对比PINN与可微有限元在路面反演中的表现,发现后者更稳定高效。
Critical evaluation of PINN for FWD inverse analysis and differentiable FEM as an alternative

- 用可微有限元(DiffFEM)替代物理信息神经网络(PINN)进行路面反演
- DiffFEM在噪声下仍保持高精度,而PINN对损失权重敏感且易失效
- 适合需要鲁棒反演的工程场景,尤其有高效前向求解器时
基于自动微分的反演方法(如物理信息神经网络PINNs和可微编程)因其能高效计算精确梯度而备受关注。然而,其在落锤式弯沉仪(FWD)反演中的应用尚未被充分探索。本研究针对多层路面系统,通过合成基准测试,批判性评估了基于PINN的反演方法,并考察了可微有限元方法(DiffFEM)作为替代方案。标准PINN因层间突变边界条件无法恢复各层模量;尽管采用域分解扩展的PINN(XPINN)在不连续域上表现更好,但其性能仍高度依赖损失权重与网络结构,且在测量噪声下显著退化。相比之下,DiffFEM始终表现出更高精度、更强稳定性与更优计算效率。结果表明,将控制方程作为硬约束的DiffFEM,在准确性、鲁棒性与计算效率上优于将物理规律作为软约束引入损失函数的PINN方法。更广泛而言,当具备高效可微前向求解器时,应优先考虑DiffFEM而非PINN进行反演分析。
原文摘要 · Abstract (English)
Automatic-differentiation-based inverse analysis methods, including physics-informed neural networks (PINNs) and differentiable programming, have recently shown great promise due to their ability to compute accurate gradients and convergence efficiency. However, their applicability to falling weight deflectometer (FWD) backcalculation remains unexplored. This study critically evaluates PINN-based inverse analysis for a multilayer pavement system and investigates differentiable finite element method (DiffFEM) as an alternative based on a synthetic benchmark. The standard PINN does not recover layer moduli because of the sharp domain discontinuities inherent to layered pavement systems. Although we use an extended PINN with domain decomposition (XPINN), which shows better performance on discontinuous domains, its performance remains highly sensitive to loss weighting and network architecture, and degrades under measurement noise. By contrast, DiffFEM consistently achieves more accurate, stable, and computationally efficient inversion results. These results indicate that DiffFEM, which enforces the governing physics as a hard constraint, yields better accuracy, robustness, and computational efficiency than PINN-based approaches, in which the governing physics is imposed as a soft constraint through the loss function. More broadly, the findings suggest that the choice between PINN- and DiffFEM-based inverse analysis needs careful consideration, with DiffFEM offering practical advantages when an efficient and robust differentiable forward solver is available.
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