Neural Lagrangian Discovery from Gravitational Wave Data: Extracting the Effective Action of Binary Black Hole Mergers from LIGO Open Data

We apply the Neural Lagrangian framework to real gravitational wave data for the first time, using the publicly available GW150914 strain data from the LIGO Hanford detector. A neural network is trained to represent an effective Lagrangian Lₑff (h, ḣ) for the strain signal h (t), minimising the Euler-Lagrange residual on filtered data surrounding the first detected binary black hole merger. The effective potential Vₑff (h) and kinetic term Tₑff (ḣ) are extracted and subjected to symbolic regression using PySR. The learned Lagrangian achieves an EL residual of 3. 18 × 10⁻³. We discuss two physical interpretations of the extracted action: (1) a phenomenological effective action governing strain evolution, and (2) a signature of the gauge freedom inherent in Lagrangian representations of GW strain. This work establishes the first variational framework for LIGO strain analysis and opens a pathway for data-driven discovery of modifications to general relativity. This is Paper 7 of the Neural Lagrangian Series. LIGO data accessed via the Gravitational Wave Open Science Center (GWOSC) under open data terms.