Spectrally Safe Neural Operator Warm-Starts for Large-Scale Newton Solvers
Neural operators are increasingly used to warm-start Newton solvers for nonlinear PDEs, on the premise that a low test error places the initial guess inside the basin of attraction. We show that this premise is unreliable. An operator trained to the relative \(L^2\) error \(O(10^{-3})\) can still produce an initial state in which the discrete Jacobian is indefinite, because the mean-squared training controls error on average while leaving localized pointwise violations of the underlying physics. For a nearly incompressible hyperelasticity problem, we trace this to the predicted volume change: the operator disperses \(\mathrm{det} F\) well away from one, and the resulting Jacobian acquires...
| Authors | Jaemin Oh, Youngkyu Lee, Jerome Darbon et al. |
|---|---|
| Primary category | math.NA |
| Published | 20 June 2026 |
| Last updated at source | 18 August 2026 |
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