Loss Landscape Diagnosis for Gradient-Based Gray-Scott System Inversion: Disentangling the Roles of PINN Components

In three linesStudy of loss landscape geometry for Gray-Scott system inversion via direct backpropagation through the PDE. Without neural networks, residual loss is quadratic and smooth; the neural network cannot repair an ill-posed parameter subspace, only completes observed data. Design implications for PINN-type methods.

Summary generated by Claude — human-verified