AI 中文总结
研究针对弹塑性分析计算成本高的问题，提出Plasolver物理信息神经算子框架，结合算子学习与经典求解器优势，预训练结合热启动阶段，实现高精度与大幅加速，减少迭代次数，为弹塑性问题提供高效计算框架。
AI 中文摘要
弹塑性分析计算成本高昂，因为其非线性、路径相关的本构行为需要增量加载和反复迭代求解。为应对这一挑战，我们提出Plasolver，一种结合了算子学习的效率与经典数值求解器的精度和鲁棒性的物理信息神经算子框架。Plasolver包含一个物理信息预训练阶段和一个可选的热启动阶段。预训练期间，神经算子仅通过最小化由Simo提出的弹塑性增量势能进行训练，无需任何标记的解数据。它通过将空间坐标、加载历史和材料属性编码为统一的逐点提示，直接在非结构化点云上运行。该公式对空间和加载路径离散化具有双重不变性，能在不同空间分辨率和代表同一加载轨迹的不同增量数量下提供一致的预测。预训练后的Plasolver实现了约1%的相对误差，同时比传统有限元模拟快约两个数量级。在热启动阶段，预训练的预测结果被作为初始解提供给经典迭代求解器，在保留其数值精度、鲁棒性和收敛特性的同时大幅加速收敛。数值结果显示，与传统零初始化求解器相比，Plasolver减少了约50%的所需迭代次数，并能收敛到任意规定容差下的解。因此，Plasolver为非线性、路径相关的弹塑性问题提供了一个高效、准确且具有离散化不变性的计算框架。
英文摘要
Elastoplastic analysis is computationally demanding because its nonlinear, path-dependent constitutive behavior requires incremental loading and repeated iterative solutions. To address this challenge, we propose Plasolver, a physics-informed neural operator framework that combines the efficiency of operator learning with the accuracy and robustness of classical numerical solvers. Plasolver consists of a physics-informed pretraining stage and an optional warm-start stage. During pretraining, the neural operator is trained solely by minimizing the incremental potential energy of elastoplasticity formulated by Simo, without requiring any labeled solution data. It operates directly on unstructured point clouds by encoding spatial coordinates, loading histories, and material properties as unified point-wise prompts. This formulation provides dual invariance to spatial and loading-path discretizations, enabling consistent predictions across different spatial resolutions and different numbers of increments representing the same loading trajectory. The pretrained Plasolver achieves relative errors on the order of 1\% while providing approximately two orders of magnitude acceleration over conventional finite element simulations. In the warm-start stage, the pretrained prediction is supplied as the initial solution to a classical iterative solver, preserving its numerical accuracy, robustness, and convergence properties while substantially accelerating convergence. Numerical results show that Plasolver reduces the required number of iterations by approximately 50\% compared with conventional zero-initialized solvers and converges to solutions at any prescribed tolerance. Plasolver thus provides an efficient, accurate, and discretization-invariant computational framework for nonlinear, path-dependent elastoplastic problems.
