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Geometry physics neural operator solver for solid mechanics
Computer-Aided Civil and Infrastructure Engineering ( IF 8.5 ) Pub Date : 2025-01-04 , DOI: 10.1111/mice.13405
Chawit Kaewnuratchadasorn, Jiaji Wang, Chul‐Woo Kim, Xiaowei Deng

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.

中文翻译:


用于固体力学的几何物理神经算子求解器



本研究开发了几何物理神经运算符 (GPO),这是一种新颖的求解器框架,用于近似不规则几何形状的固体力学问题的偏微分方程 (PDE) 解,与数值求解器相比,仿真时间显著加快。GPO 利用基于最小功原则的弱形式的偏微分方程,整合几何信息,并在网络架构中施加精确的狄利克雷边界条件,以实现准确高效的建模。本研究的重点是应用 GPO 对复杂物体的行为进行建模,而无需任何指导解决方案或标记的训练数据。GPO 采用改进的傅里叶神经算子作为主干,实现了显著提高的收敛速度,并学习了固体力学问题的复杂解领域。数值实验涉及一个带有孔的二维平面和一个具有狄利克雷边界约束的三维建筑结构。结果表明,GPO 中的几何层和精确边界约束对收敛精度和速度有显著贡献,在不规则几何仿真中优于以前的基准。比较结果还表明,在结构示例中,GPO 可以比商业数值求解器更快地收敛到解场。此外,当网格尺寸较小时,GPO 表现出比求解器更强的性能,并且在二维和三维示例中,它分别实现了超过 3 倍和 2 倍的加速,自由度很大。进一步讨论了非线性和复杂结构的局限性,以展望未来的发展。显著的结果表明,大规模基础设施的建模应用潜力巨大。
更新日期:2025-01-04
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