Abstract
Constructing free-energy landscapes without prior knowledge of their structure often requires dense sampling of the configuration space, leading to prohibitive computational costs. Here, we introduce an efficient graph-based active-learning framework that adaptively constructs free-energy landscapes while preserving the connectivity required for free-energy determination. The method employs a Gaussian-process surrogate to identify informative configurations and connects each newly sampled set of points to the existing sampled region through a shortest-path search on a graph, enabling efficient, connected exploration required for accurate free-energy determination. We validate the framework using analytical two-and three-dimensional model energy landscapes as well as a many-body free-energy landscape derived from molecular dynamics simulations of polymer-grafted nanoparticles in a polymer melt. Across all cases, the method accurately recovers the multidimensional landscape at much lower effective sampling cost than dense or predetermined grid-based sampling, with sampling efficiency quantified by the cumulative length of the connected sampling tree constructed during active learning. More broadly, this work establishes a general framework for data-efficient exploration of high-dimensional free-energy landscapes in molecular and materials simulations.