Machine learning has affected the way in which many phenomena for various domains are modelled, one of these domains being that of structural dynamics. However, because machine-learning algorithms are problem-specific, they often fail to perform efficiently in cases of data scarcity. To deal with such issues, combination of physics-based approaches and machine learning algorithms have been developed. Although such methods are effective, they also require the analyser's understanding of the underlying physics of the problem. The current work is aimed at motivating the use of models which learn such relationships from a population of phenomena, whose underlying physics are similar. The development of such models is motivated by the way that physics-based models, and more specifically finite element models, work. Such models are considered transferrable, explainable and trustworthy, attributes which are not trivially imposed or achieved for machine-learning models. For this reason, machine-learning approaches are less trusted by industry and often considered more difficult to form validated models. To achieve such data-driven models, a population-based scheme is followed here and two different machine-learning algorithms from the meta-learning domain are used. The two algorithms are the model-agnostic meta-learning (MAML) algorithm and the conditional neural processes (CNP) model. The algorithms seem to perform as intended and outperform a traditional machine-learning algorithm at approximating the quantities of interest. Moreover, they exhibit behaviour similar to traditional machine learning algorithms (e.g. neural networks or Gaussian processes), concerning their performance as a function of the available structures in the training population.

翻译：机器学习已影响了诸多领域现象建模的方式，结构动力学即为其中之一。然而，由于机器学习算法具有问题特定性，在数据稀缺情况下往往难以高效运行。为应对此类问题，物理驱动方法与机器学习算法的结合策略已被开发。尽管这些方法有效，但仍需分析人员对问题底层物理机制的理解。本研究旨在推动从具有相似底层物理机制的现象群体中学习关系的模型应用。此类模型的开发受物理模型（尤其是有限元模型）工作方式的启发。这类模型被认为具有可迁移性、可解释性和可信赖性，而这些属性对机器学习模型而言难以简单赋予或实现。正因如此，工业界对机器学习方法的信任度较低，并认为其更难形成经过验证的模型。为实现此类数据驱动模型，本文采用基于群体的方案，并从元学习领域选取两种不同机器学习算法，即模型无关元学习算法与条件神经过程模型。该算法运行符合预期，在近似目标量方面优于传统机器学习算法。此外，其性能随训练群体中可用结构数量变化的特征，与传统机器学习算法（如神经网络或高斯过程）表现相似。