Title: Gaussian process surrogate modeling with manipulating factors for carbon nanotube growth experiments Show Chinese title

Title: 高斯过程代理建模在碳纳米管生长实验中的操纵因素

Abstract: This paper presents a new Gaussian process (GP) surrogate modeling for predicting the outcome of a physical experiment where some experimental inputs are controlled by other manipulating factors. Particularly, we are interested in 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. The case is observed in our main application to carbon nanotube growth experiments, where one experimental input among many is manipulated by another manipulating factors, and the relation between the input and the manipulating factors significantly varies in the dates and times of operations. Due to this variation, the standard GP surrogate 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. Motivated by the carbon nanotube example, we propose a two-tiered GP model, where the bottom tier relates the manipulating factors to the corresponding main factors with potential biases and variation independent of the manipulating factors, 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 illustrated with the 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. Show Chinese abstract

Abstract: 本文提出了一种新的高斯过程（GP）代理建模方法，用于预测物理实验的结果，其中一些实验输入由其他操控因素控制。 特别地，我们关注的是控制精度不高的情况，因此即使在相同的操作因子设定下，输入因子值也会显著变化。 这种情况在我们的主要应用——碳纳米管生长实验中被观察到，在这些实验中，许多实验输入中的一个是由其他操作因子操控的，并且输入与操作因子之间的关系在操作日期和时间上显著变化。 由于这种变化，直接将操作因子与实验结果关联的标准GP代理无法很好地预测结果。 同时，将主因子直接与结果关联的GP模型也不适合预测目的，因为主因子不能像计划那样准确设置以适应未来的实验。 受碳纳米管实例的启发，我们提出了一个两级GP模型，其中底层将操作因子与相应的主因子（带有潜在偏差和独立于操作因子的变化）关联起来，顶层将主因子与实验结果关联起来。 我们的两级模型明确地通过两个GP建模层来建模控制不确定性向实验结果的传播。 我们介绍了所提出模型的推理和超参数估计。 该方法通过碳纳米管生长实验闭环自主研究系统的动机示例进行了说明，并与基准方法（即标准GP模型）进行了比较并报告了测试结果。