Fig. 1

Example: a Biphenyl in 2D. b Simulated energy landscape under MMFF94. The blue line and the shaded blue region in c–f represent the mean function of the Gaussian process and express the uncertainty of the function respectively. The red points are the evaluated points. The red curve at the bottom of the graph shows the acquisition function, in particular expected improvement (EI) is used in this example. The red vertical line indicates the highest value of the EI, i.e. the point to be evaluated next. Note that the we normalized the output (energy) in Bayesian optimization algorithm, hence the normalized energy landscape is shown in c–f. c Second iteration, d third iteration, e fourth iteration, f final iteration