Learning Operators by Regularized Stochastic Gradient Descent with Operator-valued Kernels
stat.ML, cs.LG, math.FA, math.ST, stat.TH
Submitted: 2025-04-25
Updated: 2026-09-25
Comments: 78 pages, 3 figures
License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
Terminology
Sources
- The Sample Complexity of Learning Lipschitz Operators with respect to Gaussian Measures
- Towards Sharp Minimax Risk Bounds for Operator Learning
- Solving Inverse Parametrized Problems via Finite Elements and Extreme Learning Networks
- Theory-to-Practice Gap for Neural Networks and Neural Operators
- Data Complexity Estimates for Operator Learning
- An Efficient Deep Learning Approach for Approximating Parameter-to-Solution Maps of PDEs
- On the Saturation Effect of Kernel Ridge Regression
- Statistical Learning Theory for Neural Operators
- Stochastic Gradient Descent for Operator Learning in Hilbert Spaces: Convergence Rates and Minimax Lower Bounds
- A Kernel-based Stochastic Approximation Framework for Nonlinear Operator Learning
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