Fig. 3

Sensitivity-guided iterative parameter identification and data generation. In the loop step n, \({\widetilde{\theta }}_n\) stands for the set of possibly identifiable parameters, \(\Theta _n\) for the the set of filtered truly identifiable parameters, and \({\widehat{\theta }}[\Theta _n]\) for the estimates of the filtered parameter with the subset \(\Theta _n\). PELS-VAE stands for a well-trained model with network parameters \(\widehat{\varvec{\varphi }}, \widehat{\varvec{\xi }}\). In each step n, first, the potentially identifiable parameters \({\widetilde{\Theta }}_n\) are selected with sensitivity analysis according to Algorithm 1 in “Selection of practically identifiable parameters by global sensitivity analysis” section. Second, except step 1, the training and test samples, which are denoted as \({\varvec{x}}|\Theta \setminus (\Theta _1\cup \cdots \cup \Theta _{n-1})\), are transformed by the well-trained PELS-VAE model. Third, \({\widetilde{\Theta }}_n\) is filtered by trial inference. At last, the parameter set \(\Theta _n\) can be identified by training a BayesFlow model. Further details are shown in Algorithm 2 in “Iterative parameter identification and data generation” section