the rates were predicted with the respective regression NN. The averaged error scores (RAE) resulting from comparing ground truth and predictions of all eight rates from a given model are depicted. The diamond indicates the median as well as the 75 and 25 percentiles, while the whiskers denote the 10 and 90 percentiles. To compare the results with the 2D-Fit²¹, an additional four-time series were simulated for each model using the ground truths. For each time series, an ensemble of 64 runs was conducted with the 2D-Fit, and the RAE of the predictions with the highest likelihood for each time series are depicted as orange dots. E, F The ranked error scores (RAE) (blue line) are related to the number of detected events of their respective 2D-histogram (orange dots). In addition, the red line displays the moving geometric average over the number of events in the 2D-histograms, with a window size of 1025 samples. The dashed blue line in (F) indicates the ranked RAE error scores for the predictions of an NN that has been trained and tested on dataset No. 4 (Table 1), which contains 2D-histograms whose underlying time series had a length of 100 million samples.