Convergence theory for Hermite approximations under adaptive coordinate transformations
Recent work has shown that parameterizing and optimizing coordinate transformations using normalizing flows, i.e., invertible neural networks, can significantly accelerate the convergence of spectral approximations. We present the first error estimates for approximating functions using Hermite expansions composed with adaptive coordinate transformations. Our analysis establishes an equivalence principle: approximating a function $f$ in the span of the transformed basis is equivalent to approximating the pullback of $f$ in the span of Hermite functions. This allows us to leverage the classical approximation theory of Hermite expansions to derive error estimates in transformed coordinates i...
| Authors | Yahya Saleh |
|---|---|
| Primary category | math.NA |
| Published | 18 April 2026 |
| Last updated at source | 18 April 2026 |
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