Fixed and Adaptive Topological DeepONets: Functional Measurements on Hausdorff Locally Convex Spaces
Khemraj Shukla, George Em Karniadakis
cs.LG, math-ph, math.GN, math.MP
Submitted: 2026-08-05
Updated: 2026-08-10
License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
Terminology
Sources
- Topological DeepONets and a generalization of the Chen-Chen operator approximation theorem
- Neural Operator Modeling of Platelet Geometry and Stress in Shear Flow
- Deep operator learning-based surrogate models for aerothermodynamic analysis of AEDC hypersonic waverider
- Universal Differential Equations for Scientific Machine Learning
- Uncertainty Quantification in PINNs for Turbulent Flows: Bayesian Inference and Repulsive Ensembles
- Variable-Input Deep Operator Networks
- BelNet: Basis enhanced learning, a mesh-free neural operator
- A discretization-invariant extension and analysis of some deep operator networks
- Error estimates for DeepOnets: A deep learning framework in infinite dimensions
- Physics-Informed Neural Operator for Learning Partial Differential Equations
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