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Plots of three of the conservation laws (equations (19)–(21)) of the nonlinear Schrödinger equation for (a)–(c) a vanilla PINN and (d)–(f) a PINN constrained by the first conservation law. The PINNs were trained with initial data corrupted with σ = 0.1 Gaussian noise. The constrained PINN has better performance of conservation laws 1 and 3, while both PINNs satisfy conservation law 2 nearly exactly.
