CNNs achieve dimension-dependent Sobolev approximation rates on manifolds, and a spectral boundary loss using Laplace-Beltrami eigenmodes enables stable PINN solutions for elliptic problems with improved accuracy over standard approaches.
Trace regularity PINNs: EnforcingH 1/2(∂Ω) for bound- ary data
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Simultaneous CNN Approximation on Manifolds with Applications to Boundary Value Problems
CNNs achieve dimension-dependent Sobolev approximation rates on manifolds, and a spectral boundary loss using Laplace-Beltrami eigenmodes enables stable PINN solutions for elliptic problems with improved accuracy over standard approaches.