AINeutralarXiv – CS AI · 11h ago6/10
🧠
Universal Approximation of Nonlinear Operators and Their Derivatives
Researchers have proven the first Universal Approximation Theorems for k-times differentiable nonlinear operators and their derivatives in infinite-dimensional Banach spaces, establishing theoretical foundations for Derivative-Informed Operator Learning (DIOL). This breakthrough extends classical approximation theory to operator learning architectures like DeepONets and enables applications in optimal control, PDEs, and inverse problems.