Gaussian process metamodeling for experiments with manipulating factors
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This paper presents a new Gaussian process (GP) metamodeling approach for predicting the outcome of a physical experiment for a given input factor setting where some of the input factors are controlled by other manipulating factors. Particularly, we study the case where the control precision is not very high, so the input factor values vary significantly even under the same setting of the corresponding manipulating factors. Due to this variability, the standard GP metamodeling that directly relates the manipulating factors to the experimental outcome does not provide a great predictive power on the outcome. At the same time, the GP model relating the main factors to the outcome directly is not appropriate for the prediction purpose because the main factors cannot be accurately set as planned for a future experiment. We propose a two-tiered GP model, where the bottom tier relates the manipulating factors to the corresponding main factors with potential biases and variability, and the top tier relates the main factors to the experimental outcome. Our two-tier model explicitly models the propagation of the control uncertainty to the experimental outcome through the two GP modeling tiers. We present the inference and hyper-parameter estimation of the proposed model. The proposed approach is tested on a motivating example of a closed-loop autonomous research system for carbon nanotube growth experiments, and the test results are reported with the comparison to a benchmark method, i.e. a standard GP model.
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