# APEX: Amplitude Anchors and Phase Priors for Target-Scarce Higher-Frequency Wave Prediction

arXiv: https://arxiv.org/abs/2605.26732 · HTML: https://mlsanity.com/paper/2605.26732/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 22 of its 36 references that are in the map.
- First posted on arXiv 26 May 2026.

## Builds on (most cited first, 22 of 22)

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- [NeurOLight: A Physics-Agnostic Neural Operator Enabling Parametric Photonic Device Simulation](https://mlsanity.com/paper/2209.10098/) (2022)
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- [A Probabilistic Framework for Solving High-Frequency Helmholtz Equations via Diffusion Models](https://mlsanity.com/paper/2602.04082/) (2026)

## Abstract (arXiv)

Learning-based surrogates have become increasingly effective for wave-field prediction, and neural operators in particular have shown strong performance within observed frequency regimes. However, higher-frequency prediction under scarce target supervision remains comparatively underexplored, especially in wave problems where higher-frequency data are substantially more expensive to simulate or measure than lower-frequency data. A central difficulty is that cross-frequency transfer is inherently asymmetric: coarse amplitude structure remains relatively stable across frequencies, whereas phase-sensitive oscillatory structure deteriorates much more rapidly as frequency increases. Motivated by this asymmetry, we propose APEX, Amplitude-anchored and Phase-prior-guided Enhancement from eXtrapolated coarse predictions, a framework for target-scarce higher-frequency wave-field prediction. A lower-frequency neural operator first provides a coarse prediction in the target-frequency regime, from which we retain only the amplitude as a transferable structural anchor. A conditional flow-matching enhancer then reconstructs the target higher-frequency field under the guidance of a Green's-function-inspired phase prior. Experiments on SimpleWave, Helmholtz, and Maxwell benchmarks show that APEX consistently outperforms direct lower-to-higher extrapolation, target-adapted operator, and joint generative baselines under limited target-frequency supervision. Our results suggest that reliable higher-frequency prediction of oscillatory wave fields should not rely on direct end-to-end transfer of the full complex field, but instead on explicitly reusing transferable coarse structure while separately recovering the missing oscillatory detail.