Neural Operators for Stochastic Modeling of Nonlinear Structural System Response to Natural Hazards

TL;DR

This paper explores neural operators, specifically DeepONet and FNO, to efficiently predict the stochastic nonlinear response of structures to natural hazards, achieving high accuracy and speed over traditional models.

Contribution

It introduces two novel neural operator architectures, a self-adaptive FNO and DeepFNOnet, for modeling stochastic nonlinear structural responses to natural hazards.

Findings

High accuracy in predicting seismic and wind responses.

Models are significantly faster than high-fidelity simulations.

Effective handling of stochastic natural hazard inputs.

Abstract

Traditionally, neural networks have been employed to learn the mapping between finite-dimensional Euclidean spaces. However, recent research has opened up new horizons, focusing on the utilization of deep neural networks to learn operators capable of mapping infinite-dimensional function spaces. In this work, we employ two state-of-the-art neural operators, the deep operator network (DeepONet) and the Fourier neural operator (FNO) for the prediction of the nonlinear time history response of structural systems exposed to natural hazards, such as earthquakes and wind. Specifically, we propose two architectures, a self-adaptive FNO and a Fast Fourier Transform-based DeepONet (DeepFNOnet), where we employ a FNO beyond the DeepONet to learn the discrepancy between the ground truth and the solution predicted by the DeepONet. To demonstrate the efficiency and applicability of the architectures, two problems are considered. In the first, we use the proposed model to predict the seismic nonlinear dynamic response of a six-story shear building subject to stochastic ground motions. In the second problem, we employ the operators to predict the wind-induced nonlinear dynamic response of a high-rise building while explicitly accounting for the stochastic nature of the wind excitation. In both cases, the trained metamodels achieve high accuracy while being orders of magnitude faster than their corresponding high-fidelity models.