[Paper Review] Physics-guided Convolutional Neural Network (PhyCNN) for Data-driven Seismic Response Modeling

Ruiyang Zhang, Yang Liu+1 more|arXiv (Cornell University)|Sep 17, 2019

Structural Health Monitoring TechniquesEngineering54 references18 citations

TL;DR

This paper proposes PhyCNN, a physics-guided convolutional neural network that leverages physical laws—such as structural dynamics—within a deep learning framework to predict seismic responses of buildings using limited data. By integrating physics constraints into the loss function and using unsupervised K-means clustering to optimize data partitioning, PhyCNN achieves high accuracy and robustness in seismic response prediction and fragility analysis, outperforming non-physics-guided models even with sparse training data.

ABSTRACT

Seismic events, among many other natural hazards, reduce due functionality and exacerbate vulnerability of in-service buildings. Accurate modeling and prediction of building's response subjected to earthquakes makes possible to evaluate building performance. To this end, we leverage the recent advances in deep learning and develop a physics-guided convolutional neural network (PhyCNN) framework for data-driven seismic response modeling and serviceability assessment of buildings. The proposed PhyCNN approach is capable of accurately predicting building's seismic response in a data-driven fashion without the need of a physics-based analytical/numerical model. The basic concept is to train a deep PhyCNN model based on available seismic input-output datasets (e.g., from simulation or sensing) and physics constraints. The trained PhyCNN can then used as a surrogate model for structural seismic response prediction. Available physics (e.g., the law of dynamics) can provide constraints to the network outputs, alleviate overfitting issues, reduce the need of big training datasets, and thus improve the robustness of the trained model for more reliable prediction. The trained surrogate model is then utilized for fragility analysis given certain limit state criteria (e.g., the serviceability state). In addition, an unsupervised learning algorithm based on K-means clustering is also proposed to partition the limited number of datasets to training, validation and prediction categories, so as to maximize the use of limited datasets. The performance of the proposed approach is demonstrated through three case studies including both numerical and experimental examples. Convincing results illustrate that the proposed PhyCNN paradigm outperforms conventional pure data-based neural networks.

Motivation & Objective

• Address the challenge of accurate seismic response prediction for civil structures under limited sensing or simulation data.
• Overcome the limitations of traditional physics-based models, which are computationally expensive and sensitive to parameter uncertainty.
• Develop a data-driven surrogate model that integrates physical laws to improve generalization and reduce overfitting without requiring large datasets.
• Enable reliable fragility curve generation for serviceability assessment using the trained model.
• Demonstrate the scalability and robustness of the approach through numerical and experimental validation.

Proposed method

• Train a deep convolutional neural network (PhyCNN) using limited seismic input-output datasets from simulations or field measurements.
• Incorporate physics constraints—specifically the equation of motion (Newton’s second law) via a graph-based tensor differentiator—to regularize network outputs.
• Formulate a physics-informed loss function that penalizes deviations from physical laws, improving model generalization and reducing overfitting.
• Apply unsupervised K-means clustering to partition the limited dataset into training, validation, and prediction sets, maximizing data utilization.
• Use the trained PhyCNN model to perform incremental dynamic analysis (IDA) with 100 ground motions to derive fragility curves for serviceability assessment.
• Compute fragility functions using the cumulative distribution function (CDF) of inter-story drift angles, with a serviceability limit state threshold of 0.5% drift angle.

Experimental results

Research questions

• RQ1 Can a physics-guided deep learning model accurately predict structural seismic responses with limited training data?
• RQ2 How does integrating physical constraints (e.g., dynamics equations) improve the robustness and generalization of data-driven seismic response models?
• RQ3 To what extent does unsupervised clustering of limited datasets enhance model performance and data efficiency?
• RQ4 Can the trained PhyCNN model generate reliable fragility curves for serviceability assessment under future seismic events?
• RQ5 How does PhyCNN compare in performance to non-physics-guided neural networks in terms of prediction accuracy and data efficiency?

Key findings

• PhyCNN achieves high accuracy in predicting seismic responses using only limited simulation or sensing data, demonstrating strong generalization capability.
• The integration of physics constraints significantly reduces overfitting and improves model robustness, especially when training data is scarce.
• The unsupervised K-means clustering strategy effectively partitions limited datasets, enhancing training efficiency and predictive performance.
• For the 6-story hotel building in San Bernardino, the predicted probability of exceeding the serviceability limit state is 47% at 0.1g PGA, 78% at 0.2g PGA, and 90% at 0.3g PGA.
• The fragility curve derived from PhyCNN predictions aligns with engineering standards and supports practical decision-making for maintenance and rehabilitation planning.
• PhyCNN outperforms non-physics-guided neural networks in both prediction accuracy and data efficiency, confirming the value of physics-informed learning in structural dynamics.