Variational and primal-dual training of multiscale PDE networks have epsilon-uniform error bounds, while strong-residual training classes provably have Rademacher complexity at least 1/(ε√N) and 1/(ε²√N).
A priori error estimate of deep mixed residual method for elliptic PDEs
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Non-Asymptotic Variational Learning for Monotone Nonlinear Multiscale Elliptic Equations: Scale-Robust Primal-Dual Bounds and Strong-Form Statistical Ill-Conditioning
Variational and primal-dual training of multiscale PDE networks have epsilon-uniform error bounds, while strong-residual training classes provably have Rademacher complexity at least 1/(ε√N) and 1/(ε²√N).