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.
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Bayesian Proper Orthogonal Decomposition for Learnable Reduced-Order Models with Uncertainty Quantification
Designing and/or controlling complex systems in science and engineering relies on appropriate mathematical modeling of systems dynamics. Classical differential equation based solutions in applied and computational mathematics are often computationally demanding. Recently, the connection between reduced-order models of high-dimensional differential equation systems and surrogate machine learning models has been explored. However, the focus of both existing reduced-order and machine learning models for complex systems has been how to best approximate the high fidelity model of choice. Due to high complexity and often limited training data to derive reduced-order or machine learning surrogate models, it is critical for derived reduced-order models to have reliable uncertainty quantification at the same time. In this paper, we propose such a novel framework of Bayesian reduced-order models naturally equipped with uncertainty quantification as it learns the distributions of the parameters of the reduced-order models instead of their point estimates. In particular, we develop learnable Bayesian proper orthogonal decomposition (BayPOD) that learns the distributions of both the POD projection bases and the mapping from the system input parameters to the projected scores/coefficients so that the learned BayPOD can help predict high-dimensional systems dynamics/fields as quantities of interest in different setups with reliable uncertainty estimates. The developed learnable BayPOD inherits the capability of embedding physics constraints when learning the POD-based surrogate reduced-order models, a desirable feature when studying complex systems in science and engineering applications where the available training data are limited. Furthermore, the proposed BayPOD method is an end-to-end solution, which unlike other surrogate-based methods, does not require separate POD and machine learning steps. The results from a real-world case study of the pressure field around an airfoil.
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- Award ID(s):
- 2119103
- PAR ID:
- 10460985
- Date Published:
- Journal Name:
- IEEE Transactions on Artificial Intelligence
- ISSN:
- 2691-4581
- Page Range / eLocation ID:
- 1 to 13
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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Abstract The development of a reliable and robust surrogate model is often constrained by the dimensionality of the problem. For a system with high‐dimensional inputs/outputs (I/O), conventional approaches usually use a low‐dimensional manifold to describe the high‐dimensional system, where the I/O data are first reduced to more manageable dimensions and then the condensed representation is used for surrogate modeling. In this study, a new solution scheme for this type of problem based on a deep learning approach is presented. The proposed surrogate is based on a particular network architecture, that is, convolutional neural networks. The surrogate architecture is designed in a hierarchical style containing three different levels of model structures, advancing the efficiency and effectiveness of the model in the aspect of training. To assess the model performance, uncertainty quantification is carried out in a continuum mechanics benchmark problem. Numerical results suggest the proposed model is capable of directly inferring a wide variety of I/O mapping relationships. Uncertainty analysis results obtained via the proposed surrogate have successfully characterized the statistical properties of the output fields compared to the Monte Carlo estimates.
- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1109/TAI.2023.3268609
