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This study demonstrates that differentiable finite element methods (DiffFEM) outperform physics-informed neural networks (PINNs) in inverse analysis for layered pavement systems by enforcing physics as hard constraints rather than soft loss terms. The findings highlight that while PINNs struggle with domain discontinuities and noise sensitivity, DiffFEM provides superior accuracy, stability, and computational efficiency when an efficient forward solver is available. For engineers and researchers, this suggests that DiffFEM is the more robust choice for practical differentiable modeling tasks involving complex, discontinuous domains.
Critical evaluation of PINN for FWD inverse analysis and differentiable FEM as an alternative
arXiv:2606.03210v1 Announce Type: cross Abstract: 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.
Abstract: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.
Computational Engineering, Finance, and Science (cs.CE); Machine Learning (cs.LG); Numerical Analysis (math.NA)
arXiv:2606.03210 [cs.CE]
(or arXiv:2606.03210v1 [cs.CE] for this version)
https://doi.org/10.48550/arXiv.2606.03210 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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