6 papers
HypNO: A Graph-Based Neural Operator with Physics-Informed Message Passing for Hyperbolic Conservation Laws
Dimitrije Ždrale, Cassie An Jeng, Katie Wang +3
We introduce HypNO, a graph-based neural operator for scalar hyperbolic conservation laws. HypNO operates directly on a space-time graph of finite-volume cells and uses adjacency-f…
Existence and uniqueness of nonlocal nonlinear conservation laws via fixed-point methods
Xiaoqian Gong, Alexander Keimer, Lorenzo Liverani +1
We investigate the well-posedness of scalar conservation laws whose flux depends on the solution both pointwise and nonlocally through integral averages. Our analysis is based on a…
Supervised and Unsupervised Neural Network Solver for First Order Hyperbolic Nonlinear PDEs
Zakaria Baba, Alexandre M. Bayen, Alexi Canesse +7
We present a neural network-based method for learning scalar hyperbolic conservation laws. Our method replaces the traditional numerical flux in finite volume schemes with a traina…
(U)NFV: Supervised and Unsupervised Neural Finite Volume Methods for Solving Hyperbolic PDEs
Nathan Lichtlé, Alexi Canesse, Zhe Fu +3
We introduce (U)NFV, a modular neural network architecture that generalizes classical finite volume (FV) methods for solving hyperbolic conservation laws. Hyperbolic partial differ…
A nonlocal degenerate macroscopic model of traffic dynamics with saturated diffusion: modeling and calibration theory
Dawson Do, Hossein Nick Zinat Matin, Masuma Mollika Miti +1
In this work, we introduce a novel first-order nonlocal partial differential equation with saturated diffusion to describe the macroscopic behavior of traffic dynamics. We show how…
Second-Order Time to Collision With Non-Static Acceleration
Hossein Nick Zinat Matin, Yuneil Yeo, Amelie Ju-Kang Ngo +3
We propose a second-order time to collision (TTC) considering non-static acceleration and turning with realistic assumptions. This is equivalent to considering that the steering wh…