CNNs achieve simultaneous Sobolev approximation on manifolds with intrinsic-dimension rates and enable a PICNN for BVPs via spectral boundary loss that improves stability over standard PINNs.
Scattered data interpolation on embedded sub- manifolds with restricted positive definite kernels: Sobolev error estimates.SIAM Journal on Numerical Analysis, 50(3):1753–1776
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Simultaneous CNN Approximation on Manifolds with Applications to Boundary Value Problems
CNNs achieve simultaneous Sobolev approximation on manifolds with intrinsic-dimension rates and enable a PICNN for BVPs via spectral boundary loss that improves stability over standard PINNs.