Abstract Numerical modelling is considered a standard tool for problem-solving in modern engineering. Based on various mechanisms, researchers have developed a collection of numerical models to simulate a complex system’s responses and provide forecasts for future physical conditions. However, deviations between the performance of each single model and real-world observations always exist. A man-machine model (MMM) is proposed for more accurate predictions based on multi-model ensembles. In the MMM, the man part reflects the usage of human-designed numerical models, and the machine part represents the application of machine learning algorithms. The MMM is depicted by a three-layered framework: an input layer loaded with simulations and target observations, a hidden layer composed of optimal factors, and an output layer that delivers approximations and forecasts. First, exploratory factor analysis is utilized to extract candidate factors from a variety of numerical models. Subsequently, an adjusted “General to Specific” rule is applied to select optimal factors in the process of best fitting the principal components of observations. Thereafter, the MMM is used to deliver a pattern recognition algorithm involving a Linear-Gaussian kernel function projecting the hidden layer to the observations. A case study of a beam loading test shows that the MMM is successful in giving robust predictions of deformation on testing data and avoids overfitting.

中文翻译：

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人机模型：多模型集成监督下复杂结构的模式识别和预测

摘要 数值建模被认为是现代工程中解决问题的标准工具。基于各种机制，研究人员开发了一系列数值模型来模拟复杂系统的响应并为未来的物理条件提供预测。然而，每个单一模型的性能与现实世界的观察结果之间始终存在偏差。提出了一种人机模型 (MMM)，用于基于多模型集成进行更准确的预测。在 MMM 中，man 部分反映了人为设计的数值模型的使用，machine 部分代表了机器学习算法的应用。MMM 由一个三层框架描述：一个加载了模拟和目标观察的输入层，一个由最优因素组成的隐藏层，以及提供近似值和预测的输出层。首先，利用探索性因子分析从各种数值模型中提取候选因子。随后，应用调整后的“一般到具体”规则来选择最佳因素，以最佳拟合观测的主成分。此后，MMM 用于提供一种模式识别算法，该算法涉及将隐藏层投影到观测值的线性高斯核函数。梁加载测试的案例研究表明，MMM 成功地对测试数据的变形进行了可靠的预测，并避免了过度拟合。应用调整后的“一般到具体”规则来选择最佳因素，以最佳拟合观测的主成分。此后，MMM 用于提供一种模式识别算法，该算法涉及将隐藏层投影到观测值的线性高斯核函数。梁加载测试的案例研究表明，MMM 成功地对测试数据的变形进行了可靠的预测，并避免了过度拟合。应用调整后的“一般到具体”规则来选择最佳因素，以最佳拟合观测的主成分。此后，MMM 用于提供一种模式识别算法，该算法涉及将隐藏层投影到观测值的线性高斯核函数。梁加载测试的案例研究表明，MMM 成功地对测试数据的变形进行了可靠的预测，并避免了过度拟合。