Critical evaluation of PINN for FWD inverse analysis and differentiable FEM as an alternative
For researchers in pavement engineering and inverse problems, this work demonstrates that DiffFEM outperforms PINNs in accuracy and robustness for FWD backcalculation, highlighting the limitations of soft-constraint physics enforcement.
This study evaluates PINN-based inverse analysis for falling weight deflectometer (FWD) backcalculation and finds it fails due to domain discontinuities, while differentiable FEM (DiffFEM) consistently achieves more accurate, stable, and computationally efficient inversion results.
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.