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.