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

2026-05-26

AI Summary

This work addresses the challenge of accurately predicting high-frequency wavefields under conditions of scarce high-frequency data and degraded cross-frequency phase structure. To overcome these limitations, the authors propose the APEX framework, which innovatively decouples amplitude and phase components. The approach first employs a low-frequency neural operator to generate a coarse prediction and extracts its cross-frequency stable amplitude as a structural anchor. It then reconstructs the high-frequency wavefield by integrating a Green’s function–inspired physical phase prior through a conditional flow-matching enhancer. Evaluated on the SimpleWave, Helmholtz, and Maxwell benchmarks, APEX significantly outperforms existing baselines, achieving superior extrapolation accuracy even with limited high-frequency supervision.

Abstract

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.

Problem

• higher-frequency wave prediction
• target-scarce learning
• cross-frequency transfer
• oscillatory wave fields
• amplitude-phase asymmetry

Innovation

• amplitude anchor
• phase prior
• neural operator
• flow matching
• cross-frequency transfer