Symbolic Neural Networks for Surrogate Modeling of Structures

Abstract

In order to evaluate urban earthquake resilience, reliable structural modeling is needed. However, detailed modeling of a large number of structures and carrying out time history analyses for sets of ground motions are not practical at an urban scale. Reduced-order surrogate models can expedite numerical simulations while maintaining necessary engineering accuracy. Neural networks have been shown to be a powerful tool for developing surrogate models, which often outperform classical surrogate models in terms of scalability of complex models. Training a reliable deep learning model, however, requires an immense amount of data that contain a rich input-output relationship, which typically cannot be satisfied in practical applications. In this paper, we propose model-informed symbolic neural networks (MiSNN) that can discover the underlying closed-form formulations (differential equations) for a reduced-order surrogate model. The MiSNN will be trained on datasets obtained from dynamic analyses of detailed reinforced concrete special moment frames designed for San Francisco, California, subject to a series of selected ground motions. Training the MiSNN is equivalent to finding the solution to a sparse optimization problem, which is solved by the Adam optimizer. The earthquake ground acceleration and story displacement, velocity, and acceleration time histories will be used to train 1) an integrated SNN, which takes displacement and velocity states and outputs the absolute acceleration response of the structure; and 2) a distributed SNN, which distills the underlying equation of motion for each story. The results show that the MiSNN can reduce computational cost while maintaining high prediction accuracy of building responses.