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

arXiv: https://arxiv.org/abs/2606.03210 · HTML: https://mlsanity.com/paper/2606.03210/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 11 of its 38 references that are in the map.
- First posted on arXiv 2 Jun 2026.

## Builds on (most cited first, 11 of 11)

- [Automatic differentiation in machine learning: a survey](https://mlsanity.com/paper/1502.05767/) (2015)
- [DiffTaichi: Differentiable Programming for Physical Simulation](https://mlsanity.com/paper/1910.00935/) (2019)
- [Challenges in Training PINNs: A Loss Landscape Perspective](https://mlsanity.com/paper/2402.01868/) (2024)
- [A Differentiable Programming System to Bridge Machine Learning and Scientific Computing](https://mlsanity.com/paper/1907.07587/) (2019)
- [On weight initialization in deep neural networks](https://mlsanity.com/paper/1704.08863/) (2017)
- [A physics-informed deep neural network for surrogate modeling in classical elasto-plasticity](https://mlsanity.com/paper/2204.12088/) (2022)
- [Deep Learning for One-dimensional Consolidation](https://mlsanity.com/paper/2004.11689/) (2020)
- [Enhancing Physics-Informed Neural Networks Through Feature Engineering](https://mlsanity.com/paper/2502.07209/) (2025)
- [Impact of Loss Weight and Model Complexity on Physics-Informed Neural Networks for Computational Fluid Dynamics](https://mlsanity.com/paper/2509.21393/) (2025)
- [SoftJAX & SoftTorch: Empowering Automatic Differentiation Libraries with Informative Gradients](https://mlsanity.com/paper/2603.08824/) (2026)
- [Visualizing the loss landscapes of physics-informed neural networks](https://mlsanity.com/paper/2602.05849/) (2026)

## Abstract (arXiv)

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.