Sparse-Aware Neural Networks for Nonlinear Functionals: Mitigating the Exponential Dependence on Dimension

Researchers propose a sparse-aware neural network framework that combines convolutional architectures with fully connected networks to improve operator learning over infinite-dimensional function spaces. The approach significantly reduces the curse of dimensionality and sample complexity requirements for approximating nonlinear functionals, with improved theoretical guarantees for both deterministic and random sampling schemes.