ROADEF 2026 - Tours, France - February 24, 2026. Sampling methods for probabilistic approximations of ODEs

These slides were presented at ROADEF 2026 in Tours, France. The work addresses parameter estimation in biochemical reaction networks modeled by ODEs. We rely on a Dynamic Bayesian Network (DBN) approximation to reduce repeated ODE simulations and quantify uncertainty, but the quality of the DBN strongly depends on how the state space is discretized and sampled. Low-discrepancy sequences (e.g., Halton) may lead to uneven coverage of discrete regions, introducing bias in the conditional probability tables. We therefore propose a structured enumerative sequence that guarantees uniform coverage of the discretized state space. On a 7-dimensional enzyme-catalyzed reaction model, the enumerative strategy yields lower median MSE and fewer outliers than Halton sampling, leading to more accurate and stable parameter estimation.