Hosung Kim

Su Yeong Jo, Sanghyeon Park, Seungchan Ko et al.

The Saint-Venant torsion theory is a classical theory for analyzing the torsional behavior of structural components, and it remains critically important in modern computational design workflows. Conventional numerical methods, including the finite element method (FEM), typically rely on mesh-based approaches to obtain approximate solutions. However, these methods often require complex and computationally intensive techniques to overcome the limitations of approximation, leading to significant increases in computational cost. The objective of this study is to develop a series of novel numerical methods based on physics-informed neural networks (PINN) for solving the Saint-Venant torsion equations. Utilizing the expressive power and the automatic differentiation capability of neural networks, the PINN can solve partial differential equations (PDEs) along with boundary conditions without the need for intricate computational techniques. First, a PINN solver was developed to compute the torsional constant for bars with arbitrary cross-sectional geometries. This was followed by the development of a solver capable of handling cases with sharp geometric transitions; variable-scaling PINN (VS-PINN). Finally, a parametric PINN was constructed to address the limitations of conventional single-instance PINN. The results from all three solvers showed good agreement with reference solutions, demonstrating their accuracy and robustness. Each solver can be selectively utilized depending on the specific requirements of torsional behavior analysis.

Zhuoshuo Li, Jiong Zhang, Youbing Zeng et al.

Current brain surface-based prediction models often overlook the variability of regional attributes at the cortical feature level. While graph neural networks (GNNs) excel at capturing regional differences, they encounter challenges when dealing with complex, high-density graph structures. In this work, we consider the cortical surface mesh as a sparse graph and propose an interpretable prediction model-Surface Graph Neural Network (SurfGNN). SurfGNN employs topology-sampling learning (TSL) and region-specific learning (RSL) structures to manage individual cortical features at both lower and higher scales of the surface mesh, effectively tackling the challenges posed by the overly abundant mesh nodes and addressing the issue of heterogeneity in cortical regions. Building on this, a novel score-weighted fusion (SWF) method is implemented to merge nodal representations associated with each cortical feature for prediction. We apply our model to a neonatal brain age prediction task using a dataset of harmonized MR images from 481 subjects (503 scans). SurfGNN outperforms all existing state-of-the-art methods, demonstrating an improvement of at least 9.0% and achieving a mean absolute error (MAE) of 0.827+0.056 in postmenstrual weeks. Furthermore, it generates feature-level activation maps, indicating its capability to identify robust regional variations in different morphometric contributions for prediction.