On the reproducibility of free energy surfaces in machine-learned collective variable spaces

As Machine-Learned Collective Variables (MLCVs) are becoming increasingly relevant in the molecular simulation literature, we discuss the necessary conditions to enable reproducibility in calculating and representing free energy surfaces. We note that the variability of the training process and the roughness of the hyperparameter space impose inherent limits on the reproducibility of results even when the mathematical structure of the model defining a collective variable is consistent. To this end, we propose the adoption of a geometric (gauge invariant) free energy representation to obtain consistent free energy differences across training instances and architectures. Furthermore, we introduce a normalization factor to model gradients for biased enhanced sampling. This factor effectively unifies free energy definitions and addresses practical issues preventing the widespread use and deployment of MLCVs.