Deep Learning Detection of Beyond-General-Relativity Deviations in Gravitational-Wave Signals: A Detection-Threshold Study with Real LIGO Noise

We study machine-learning detection of controlled beyond-General-Relativity (beyond-GR) deviations in gravitational-wave signals, using both synthetic aLIGO-PSD noise and real LIGO H1 detector strain. Three deviation families are applied to General-Relativistic inspiral-merger-ringdown waveforms: amplitude modulation, phase modulation, and frequency modulation, each parameterized by a dimensionless strength coefficient $β$. A hybrid classifier combining a one-dimensional convolutional neural network with ten hand-crafted waveform statistics is trained on GR and modified waveforms and tested on a deviation type excluded from training. The central result is a quantitative detectability curve as a function of $β$. Using the real GW150914 strain as a template and real H1 detector noise, we find a detection threshold at $β\approx 0.25$, with accuracy rising smoothly from chance at $β\leq 0.2$ to perfect classification at $β\geq 0.5$. The threshold value is specific to the quadratic-in-time modulation form adopted here and should not be interpreted as a generic constraint on beyond-GR parameters. We nevertheless argue that the negative result at small $β$ is informative: it establishes a quantitative limit on machine-learning-only beyond-GR searches in real detector noise, in the absence of matched-filter signal extraction.