This study developed Geometry Physics neural Operator (GPO), a novel solver framework to approximate the partial differential equation (PDE) solutions for solid mechanics problems with irregular geometry and achieved a significant speedup in simulation time compared to numerical solvers. GPO leverages a weak form of PDEs based on the principle of least work, incorporates geometry information, and imposes exact Dirichlet boundary conditions within the network architecture to attain accurate and efficient modeling. This study focuses on applying GPO to model the behaviors of complicated bodies without any guided solutions or labeled training data. GPO adopts a modified Fourier neural operator as the backbone to achieve significantly improved convergence speed and to learn the complicated solution field of solid mechanics problems. Numerical experiments involved a two-dimensional plane with a hole and a three-dimensional building structure with Dirichlet boundary constraints. The results indicate that the geometry layer and exact boundary constraints in GPO significantly contribute to the convergence accuracy and speed, outperforming the previous benchmark in simulations of irregular geometry. The comparison results also showed that GPO can converge to solution fields faster than a commercial numerical solver in the structural examples. Furthermore, GPO demonstrates stronger performance than the solvers when the mesh size is smaller, and it achieves over 3 and 2 speedup for a large degree of freedom in the two-dimensional and three-dimensional examples, respectively. The limitations of nonlinearity and complicated structures are further discussed for prospective developments. The remarkable results suggest the potential modeling applications of large-scale infrastructures.
The cover image is based on the article Hybrid structural analysis integrating physical model and continuous-time state-space neural network model by Yi-QIng Ni et al., https://doi.org/10.1111/mice.13282.
Over the past decade, pavement imaging systems, particularly 3D laser technology, have been widely adopted by transportation agencies for network-level pavement condition evaluations. State Highway Agencies, including Georgia Department of Transportation (DOT), Florida DOT, and Texas DOT, have been collecting pavement images for over 5 years. However, these multi-year pavement images have not been fully utilized for analyzing detailed pavement deterioration. One challenge is the accurate and efficient registration of multi-temporal pavement images. This study pioneers the use of feature-based methods to address this challenge. It evaluates various feature-based image registration methods, including both state-of-the-art and novel combinations of feature detectors and descriptors. These methods are rigorously assessed using hybrid “step-by-step” and “end-to-end” performance evaluation metrics, with a ground reference dataset containing 100 pavement image pairs featuring diverse crack types and varying year gaps. The results confirm the feasibility of using feature-based techniques to register multi-temporal pavement images. A novel combination of the AKAZE detector and the Binary Robust Independent Elementary Features (BRIEF) descriptor was identified as the best-performing method, successfully registering 96 out of 100 image pairs. This advancement enables pavement engineers to accurately monitor pavement deterioration using multi-temporal images.