Data and Computation Efficient Structural Nonlinear System Identification via Meta-Learning of a Foundation Model

Structural nonlinear system identification (NSI) through data-driven approaches has become indispensable in scenarios where prior physical knowledge proves inadequate for first-principle modeling. Unlike white-box methodologies that rely on comprehensive domain knowledge and physical insights, black-box methods demand minimal prior understanding of system physics. However, this advantage comes with dual challenges: (1) substantial data requirements that conflict with practical constraints in structural engineering, where data acquisition is often costly and sparse; and (2) computational intensiveness arising from nonlinear optimization processes inherent to NSI, leading to extended convergence times. These intertwined challenges of data efficiency and computational efficiency critically hinder practical implementations of data-driven structural NSI. This study proposes a metalearning-enhanced framework to address these fundamental limitations. Our framework integrates a deep neural network for autonomous discovery of nonlinear transient dynamics with a metalearning algorithm that systematically extracts transferable identification knowledge from diverse structural systems. The metalearning component develops a cross-structure foundation model providing the initial parameters that serve as a strong starting point for rapid adaptation to new target structural systems through few-shot learning. Numerical simulations are performed to validate the method on shear-type multiple-degree-of-freedom nonlinear systems created based on an IASC-ASCE benchmark structure. Furthermore, laboratory experiments of a nonlinear beam and numerical simulations of different nonlinear beams are conducted to demonstrate a potential application example of the proposed method: leveraging abundant numerical models/data of different virtual structures to improve data and computation efficiency of the data-driven NSI of real structures, whose data acquisition is relatively difficult or scarce. It is observed that the presented metalearning-based method outperforms the conventional data-driven method without metalearning in terms of both data and computation efficiency. The applicability and limitations of this method are also discussed.