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.
Sharp lower bounds on the manifold widths of Sobolev and Besov spaces.Journal of Complexity, 85:101884, 2024
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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.