Surface wave experiments in laboratory vessels suffer from a persistent problem: the boundary conditions at the vessel walls are difficult to determine theoretically, which means the spatial profiles of the wave modes are not known in advance. Gregory, Barroso, Schiattarella, Avgoustidis, and Weinfurtner address this with Extracted Mode Tracking (EMT), a data-analysis framework that uses unsupervised machine learning to extract a basis of wave modes directly from experimental measurements, bypassing the need for any theoretical assumption about modal shape.

The method works by treating the measured surface height field as a superposition of unknown spatial profiles with time-varying amplitudes. Unsupervised learning decomposes the data into these components without being told what to look for. The reconstruction of instantaneous amplitudes proceeds through geometric fitting across temporal snapshots, and the framework includes noise-resilience metrics that quantify how reliably each mode has been extracted. Validation against Faraday wave experiments – where parametric forcing generates known resonance patterns – confirms that EMT recovers the expected mode structure and, critically, provides access to nonlinear interactions between modes that analytical methods would miss because they assume the modes are already known.

The significance lies in the inversion of the standard workflow. Normally, one derives the modes from theory and fits amplitudes from data. EMT derives both from data alone. This makes the method applicable to any axially symmetric fluid interface system, including experimental configurations where walls are rough, deformable, or partially submerged – situations where boundary conditions are genuinely unknown rather than merely inconvenient to compute.

(arXiv:2603.06891)