Fixed and Adaptive Topological DeepONets: Functional Measurements on Hausdorff Locally Convex Spaces
Deep Operator Networks (DeepONets; arXiv:1910.03193) typically encode an input function through point values on a fixed discretization. Building on the Topological DeepONet framework of Ismailov (arXiv:2603.11972), we replace point samples by continuous linear functionals drawn from the continuous dual of a Hausdorff locally convex space $({V},\{p_α\}_{α\in A})$, whose topology is generated by a point-separating family of seminorms rather than a single norm, and develop fixed and adaptive functional measurement systems. Measurements are combined with the coefficient-space Two-Step procedure of Lee and Shin (arXiv:2309.01020), while a training-only decoder and regularization stabilize the ...
| Authors | Khemraj Shukla, George Em Karniadakis |
|---|---|
| Primary category | cs.LG |
| Published | 5 August 2026 |
| Last updated at source | 5 August 2026 |
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