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The future space mission LISA will observe a wealth of gravitational-wavesources at millihertz frequencies. Of these, the extreme-mass-ratio inspiralsof compact objects into massive black holes are the only sources that combinethe challenges of strong-field complexity with that of long-lived signals. Suchsignals are found and characterized by comparing them against a large number ofaccurate waveform templates during data analysis, but the rapid generation ofsuch templates is hindered by computing the $\sim10^3$-$10^5$ harmonic modes ina fully relativistic waveform. We use order-reduction and deep-learningtechniques to derive a global fit for these modes, and implement it in acomplete waveform framework with hardware acceleration. Our high-fidelitywaveforms can be generated in under $1\,\mathrm{s}$, and achieve a mismatch of$\lesssim 5\times 10^{-4}$ against reference waveforms that take $\gtrsim 10^4$times longer. This marks the first time that analysis-length waveforms withfull harmonic content can be produced on timescales useful for directimplementation in LISA analysis algorithms.

Rapid generation of fully relativistic extreme-mass-ratio-inspiral waveform templates for LISA data analysis