Realizing Reduced and Sparse Biochemical Reaction Networks from Dynamics

We propose a direct optimization framework for learning reduced and sparse chemical reaction networks (CRNs) from time-series trajectory data. In contrast to widely used indirect methods—such as those based on sparse identification of nonlinear dynamics (SINDy)—which infer reaction dynamics by fitting numerically estimated derivatives, our approach fits entire trajectories by solving a dynamically constrained optimization problem. This formulation enables the construction of reduced CRNs that are both low-dimensional and sparse, while preserving key dynamical behaviors of the original system. We develop an accelerated proximal gradient algorithm to efficiently solve the resulting non-convex optimization problem. Through illustrative examples, including a Drosophila circadian oscillator and a glycolytic oscillator, we demonstrate the ability of our method to recover accurate and interpretable reduced-order CRNs. Notably, the direct approach avoids the derivative estimation step and mitigates error accumulation issues inherent in indirect methods, making it a robust alternative for data-driven CRN realizations.