# Parameter estimation of structural dynamics with neural operators enabled surrogate modeling

arXiv: https://arxiv.org/abs/2410.11712 · HTML: https://mlsanity.com/paper/2410.11712/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Oct 2024.

## Built on by (most cited first, 3 of 3)

- [Estimating Parameter Fields in Multi-Physics PDEs from Scarce Measurements](https://mlsanity.com/paper/2509.00203/) (2025)
- [Deep Learning-Based Metamodeling of Nonlinear Stochastic Dynamic Systems under Parametric and Predictive Uncertainty](https://mlsanity.com/paper/2603.12012/) (2026)
- [Adaptive Distance-Aware Trunk Deep Operator Learning for Long-Span Roadway Bridges](https://mlsanity.com/paper/2606.20015/) (2026)

## Abstract (arXiv)

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.