Fig. 7: Illustration of the steps within a single iteration of the TVR-EI algorithm applied to a three-fidelity problem.
From: A multi-fidelity machine learning approach to high throughput materials screening
a–f Show the 6 stages of the algorithm. Within each panel the top (blue) plots refer to the ground truth fidelity whilst the middle (green) and lower (orange) plots refer to the two approximate fidelities. a, b Show a set of initial data points (a) used to train a Bayesian model and the posterior predictions of that Bayesian model (b) juxtaposed against the reference fidelity functions (dashed lines). c Shows the Expected Improvement acquisition function applied to the high fidelity posterior used to discover the optimal high fidelity point which is highlighted with a dashed blue line. d Shows the posterior squared correlation between the identified optimal high fidelity point (location shown again with the dashed blue line) and points within the domain for the three different fidelities. e Shows the final scoring function which is a scaled version of d that takes into account the cost of evaluating the different fidelities and shows the highest scoring point chosen (shown with a dashed green line) which in this case is within the second fidelity. f Shows the new set of data points after evaluating the highest scoring point (indicated with the green circle).
