Committor-Regularized Learning of Differentiable Collective Variables from Non-Differentiable Structural Descriptors

Collective variables (CVs) are essential for interpreting and accelerating rare events in molecular simulations. However, their design remains limited by the requirement of differentiability with respect to atomic coordinates. This constraint excludes many powerful structural descriptors that are routinely used for analysis, but are unsuitable for biasing. Here, we introduce a physics-informed machine learning framework that transforms such non-differentiable descriptors into fully differentiable, bias-ready collective variables. The approach leverages graph neural networks to train differentiable surrogates of discontinuous descriptors while preserving their structural interpretability. To ensure physically meaningful interpolation between metastable states, we propose Committor Regularization —a theoretically motivated constraint derived from transition path theory that guides learning toward committor-like behavior. Applied to crystal nucleation in a supercooled metal melt, this framework yields reproducible free-energy surfaces across independently trained models, resolving the inherent issues of stochastic variability in machine-learned CVs. By bridging discrete physics-based descriptors and continuous differentiable representations, our method establishes a general route to reproducible, interpretable, and physically grounded collective variables for biased enhanced sampling.