Neural Shape Operator Surrogates -- Expression Rate Bounds
We prove error bounds for operator surrogates of solution operators for partial differential and boundary integral equations on families of domains which are diffeomorphic to one common reference (or latent) domain $D_{ref}$. The pullback of the PDE to $D_{ref}$ via affine-parametric shape encoding produces a collection of holomorphic parametric PDEs on $D_{ref}$. Sufficient conditions for (uniformly with respect to the parameter) well-posedness are given, implying existence, uniqueness and stability of parametric solution families on $D_{ref}$. We illustrate the abstract hypotheses by reviewing recent holomorphy results for a suite of elliptic and parabolic PDEs. Quantified parametric ho...
| Authors | Helmut Harbrecht, Christoph Schwab |
|---|---|
| Primary category | cs.LG |
| Published | 20 April 2026 |
| Last updated at source | 20 April 2026 |
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