# Potential failures of physics-informed machine learning in traffic flow modeling: theoretical and experimental analysis

arXiv: https://arxiv.org/abs/2505.11491 · HTML: https://mlsanity.com/paper/2505.11491/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 54 references that are in the map.
- First posted on arXiv 16 May 2025.

## Builds on (most cited first, 10 of 10)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Multi-Task Learning as Multi-Objective Optimization](https://mlsanity.com/paper/1810.04650/) (2018)
- [Characterizing possible failure modes in physics-informed neural networks](https://mlsanity.com/paper/2109.01050/) (2021)
- [PyHessian: Neural Networks Through the Lens of the Hessian](https://mlsanity.com/paper/1912.07145/) (2019)
- [Hessian-based Analysis of Large Batch Training and Robustness to Adversaries](https://mlsanity.com/paper/1802.08241/) (2018)
- [A Physics-Informed Deep Learning Paradigm for Car-Following Models](https://mlsanity.com/paper/2012.13376/) (2020)
- [A Physics-Informed Deep Learning Paradigm for Traffic State and Fundamental Diagram Estimation](https://mlsanity.com/paper/2106.03142/) (2021)
- [Macroscopic Traffic Flow Modeling with Physics Regularized Gaussian Process: A New Insight into Machine Learning Applications](https://mlsanity.com/paper/2002.02374/) (2020)
- [Short-term traffic prediction using physics-aware neural networks](https://mlsanity.com/paper/2109.10253/) (2021)
- [Modeling Stochastic Microscopic Traffic Behaviors: a Physics Regularized Gaussian Process Approach](https://mlsanity.com/paper/2007.10109/) (2020)

## Built on by (most cited first, 2 of 2)

- [Reconstructing Physics-Informed Machine Learning for Traffic Flow Modeling: a Multi-Gradient Descent and Pareto Learning Approach](https://mlsanity.com/paper/2505.13241/) (2025)
- [Observation-Aligned Two-Stage Domain Decomposition for Physics-Informed Traffic State Estimation with Sparse Fixed Sensors](https://mlsanity.com/paper/2605.08028/) (2026)

## Abstract (arXiv)

This study investigates why physics-informed machine learning (PIML) can fail in macroscopic traffic flow modeling. We define failure as cases where a PIML model underperforms both purely data-driven and purely physics-based baselines by a given threshold. Unlike in other fields, physics residuals themselves do not hinder optimization in this setting. Instead, effective updates require both data and physics gradients to form acute angles with the true gradient, a condition difficult to satisfy with low-resolution loop data. In such cases, neural networks cannot accurately approximate density and speed, and the constructed physics residuals, already degraded by discrete sampling and temporal averaging, lose their ability to capture PDE dynamics, which directly leads to PIML failure. Theoretically, although LWR and ARZ solutions are weak solutions, for piecewise Ck initial data they remain Ck off the shock set under mild conditions, which has Lebesgue measure zero. Thus, almost all detector or collocation points lie in smooth regions where residuals are valid, and the MLP's inability to exactly represent discontinuities is immaterial. Finally, we establish MSE lower bounds of physics residuals: higher-order models such as ARZ have strictly larger consistency error bounds than LWR under mild conditions. This explains why LWR-based PIML can outperform ARZ-based PIML even with high-resolution data, with the gap shrinking as resolution increases, consistent with prior empirical findings.