Direct gradient-based inversion of the Gray-Scott system fails due to flat loss plateaus at bifurcations, while the residual loss alone produces a smooth landscape by encoding full PDE dynamics.
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Loss Landscape Diagnosis for Gradient-Based Gray-Scott System Inversion: Disentangling the Roles of PINN Components
Direct gradient-based inversion of the Gray-Scott system fails due to flat loss plateaus at bifurcations, while the residual loss alone produces a smooth landscape by encoding full PDE dynamics.