Contrastive Regularization of Machine Learning Potentials

Machine learning interatomic potentials are trained to predict energies and forces but built to be sampled: their purpose is to drive molecular simulations whose observables average over the equilibrium distribution the potential defines.

They exemplify a broader AI problem -- learned regressors deployed as generators -- where pointwise accuracy does not guarantee a correct distribution.

We show that potentials trained by standard Mean Squared Error (MSE) minimization on Density Functional Theory (DFT) data can reach chemical accuracy on held-out data, yet still fail as samplers: their trajectories drift into spurious low-energy minima and return thermodynamic observables that depart sharply from the reference.

To correct this, we introduce Contrastive Regularized MSE (CRMSE), a post-training step that augments the MSE with a contrastive term derived from the Kullback--Leibler divergence between the potential's implicit Boltzmann distribution and the target.

The network serves as its own energy-based model: persistent Langevin chains expose the configurations it drifts into and raise their energy, adding no new ab initio data.

On the ethanol and aspirin molecules of the MD17 dataset, CRMSE confines the sampler to the physical basin and recovers the energy distribution, interatomic-distance distributions, and dihedral free-energy profiles to near-quantitative agreement with DFT, while preserving force accuracy and keeping energy errors within chemical accuracy; it remains effective when the training set is sharply reduced.

That MSE training fails this way on MD17 -- one of the most widely used benchmarks -- while a minimal contrastive correction repairs it suggests that reliable sampling depends less on data volume than on training the model against the distribution it produces: distribution-level training is not a refinement of regression accuracy, but a distinct requirement.