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math.NA2026
A diffusion-free multi-layer neural-network method for multidimensional nonlinear hyperbolic equations
Emmanuel Lorin, Arian Novruzi
This paper is devoted to the non-diffusive computation of solutions to -dimensional hyperbolic systems of conservation laws (HCL) and more specifically the accurate approximatio…
math.NA2026
A Jin--Xin Relaxation Gradual Convergence Method for Conservation-Law PINNs
Emmanuel Lorin, Yuchong Tang, Xu Yang +1
The Jin--Xin relaxation of a nonlinear hyperbolic conservation law introduces a relaxation parameter that controls the width of the internal layer resolving a shock; the discontinu…