Fig. 3: Evaluating the performance of the ANN-aided model approximation.
a Precision and computational efficiency of the ANN-aided model approximation as a function of sample size and number of snapshots. The method is benchmarked on Model I since the time-dependent solution of the delay CME is exactly known (see SI Note 1) and hence the accuracy of our method can be precisely quantified. A measure of the accuracy is the average Hellinger distance (HD) between the NN-CME and exact distributions at four different time points. The computation time is equal to the time-to-acquire samples plus time for training. Each data point in the graphs is averaged on three independent trainings. Note that the NN-CME obtained from training with 103 samples produces a distribution that is as precise as that from 3 × 104 samples using the SSA of the delay CME (shown as a black dashed line); in this case the computation time of the NN-CME is also just 1/6 of the SSA. b Comparison of the NN-CME distributions, exact analytical distributions and histograms from stochastic SSA simulations of the delay CME at two different time points; the sampling for both training and the SSA is 103. Note that the NN-CME leads to much more accurate distributions than the SSA for the same number of samples. The rate constants and other parameters related to the ANN’s training are specified in SI Table 1.
