AI 中文总结
针对岩土材料弹塑性分析问题，提出傅里叶特征物理信息神经网络（FF-PINN）。通过嵌入随机傅里叶特征映射减轻频谱偏差，结合多目标损失函数和应变自适应采样策略。相比传统方法，它收敛更快、精度更高，为弹塑性岩土分析提供了高效且物理一致的替代方案。
AI 中文摘要
岩土工程中的弹塑性边值问题传统上通过有限元法（FEM）求解，该方法因增量迭代过程而计算成本高昂。物理信息神经网络（PINNs）提供了无网格替代方案，但存在频谱偏差，无法解决弹塑性边界和局部塑性区内出现的急剧梯度。本研究针对受该模型控制的二维弹塑性问题提出了一种傅里叶特征物理信息神经网络（FF-PINN）。将随机傅里叶特征映射嵌入输入层以减轻频谱偏差，由多目标损失函数支持，该函数针对高保真FEM数据强制执行平衡、本构关系和Karush-Kuhn-Tucker条件，以及应变自适应采样策略。在三个测试案例中进行基准测试，FF-PINN在大多数预测场中实现了更高的精度，位移误差降低高达约66%，应力分量误差降低27%，并以明显更高的保真度再现了塑性破坏区几何形状。敏感性分析证实了在训练数据大小、配置密度、损失加权和高达2.0%的噪声水平下的鲁棒性。FF-PINN在传统PINN所需训练轮次的一半内收敛，将训练时间减半，同时实现更高的预测精度。因此，该框架为弹塑性岩土分析提供了一种计算高效且物理一致的FEM替代方案。
英文摘要
Elasto-plastic boundary value problems in geotechnical engineering are conventionally solved by the Finite Element Method (FEM), which incurs high computational cost from incremental-iterative procedures. Physics-Informed Neural Networks (PINNs) offer a mesh-free alternative but suffer from spectral bias, failing to resolve the sharp gradients arising at elastic-plastic boundaries and within localized plastic zones. This limitation is particularly consequential for the non-associative Mohr-Coulomb model, whose pressure-dependent yield surface and dilatant flow rule generate narrower plastic zones and steeper stress gradients than pressure-independent criteria. This study proposes a Fourier Feature Physics-Informed Neural Network (FF-PINN) for two-dimensional elasto-plastic problems governed by this model. Random Fourier feature mapping is embedded into the input layer to mitigate spectral bias, supported by a multi-objective loss function enforcing equilibrium, constitutive relations, and Karush-Kuhn-Tucker conditions against high-fidelity FEM data, together with a strain-adaptive sampling strategy. Benchmarked across three test cases, FF-PINN achieves superior accuracy across most predicted fields, with error reductions up to approximately 66 percent in displacement and 27 percent in stress components, and reproduces the plastic failure zone geometry with markedly closer fidelity to FEM. Sensitivity analysis confirms robustness across training data size, collocation density, loss weighting, and noise levels up to 2.0 percent. FF-PINN converges in half the training epochs required by the conventional PINN, halving wall-clock training time while achieving greater predictive accuracy. The framework therefore offers a computationally efficient and physics-consistent alternative to FEM for elasto-plastic geotechnical analysis.
