Learning thermodynamically-consistent dynamics of binary black hole systems from gravitational wave measurements*

We introduce a Neural ODE model for the inverse problem of determining the equations of motion of a binary black hole system from its gravitational waves. The orbital dynamics of the binary system is characterized by a neural ODE in the GENERIC formalism $\dot x = L\nabla E + M\nabla S$. This formalism enables an interpretable neural network architecture capable of adding relativistic corrections to the dissipation term $M \nabla S$. We validate the neural ODE model using waveform data from the geodesics of the Schwarzschild metric. The Neural ODE is able to solve the inverse problem for both circular and eccentric inspirals by learning the angular momentum dissipative flux term. This GENERIC-formalism inspired Neural ODE enables a thermodynamically consistent approach to determining the orbital dynamics of binary black holes from their gravitational waves. We seek to extend this approach to determine the orbital dynamics of more astrophysically relevant systems, such as rotating Kerr black holes and binary black hole systems embedded in accretion disks.