Parameter estimation of structural dynamics with neural operators enabled surrogate modeling

TL;DR

This paper introduces a deep learning framework using neural operators for flexible parameter estimation, forward response prediction, and inverse modeling in structural dynamics, enhancing accuracy and robustness in complex systems.

Contribution

It presents a unified neural operator-based approach for both forward and inverse modeling of structural dynamics, including a neural refinement method for improved parameter estimation.

Findings

Effective in both interpolation and extrapolation scenarios

Accurately captures intrinsic structural dynamics

Supports diverse applications like damage detection and inverse design

Abstract

Parameter estimation in structural dynamics generally involves inferring the values of physical, geometric, or even customized parameters based on first principles or expert knowledge, which is challenging for complex structural systems. In this work, we present a unified deep learning-based framework for parameterization, forward modeling, and inverse modeling of structural dynamics. The parameterization is flexible and can be user-defined, including physical and/or non-physical (customized) parameters. In the forward modeling, we train a neural operator for response prediction -- forming a surrogate model, which leverages the defined system parameters and excitation forces as inputs to the model. The inverse modeling focuses on estimating system parameters. In particular, the learned forward surrogate model (which is differentiable) is utilized for preliminary parameter estimation via gradient-based optimization; to further boost the parameter estimation, we introduce a neural refinement method to mitigate ill-posed problems, which often occur in the former. The framework's effectiveness is verified numerically and experimentally, in both interpolation and extrapolation cases, indicating its capability to capture intrinsic dynamics of structural systems from both forward and inverse perspectives. Moreover, the framework's flexibility is expected to support a wide range of applications, including surrogate modeling, structural identification, damage detection, and inverse design of structural systems.