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.

翻译：基于自动微分的反演分析方法，包括物理信息神经网络（PINN）和可微编程，近年来因其精确梯度计算能力和收敛效率展现出巨大潜力。然而，这些方法在落锤式弯沉仪（FWD）反算中的应用尚未被探索。本研究基于合成基准，对多层路面系统的PINN反演分析进行了关键性评估，并研究了作为替代方案的可微有限元方法（DiffFEM）。标准PINN由于层状路面系统固有的域不连续性，无法恢复层模量。尽管我们采用具有域分解功能的扩展PINN（XPINN）在不连续域上表现出更好的性能，但其性能仍高度依赖于损失权重和网络结构，且在测量噪声下会退化。相比之下，DiffFEM始终能获得更准确、稳定且计算高效的反演结果。这些结果表明，将控制物理方程作为硬约束强加的DiffFEM，在精度、鲁棒性和计算效率方面均优于通过损失函数将控制物理方程作为软约束施加的PINN方法。更广泛而言，研究发现表明，基于PINN和DiffFEM的反演分析选择需要谨慎权衡，当存在高效且稳健的可微正演求解器时，DiffFEM具有实际应用优势。