Performance of Neural and Polynomial Operator Surrogates
We consider the problem of constructing surrogate operators for parameter-to-solution maps arising from parametric partial differential equations, where repeated forward model evaluations are computationally expensive. We present a systematic empirical comparison of neural operator surrogates, including a reduced-basis neural operator trained with $L^2_μ$ and $H^1_μ$ objectives and the Fourier neural operator, against polynomial surrogate methods, specifically a reduced-basis sparse-grid surrogate and a reduced-basis tensor-train surrogate. All methods are evaluated on a linear parametric diffusion problem and a nonlinear parametric hyperelasticity problem, using input fields with algebra...
| Authors | Josephine Westermann, Benno Huber, Thomas O'Leary-Roseberry et al. |
|---|---|
| Primary category | cs.LG |
| Published | 1 April 2026 |
| Last updated at source | 1 April 2026 |
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