Derivative-Free Domain-Informed Data-Driven Discovery of Sparse Kinetic Models

Developing data-driven kinetic models from reaction data is valuable for inferring the underlying reactions and designing reactive processes without needing first-principles models. However, recently developed techniques to learn interpretable dynamical models from data are susceptible to inherent experimental noise, especially in reaction kinetics data. Here, we address these issues by (1) employing a new derivative-free technique for sparse identification of dynamical equations that approximates the integral rather than the derivative (which we call as <i>DF-SINDy</i>) and (2) including domain information such as mass balance and chemistry information. We demonstrate this using retrospective examples to recover the true (known) governing equations from synthetic data under varying noise levels, sampling frequencies, and number of experiments. We observe that (1) models discovered from <i>DF-SINDy</i> have lower errors than those discovered from <i>SINDy</i> (Proc. Natl. Acad. Sci. U.S.A.2016, 113, 3932-3937, DOI: 10.1073/pnas.1517384113) and (2) adding domain knowledge further helps recover correct terms, thereby improving the reliability of the interpretations obtained from these models. This work is chemistry agnostic and represents a step toward developing domain-informed interpretable kinetic models for complex reaction networks.