Towards a population-informed approach to the definition of data-driven
  models for structural dynamics
G. Tsialiamanis N. Dervilis D. J. Wagg K. Worden
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.