Critical evaluation of PINN for FWD inverse analysis and differentiable FEM as an alternative

2026-06-02

AI Summary

This study addresses the challenge of accurately recovering layer moduli in falling weight deflectometer (FWD) inversion when dealing with discontinuous multi-layer pavement media, where physics-informed neural networks (PINNs) often struggle. The authors systematically compare the performance of PINN, domain-decomposed extended PINN (XPINN), and differentiable finite element method (DiffFEM). They reveal, for the first time, that PINN-based approaches are highly sensitive to loss weighting and network architecture and are adversely affected by interfacial discontinuities. To overcome these limitations, the paper proposes DiffFEM, which enforces governing equations as hard constraints. Experimental results demonstrate that DiffFEM achieves efficient, stable, and high-accuracy modulus inversion even under noisy data conditions, significantly outperforming PINN-type methods and highlighting the critical role of differentiable forward solvers in inverse problems.

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.

Problem

• FWD backcalculation
• inverse analysis
• layered pavement system
• discontinuous domains
• measurement noise

Innovation

• differentiable FEM
• physics-informed neural networks
• inverse analysis
• FWD backcalculation
• domain discontinuities