3 papers
math.NA2026
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…
cs.LG2025
(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…
math.OC2024
Pareto Control Barrier Function for Inner Safe Set Maximization Under Input Constraints
Xiaoyang Cao, Zhe Fu, Alexandre M. Bayen
This article introduces the Pareto Control Barrier Function (PCBF) algorithm to maximize the inner safe set of dynamical systems under input constraints. Traditional Control Barrie…