Parameter estimation of structural dynamics with neural operators enabled surrogate modeling

2024-10-15

arXiv.org

AI Summary

In structural dynamics, physics- or expert knowledge–driven inversion of complex system parameters—such as geometry and material properties—is hindered by severe ill-posedness and poor generalization. To address this, we propose the first differentiable neural operator–driven parameter estimation framework tailored for structural dynamics. Our method employs forward-differentiable neural operators (e.g., Fourier Neural Operators or DeepONets) to construct high-fidelity surrogate models and introduces a novel two-stage inversion mechanism: gradient-guided initial estimation followed by end-to-end neural refinement, integrated with physics-informed training. This design substantially mitigates ill-posedness and ensures robust performance in both interpolation and extrapolation tasks. Numerical experiments and physical validation demonstrate over 40% reduction in extrapolation error, alongside superior accuracy and stability compared to conventional approaches. The framework enables diverse engineering applications, including structural identification, damage detection, and inverse design.

Technology Category

• Machine Learning: Structured Learning
• Intelligent Robots: State Estimation
• Search and Optimization: Sampling/Simulation-based Search

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

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.

Problem

• Estimating structural dynamics parameters using neural operators
• Developing a flexible deep learning framework for forward and inverse modeling
• Improving parameter estimation accuracy with gradient-based optimization and neural refinement

Innovation

• Neural operator surrogate modeling for dynamics
• Differentiable surrogate enables gradient optimization
• Neural refinement mitigates ill-posed inverse problems