(199f) Learning Kinetic Models from Data Using a Derivative-Free Sparse Identification Method and Domain Information

Developing data-driven kinetic models from reaction data is valuable to infer the underlying reaction mechanism and design reactive processes without needing first-principles models. Many recently developed techniques to learn interpretable dynamical models from data, such as SINDy, use numerical approximation techniques such as finite difference to approximate derivatives. The accuracy of the models obtained from such methods can be compromised when data is noisy, as is often the case with experimental kinetics data.

To overcome this limitation, in this research, we propose to: (1) build an alternative method that learns a sparse model similar to SINDy but without requiring derivatives of the measured states; (2) incorporate domain information. The derivative-free SINDy, DF-SINDy, integrates the library of basis functions using interpolation and then minimizes the errors on measurements rather than their derivatives while keeping the problem convex in parameter space. In the context of chemical reaction networks, we propose three different formulations of DF-SINDy, viz., 1) the naïve (unconstrained) formulation, 2) mass balance formulation where the mass of all species involved is always conserved, and 3) chemistry formulation where we specify plausible chemical reactions. To illustrate this method, we consider a retrospective study by synthesizing noisy data from a known model and recovering models based on the aforementioned three formulations. We show that the derivative-free method is, in general, more robust than the naïve SINDy, while inclusion of domain information leads to better recovery in the presence of nonidealities such as noisy or limited data. Finally, we show the extensions of this method to cases where we explicitly consider the temperature-dependency of kinetics in isothermal and non-isothermal experiments.