Title: A Critical Assessment of PINNs in FWD Inverse Analysis and the Viability of Differentiable FEM

Abstract:

Recent advancements in automatic-differentiation-based inverse analysis, encompassing both physics-informed neural networks (PINNs) and differentiable programming, have highlighted their potential for accurate gradient computation and efficient convergence. Despite this promise, their application to falling weight deflectometer (FWD) backcalculation has not yet been thoroughly examined. This research provides a critical evaluation of PINN-based inverse analysis for multilayer pavement systems and explores differentiable finite element method (DiffFEM) as a comparative alternative, utilizing a synthetic benchmark for assessment.

The study reveals that standard PINNs fail to accurately recover layer moduli in layered pavement systems due to the inherent sharp domain discontinuities. While an extended PINN approach using domain decomposition (XPINN) demonstrates improved performance on such discontinuous domains, it exhibits significant limitations. Specifically, its efficacy is highly dependent on loss weighting and network architecture, and its performance deteriorates notably in the presence of measurement noise.

In contrast, DiffFEM delivers inversion results that are consistently more accurate, stable, and computationally efficient. These findings underscore that DiffFEM, which incorporates governing physics as a hard constraint, outperforms PINN-based methods, where physics are enforced as a soft constraint via the loss function. Broadly, the results suggest that selecting between PINN and DiffFEM for inverse analysis requires careful deliberation; DiffFEM presents distinct practical advantages, provided that an efficient and robust differentiable forward solver is accessible.

Source: arXiv Generated at: 2026-06-03 00:00:00 UTC