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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…
math.NA2024
Non-diffusive neural network method for hyperbolic conservation laws
Emmanuel Lorin, Arian Novruzi
In this paper we develop a non-diffusive neural network (NDNN) algorithm for accurately solving weak solutions to hyperbolic conservation laws. The principle is to construct these…