A novel physics-constrained neural network: An illustration of ground motion models

Ground motion model (GMM) is essential for seismic hazard analysis and can be developed using either empirical or machine learning approaches. The former often results in suboptimal predictive performance, and the latter frequently faces challenges related to interpretability and explainability although providing more accurate results. To overcome these limitations, this study proposes a novel physics-constrained neural network (PCNN) that incorporates constraints on the hypothesis space through designing specialized neural network architectures informed by physical domain knowledge. This approach enables the updating or derivation of biased or unknown components through data-driven learning. Using the development of GMMs as an illustration, the PCNN is constructed to maintain the mathematical form consistent with established empirical models by reconfiguring parameters, activation functions, and layer connections within a conventional neural network. This physics-constrained approach enhances both the interpretability of the network's architecture and the explainability of its outputs. By leveraging both the advanced machine learning techniques and the domain-specific physical constraints, the PCNN refines the suboptimal coefficients in empirical models, which could achieve the globally optimal model coefficients and improve predictive performance.