对比多种神经网络在岩土工程中的表现，发现其外推能力差且训练成本高。
A Critical Assessment of PINNs and Operator Learning for Geotechnical Engineering
- 用多层感知机、物理信息神经网络等方法替代传统数值求解
- PINN在域外预测误差超200%，训练速度慢于有限差分法96000倍
- 建议有可靠前向求解器时优先用可微分物理求解器做反演分析
科学机器学习（SciML）为岩土工程提供了神经网络替代数值流程的可能。本文在岩土基准问题上，将多层感知机（MLP）、物理信息神经网络（PINN）、深度算子网络（DeepONet）和图网络模拟器（GNS）与有限差分法和粒子基参考解进行对比，并比较了PINN反演与通过传统求解器自动微分（AD）的差异。评估涵盖外推能力、训练与推理成本、跨问题实例迁移性及物理准确性。一个在两年太沙基固结数据上训练的MLP，在第十年预测值分别为：使用ReLU时约290 mm，使用tanh或sigmoid时约60 mm，而参考值为99.3 mm。在阻尼振子问题中，时间域[0,1]内PINN拟合闭式解，但域外失效，因残差约束仅作用于采样点。对于一维波动方程，PINN训练速度比有限差分法慢约96,000倍，且精度更低。DeepONet避免重训，但在弹性地基梁问题上训练成本相当于约180万次有限差分求解，单次推理也慢于直接求解器。GNS通过局部粒子交互提升几何迁移性，但仍需轨迹数据、大规模训练集和大量内存。在反波传播基准测试中，通过有限差分求解器的自动微分可在数秒内以约1%误差恢复材料分布。结果表明应谨慎看待SciML应用。神经网络适用于验证域内的插值与模式识别，而反演分析在存在可靠前向求解器时，应优先尝试可微分物理求解器。
原文摘要 · Abstract (English)
Scientific machine learning (SciML) offers neural-network alternatives to numerical workflows in geotechnical engineering. This paper benchmarks multi-layer perceptrons (MLPs), physics-informed neural networks (PINNs), deep operator networks (DeepONet), and graph network simulators (GNS) against finite-difference and particle-based references on geotechnical benchmarks, and compares PINN inversion with automatic differentiation (AD) through a conventional solver. We evaluate each method for extrapolation, training, and inference cost, transfer across problem instances, and physics accuracy. An MLP trained on two years of Terzaghi consolidation fits the data, but at year ten predicts ~290 mm with ReLU and ~60 mm with tanh or sigmoid, against a reference of 99.3 mm. A PINN on a damped oscillator with a time domain inside [0,1] matches the closed form within that interval but fails outside, since the residual constrains the fit only where it is sampled. For the 1D wave equation, PINN training is ~96,000 times slower than finite-difference methods and less accurate. DeepONet avoids PINN retraining, yet for the beam on elastic foundation, its training cost equals ~1.8 million finite-difference solves, and inference is slower per query than the direct solver. GNS improves geometric transfer through local particle interactions, though formulations still need trajectories, large training sets, and substantial memory. In the inverse wave benchmark, AD through the finite-difference solver recovers the material profile in seconds with ~1% error. The results support a cautious role for SciML. Neural networks suit interpolation and pattern recognition inside validated domains, while inverse analysis should first try differentiable physics-based solvers when a reliable forward solver exists.
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