A deep learning framework for amplitude generation of generic EMRIs

Abstract

Abstract One of the main targets for space-borne gravitational wave detectors is the detection of Extreme Mass Ratio Inspiral (EMRIs). Data analysis of EMRIs requires waveform models that are both accurate and fast. The major challenge for the fast generation of such waveforms is the generation of the Teukolsky amplitudes for generic (eccentric and inclined) Kerr orbits. The requirement for modeling $${\sim 10^5}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mo>∼</mml:mo> <mml:msup> <mml:mn>10</mml:mn> <mml:mn>5</mml:mn> </mml:msup> </mml:mrow> </mml:math> harmonic modes in a four-dimensional parameter space makes traditional approaches, including direct computation or dense interpolation, computationally prohibitive. To overcome this issue, we introduce a convolutional encoder–decoder architecture for a fast and end-to-end global fitting of the Teukolsky amplitudes. We also adopt a transfer learning strategy to reduce the size of the training dataset, and the model is gradually trained from the simplest Schwarzschild circular orbits to generic Kerr orbits step by step. Within this framework, we obtain a surrogate model based on a semi-analytical Post-Newtonian dataset, and the full harmonic amplitudes can be generated within milliseconds, while the median mode-distribution error for generic orbits is $$\sim 10^{-3}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mo>∼</mml:mo> <mml:msup> <mml:mn>10</mml:mn> <mml:mrow> <mml:mo>-</mml:mo> <mml:mn>3</mml:mn> </mml:mrow> </mml:msup> </mml:mrow> </mml:math> . This result indicates that the framework is viable for the construction of efficient waveform models for EMRIs.