Generating Adsorption Equations Using Symbolic Regression

Adsorption is relevant to a wide variety of chemical engineering problems from gas separation, pollutant treatment, and catalysis. Adsorption isotherms relate the amount adsorbed at equilibrium as a function of pressure or concentration, and are commonly expressed as equations which are either empirical or derived from theory. While several equations for adsorption have been proposed in the literature, we wonder how many more we could find. Symbolic regression is a machine learning technique that searches a space of mathematical expressions to find those that best fit a given dataset.

In this work, we use a Bayesian symbolic regression technique to analyze adsorption datasets and generate accurate and plausible adsorption isotherm expressions. Notably, we consider the effect of including prior knowledge of thermodynamic constraints to narrow the search space to find our desired model. The first thermodynamic constraint requires the loading on the surface to be 0 when the pressure is 0. The second constraint requires the adsorption isotherm to converge to Henry’s Law when approaching a pressure of 0, which means that at low pressure, the limiting slope of the adsorption isotherm must be finite. We compare this technique to a genetic algorithm-based symbolic regression method that doesn’t include this prior knowledge in the search. We show that we can use Bayesian symbolic regression to rediscover many common adsorption equations from experimental data, including the Langmuir and two-site Langmuir equations.