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.

通过基于物理的方法和元学习算法开发适应于数据稀缺性问题的模型，为解决机器学习算法的不足和工业界对其不信任问题提供了一种可行的方案。

走向以人口信息为基础的结构动力数据驱动模型定义方法

Towards a population-informed approach to the definition of data-driven  models for structural dynamics

In this paper we demonstrate a new technique for deriving discrete adjoint
and tangent linear models of finite element models. The technique is
significantly more efficient and automatic than standard algorithmic
differentiation techniques. The approach relies on a high-level symbolic
representation of the forward problem. In contrast to developing a model
directly in Fortran or C++, high-level systems allow the developer to express
the variational problems to be solved in near-mathematical notation. As such,
these systems have a key advantage: since the mathematical structure of the
problem is preserved, they are more amenable to automated analysis and
manipulation. The framework introduced here is implemented in a freely
available software package named dolfin-adjoint, based on the FEniCS Project.
Our approach to automated adjoint derivation relies on run-time annotation of
the temporal structure of the model, and employs the FEniCS finite element form
compiler to automatically generate the low-level code for the derived models.
The approach requires only trivial changes to a large class of forward models,
including complicated time-dependent nonlinear models. The adjoint model
automatically employs optimal checkpointing schemes to mitigate storage
requirements for nonlinear models, without any user management or intervention.
Furthermore, both the tangent linear and adjoint models naturally work in
parallel, without any need to differentiate through calls to MPI or to parse
OpenMP directives. The generality, applicability and efficiency of the approach
are demonstrated with examples from a wide range of scientific applications.

本文提出了新的技术，通过高层次的符号表示法实现了有限元模型的离散伴随和正切线性模型的推导，相比于标准的算法区分技术，该方法更加高效和自动化，适用于一类大规模和复杂的前向模型，并在各种科学应用中证明了其普遍性和适用性。