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The fitting of physical models is often done only using a single targetobservable. However, when multiple targets are considered, the fittingprocedure becomes cumbersome, there being no easy way to quantify therobustness of the model for all different observables. Here, we illustrate thatone can jointly search for the best model for each desired observable throughmulti-objective optimization. To do so we construct the Pareto front to studyif there exists a set of parameters of the model that can jointly describemultiple, or all, observables. To alleviate the computational cost, thepredicted error for each targeted objective is approximated with a Gaussianprocess model, as it is commonly done in the Bayesian optimization framework.We applied this methodology to improve three different models used in thesimulation of stationary state $cis-trans$ photoisomerization of retinal inrhodopsin. Optimization was done with respect to different experimentalmeasurements, including emission spectra, peak absorption frequencies for the$cis$ and $trans$ conformers, and the energy storage.

Multi-objective optimization for retinal photoisomerization models with respect to experimental observables