Combination of physics-based and data-driven modeling for nonlinear structural seismic response prediction through deep residual learning

Despite great progress in seeking accurate numerical approximator to nonlinear structural seismic response prediction using deep learning approaches, tedious training process and large volume of structural response data under earthquakes for training and validation are often prohibitively accessible. In our methodology, the main innovation can be seen in the incorporation of deep neural networks (DNNs) into a classical numerical integration method by using a hybridized integration time-stepper. In this way, the linear physics information of the structure and the obscure nonlinear dynamics are smoothly combined. We propose to use residual network (ResNet) to learn time-stepping schemes specifically for the nonlinear state variables of the system. Our Physics-DNN hybridized integration (PDHI) time-stepping scheme provides important advantages over current pure data-driven approaches, including (i) a flexible framework incorporating known time-invariant physics information, (ii) requirement of structural seismic response data being circumvented by simple short bursts of trajectories collected from underlying nonlinear components, and (iii) efficiency in training and validation process. Besides, our results indicate that a simple feedforward or convolutional architecture outperforms recurrent networks to fulfill the requirement of prediction accuracy as well as long-range memory in structural dynamic analysis. Several numerical and experimental examples are presented to demonstrate the performance of the method.

Automated summary

By incorporating deep neural networks into a classical numerical integration method, we propose a hybridized integration time-stepper that combines the linear physics information with the nonlinear dynamics of structures. Our method has several advantages over current pure data-driven approaches, including the ability to incorporate known physics information, the circumvention of the requirement for large volume of structural response data, and efficiency in training and validation process.