Neural Networks Enabled Discovery On the Higher-Order Nonlinear Partial Differential Equation of Traffic Dynamics

TL;DR

This paper presents a deep learning framework that discovers high-order nonlinear PDE models of traffic dynamics directly from measurement data, enhancing understanding and prediction of traffic evolution.

Contribution

It introduces TRAFFIC-PDE-LEARN, a novel method combining neural networks, automatic differentiation, and sparse regression to identify interpretable PDEs from real-world traffic data.

Findings

Successfully identified high-order nonlinear PDEs governing traffic dynamics

Demonstrated accurate traffic prediction using the learned PDE models

Validated approach on real-world traffic network data

Abstract

Modeling the traffic dynamics is essential for understanding and predicting the traffic spatiotemporal evolution. However, deriving the partial differential equation (PDE) models that capture these dynamics is challenging due to their potential high order property and nonlinearity. In this paper, we introduce a novel deep learning framework, "TRAFFIC-PDE-LEARN", designed to discover hidden PDE models of traffic network dynamics directly from measurement data. By harnessing the power of the neural network to approximate a spatiotemporal fundamental diagram that facilitates smooth estimation of partial derivatives with low-resolution loop detector data. Furthermore, the use of automatic differentiation enables efficient computation of the necessary partial derivatives through the chain and product rules, while sparse regression techniques facilitate the precise identification of physically interpretable PDE components. Tested on data from a real-world traffic network, our model demonstrates that the underlying PDEs governing traffic dynamics are both high-order and nonlinear. By leveraging the learned dynamics for prediction purposes, the results underscore the effectiveness of our approach and its potential to advance intelligent transportation systems.