  We introduce an explorative active learning (AL) algorithm based on Gaussian
process regression and marginalized graph kernel (GPR-MGK) to explore chemical
space with minimum cost. Using high-throughput molecular dynamics simulation to
generate data and graph neural network (GNN) to predict, we constructed an
active learning molecular simulation framework for thermodynamic property
prediction. In specific, targeting 251,728 alkane molecules consisting of 4 to
19 carbon atoms and their liquid physical properties: densities, heat
capacities, and vaporization enthalpies, we use the AL algorithm to select the
most informative molecules to represent the chemical space. Validation of
computational and experimental test sets shows that only 313 (0.124\% of the
total) molecules were sufficient to train an accurate GNN model with $\rm R^2 >
0.99$ for computational test sets and $\rm R^2 > 0.94$ for experimental test
sets. We highlight two advantages of the presented AL algorithm: compatibility
with high-throughput data generation and reliable uncertainty quantification.
