Multi-objective optimization techniques to design the Pareto front of organic dielectric polymers

We present two Monte Carlo algorithms to find the Pareto front of the chemical space of a class of dielectric polymers that is most interesting with respect to optimizing both the bandgap and dielectric constant. Starting with a dataset generated from density functional theory calculations, we used machine learning to construct surrogate models for the bandgaps and dielectric constants of all physically meaningful 4-block polymers (that is, polymer systems with a 4-block repeat unit). We parameterized these machine learning models in such a way that the surrogates built for the 4-block polymers were readily extendable to polymers beyond a 4-block repeat unit. By using translational invariance, chemical intuition, and domain knowledge, we were able to enumerate all possible 4, 6, and 8 block polymers and benchmark our Monte Carlo sampling of the chemical space against the exact enumeration of the surrogate predictions. We obtained exact agreement for the fronts of 4-block polymers and at least a 90% agreement for those of 6 and 8-block polymers. We present fronts for 10-block polymer that are not possible to obtain by direct enumeration. We note that our Monte Carlo methods also return polymers close to the predicted front and a measure of the closeness. Both quantities are useful information for the design and discovery of new polymers.