A Jin--Xin Relaxation Gradual Convergence Method for Conservation-Law PINNs

What the math gives to ML

The paper gives a constructive continuation strategy for neural approximations of hyperbolic conservation laws with shocks. Instead of optimizing directly at a nearly singular relaxation scale, a network first solves a smooth Jin–Xin system and is then warm-started through progressively smaller relaxation parameters. The transferable asset is the homotopy between smooth finite-width profiles and the entropy solution, together with an auxiliary flux variable and a sub-characteristic stability condition. This should be tested as a training curriculum for shock-containing PINNs and neural PDE solvers.