Learning Solutions for LWR-type Traffic Flow Models

Abstract

First-order macroscopic traffic flow models in the form of partial differential equations are conventionally solved using numerical schemes which are grid-dependent. We propose a kernel-based method for learning solutions of first-order traffic flow models. The solution kernels are approximated by Fourier Neural Operators - a variant of deep neural networks. Unlike the conventional schemes, our method learns solutions to arbitrary initial and boundary conditions. This avoids resolving the problem for every new instance of input conditions, thereby lowering the computational cost. We apply this method for learning traffic density solutions of the Lighthill-WithamRichards (LWR) traffic flow model. Numerical experiments to show the neural network solution’s accuracy, grid-independence, robustness, and computational complexity are included.