Metamodeling of nonlinear stochastic dynamic systems with hybrid neural operator schemes

In evaluating high-dimensional, nonlinear, and dynamic structural systems subjected to extreme natural hazards, incorporating uncertainty remains a challenging computational task.Recent advancements in neural networks as metamodeling techniques have shown promise in addressing this issue, yet significant hurdles persist.First, traditional neural networks are fundamentally designed to map finite-dimensional vector spaces, while dynamic structural systems inherently exist in infinite-dimensional function spaces characterized by continuous temporal and spatial variations.Consequently, conventional architectures often struggle to capture the complex behaviors of such systems over time histories and exhibit limited generalization outside their training distribution.Second, many existing approaches, including physics-informed machine learning frameworks, fail to guarantee that predicted solutions during inference strictly adhere to essential physical constraints, reducing their reliability for practical applications.This study presents a novel framework that integrates neural operators-an emerging machine learning paradigm designed to learn mappings between infinitedimensional function spaces-with traditional numerical methods such as the Newmark-beta scheme.The framework's effectiveness is validated through its application to a steel moment-resisting frame subjected to stochastic seismic loads.Results demonstrate that the proposed approach achieves high accuracy and considerable computational speed-up compared to traditional numerical methods.