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.
Cambridge University Press
2 Pith papers cite this work. Polarity classification is still indexing.
2
Pith papers citing it
verdicts
UNVERDICTED 2representative citing papers
Establishes near-optimal dimension-independent convergence rates for regularized SGD with operator-valued kernels in statistical inverse problems for operator learning.
citing papers explorer
-
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.
-
Learning Operators by Regularized Stochastic Gradient Descent with Operator-valued Kernels
Establishes near-optimal dimension-independent convergence rates for regularized SGD with operator-valued kernels in statistical inverse problems for operator learning.