Universal Approximation of Nonlinear Operators and Their Derivatives
cs.LG, cs.AI, cs.NA, math.FA, math.NA, math.OC
Submitted: 2026-05-14
Updated: 2026-09-01
License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
Terminology
Sources
- Tucker Tensor Train Taylor Series
- Derivative-Informed Operator Learning for Finance: On-the-Fly Greeks, Surfaces, Hedging, and Control
- Optimal control of stochastic Volterra integral equations with completely monotone kernels and stochastic differential equations on Hilbert spaces with unbounded control and diffusion operators
- Universal approximation with signatures of non-geometric rough paths
- Deep Hilbert--Galerkin Methods for Infinite-Dimensional PDEs and Optimal Control
- Stochastic Optimal Control of Interacting Particle Systems in Hilbert Spaces and Applications
- New universal operator approximation theorem for encoder-decoder architectures
- Shape Derivative-Informed Neural Operators with Application to Risk-Averse Shape Optimization
- The Volterra signature
- An operator learning perspective on parameter-to-observable maps
- Topological DeepONets and a generalization of the Chen-Chen operator approximation theorem
- Learning in Mean Field Games: A Survey
- DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators
- Dimension reduction for derivative-informed operator learning: An analysis of approximation errors
- Learning operators on labelled conditional distributions with applications to mean field control of non exchangeable systems
- A path-dependent PDE solver based on signature kernels
- Optimal control of Volterra integral diffusions and application to contract theory
- On the convergence of physics informed neural networks for linear second-order elliptic and parabolic type PDEs
- Performance of Neural and Polynomial Operator Surrogates
- Derivative-Informed Fourier Neural Operator: Universal Approximation and Applications to PDE-Constrained Optimization
Related papers
- Polynomial-Augmented Neural Networks (PANNs) with Weak Orthogonality Constraints for Enhanced Function and PDE Approximation
- AIRL-S: Unifying Reinforcement Learning and Search-Based Test-Time Scaling via Adversarial Inverse Reinforcement Learning
- Transformers as Bayesian In-Context Experimenters: Smoothness-Adaptive Efficient ATE Estimation
- Convergence issues in Relational Concept Analysis based on AOC-posets
- Beliefs Beyond Posteriors: Local-Consistency Optimisation for Bayesian Neural Networks
- Understanding Diffusion Models via Ratio-Based Function Approximation with SignReLU Networks