# Neural Operators for Adaptive Control of Traffic Flow Models

arXiv: https://arxiv.org/abs/2505.07353 · HTML: https://mlsanity.com/paper/2505.07353/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 12 May 2025.

## Built on by (most cited first, 1 of 1)

- [Lotka-Sharpe Neural Operators for Control of Population PDEs](https://mlsanity.com/paper/2604.03892/) (2026)

## Abstract (arXiv)

The uncertainty in human driving behaviors leads to stop-and-go instabilities in freeway traffic. The traffic dynamics are typically modeled by the Aw-Rascle-Zhang (ARZ) Partial Differential Equation (PDE) models, in which the relaxation time parameter is usually unknown or hard to calibrate. This paper proposes an adaptive boundary control design based on neural operators (NO) for the ARZ PDE systems. In adaptive control, solving the backstepping kernel PDEs online requires significant computational resources at each timestep to update estimates of the unknown system parameters. To address this, we employ DeepONet to efficiently map model parameters to kernel functions. Simulations show that DeepONet generates kernel solutions nearly two orders of magnitude faster than traditional solvers while maintaining a loss on the order of (10-2). Lyapunov analysis further validates the stability of the system when using DeepONet-approximated kernels in the adaptive controller. This result suggests that neural operators can significantly accelerate the acquisition of adaptive controllers for traffic control.