Ordinary differential equations (ODE) are used to model dynamical systems, notably in biology and biochemistry.

In such systems, the estimation of parameters from experimental data is a central challenge, with applications such as drug discovery or clinical diagnosis.

Liu B. et al. proposed to transform ODEs into dynamic Bayesian networks (DBN) to speed up cost function calculations, limit repeated ODEs simulations, and quantify the uncertainty on states and parameters, obtaining better results than classical optimization techniques for systems with about 25 variables.

The construction of a DBN requires to discretize the state space and generate a training data set (a set of many ODE simulations) to fill the conditional probability tables (CPT). Low-discrepancy sequences, like those of Halton, used previously, do not guarantee good coverage of discrete intervals, certain regions of space being under-represented. This can bias the tables of the DBN and affect the quality of the probabilistic approximation.

In this paper, we propose a structured enumerative sequence ensuring uniform coverage of discrete intervals, allowing more representative tables and a better probabilistic approximation of the dynamic system by the DBN.