Accelerating Metadynamics-Based Free-Energy Calculations with Adaptive Machine Learning Potentials

There is an increasing demand for free-energy calculations using ab initio molecular dynamics these days. Metadynamics (MetaD) is frequently utilized to reconstruct the free-energy surface, but it is often computationally intractable for the first-principles calculations. Machine learning potentials (MLPs) have become popular alternatives. However, the training could be a long and arduous process before using them in practical applications. To accelerate MetaD use with MLPs for the free-energy calculation in an easy manner, we propose the adaptive machine learning potential-accelerated metadynamics (AMLP-MetaD). In this method, the MLP in the form of a Gaussian approximation potential (GAP) can adapt itself based on its uncertainty estimation, which decides whether to accept the model prediction or recalculate it with a reference method (usually density functional theory) for further training during the MetaD simulation. We demonstrate that the free-energy landscape similar to the ab initio one can be obtained using AMLP-MetaD with a 10-time speedup. Moreover, the quality of the free-energy results can be deeply improved using Δ-MLP, which is the GAP-corrected density functional tight binding in our case. We exemplify this novel method with two model systems, CO adsorption on the Pt₁₃ cluster and the Pt(111) surface, which are of vital importance in heterogeneous catalysis. The successful application in these two tests highlights that our proposed method can be used in both cluster and periodic systems and for up to two collective variables.