The Coercivity Gap in Neural
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The Coercivity Gap in Neural PDE Solvers: Parameter Escape and Functional Convergence
arXiv:2606.04018v1 Announce Type: new Abstract: We study neural approximation of elliptic PDE solutions from a variational perspective. The central point is the distinction between the geometry of neural parameters and the convergence of the corresponding physical states. Even when the original elliptic energy is coercive and strictly convex in the natural energy space, its restriction to a nonlinear neural ansatz may fail to be coercive in parameter space.