Comment on “Mix-training physics-informed neural networks for the rogue waves of nonlinear Schrödinger equation” [Chaos, Solitons and Fractals 164 (2022) 112712]

While the commented paper introduced physics-informed neural networks (PINNs) with mix-training or adaptive search methods for the rogue wave solutions of nonlinear Schrödinger (NLS) equation, we raise several critical points. First, we argue that the proposed mix-training PINNs (MTPINNs) are essentially standard PINNs, as the simultaneous training on residual and initial/boundary (IB) points is an inherent feature of the original framework by Raissi et al. (2019). Second, the MTPINNs PLUS model description in Formula (4) is inaccurate: adaptively sampled points with large gradients are claimed to augment the supervised loss term, yet the true solution values at these points are unknown. Third, we identify two technical errors in the main results: (i) The exact second-order solutions in Formulas (7) and (8) do not satisfy Formula (5). (ii) The Dirichlet boundary conditions in Formulas (1), (5), (9), and (10) contradict the periodic boundary conditions depicted in Figure 1. Several of the methodological and technical flaws have been identified and addressed in the current work. Furthermore, we propose enhanced self-adaptive PINNs with partition training to extend the previous study, achieving significantly higher accuracy.