| Abstract: |
| First-order macroscopic traffic flow models, which are instances of nonlinear hyperbolic partial differential equations, are conventionally solved using numerical schemes which are grid-dependent and require complete knowledge of initial and boundary data. We study learning a generic inverse solver for approximating weak solutions to arbitrary input conditions, e.g., spatial boundary or random collocation points, using an operator learning framework. Under this framework, the inverse solver is a parametric operator that learns a family of weak solutions offline from data (historical simulation). Computing solution to new inputs is then a single forward evaluation of the operator. This avoids resolving the problem for every new input instance, lowering the computational cost. We also present algorithms to generate sparse training datasets and efficiently learn the essential features of the hyperbolic solutions, namely, shocks and rarefaction waves. We illustrate the proposed method for solving Lighthill-Witham-Richards (LWR) traffic flow model and discuss the generalization error growth. These fast inverse solvers can be potentially used for real-time traffic monitoring and control. |
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