Globally Approximate Gaussian Processes for Big Data With Application to Data-Driven Metamaterials Design
Globally Approximate Gaussian Processes for Big Data With Application to Data-Driven Metamaterials Design
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DOI：
10.1115/1.4044257
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发表时间：
2019-09
影响因子：
3.3
通讯作者：
R. Bostanabad;Yu-Chin Chan;Liwei Wang;P. Zhu;Wei Chen
中科院分区：
文献类型：
--
作者：
R. Bostanabad;Yu-Chin Chan;Liwei Wang;P. Zhu;Wei Chen
介绍了一种新的海量数据集高斯过程建模方法--全局近似高斯过程（GAGP）。与大多数大规模监督学习器（如神经网络和树）不同，GAGP易于拟合，并且可以解释模型行为，这使得它在大数据的工程设计中特别有用。GAGP的核心思想是建立一个独立的GP集合，这些GP使用相同的超参数，但随机分布整个训练数据集。这是基于我们的观察，即当训练数据的大小超过一定水平时，GP超参数近似值的变化可以忽略不计，这可以系统地估计。对于推理，集合中所有GP的预测都被合并，从而允许整个训练数据集被有效地用于预测。通过分析示例，我们证明了GAGP实现了非常高的预测能力匹配（在某些情况下超过）最先进的监督学习方法。以数据驱动的超材料为例，说明了GAGP在工程设计中的应用，用它来连接单元格的降维几何描述符及其属性。搜索新的单位单元设计所需的性能，然后实现采用GAGP在逆优化。
We introduce a novel method for Gaussian process (GP) modeling of massive datasets called globally approximate Gaussian process (GAGP). Unlike most large-scale supervised learners such as neural networks and trees, GAGP is easy to fit and can interpret the model behavior, making it particularly useful in engineering design with big data. The key idea of GAGP is to build a collection of independent GPs that use the same hyperparameters but randomly distribute the entire training dataset among themselves. This is based on our observation that the GP hyperparameter approximations change negligibly as the size of the training data exceeds a certain level, which can be estimated systematically. For inference, the predictions from all GPs in the collection are pooled, allowing the entire training dataset to be efficiently exploited for prediction. Through analytical examples, we demonstrate that GAGP achieves very high predictive power matching (and in some cases exceeding) that of state-of-the-art supervised learning methods. We illustrate the application of GAGP in engineering design with a problem on data-driven metamaterials, using it to link reduced-dimension geometrical descriptors of unit cells and their properties. Searching for new unit cell designs with desired properties is then achieved by employing GAGP in inverse optimization.