Differentiable FEM versus PINN for pavement layer inverse analysis: enforcing physics as hard or soft constraints
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 show and quantify the expected advantage of DiffFEM, which enforces the governing physics as a hard constraint in the solver, over PINN-based approaches, where 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.
Versions
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BibTeX
@misc{choi2026differentiable,
title = {{Differentiable FEM versus PINN for pavement layer inverse analysis: enforcing physics as hard or soft constraints}},
author = {Yongjin Choi and Hyeonbin Moon and Seunghwa Ryu},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2606.03210},
eprint = {2606.03210},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2606.03210},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Differentiable FEM versus PINN for pavement layer inverse analysis: enforcing physics as hard or soft constraints
AU - Yongjin Choi
AU - Hyeonbin Moon
AU - Seunghwa Ryu
PY - 2026
DA - 2026/10/26
PB - arXiv
DO - 10.48550/arxiv.2606.03210
UR - https://arxiv.org/abs/2606.03210
AB - 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 show and quantify the expected advantage of DiffFEM, which enforces the governing physics as a hard constraint in the solver, over PINN-based approaches, where 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.
ER -