(659h) Prospects for Solving Micro-Kinetic Models with Automatic Differentiation and Regression

Micro-kinetic models provide a link between the molecular-scale mechanism of a catalytic reaction and the macro-scale observation of catalytic activity, and are central to computational catalysis. Micro-kinetic models commonly employ the mean-field approximation, which results in a series of coupled ordinary differential equations (ODE's). These ODE's are typically solved under simplifying assumptions such as a single rate-limiting step, or a quasi-steady state; the resulting equations are typically solved through standard numerical techniques such as finite differences or root finding. While these approaches provide valid solutions, each different approximation requires a different solution method. Similarly, coupling the micro-kinetic models to reactor models or including more complex rate constant expressions often requires substantial changes to the solution approach. Furthermore, the resulting numerical solutions are difficult to integrate with parameter fitting or uncertainty estimates. In this talk a different approach to solving micro-kinetic models will be introduced. This approach utilizes a combination of automatic differentiation and non-linear regression in order to establish a continuous function that approximates the solution to the micro-kinetic model. The approach is flexible, and the same basic framework can be used to solve the model with various types of approximations, including with constraints on parameter values; furthermore, the resulting solution is easily differentiable with respect to parameters, facilitating sensitivity analyses and parameter fitting. The approach is demonstrated for several model systems and strengths and weaknesses compared to traditional numerical techniques are discussed.