Amortised Time-Domain Simulation Based Inference for Short Gravitational Wave Transients*

Ringdown is a brief phase after a compact-binary merger when the remnant black hole settles, and its damped oscillations encode properties of the spacetime. Its millisecond-scale duration and simple morphology make it especially well-suited to time-domain inference, where a short window cleanly captures the signal with no spectral leakage and straightforward noise handling. While ringdown inference in the time-domain is already fast due to the signal's short duration, it provides a clean testbed for a general, amortised Simulation Based Inference (SBI) workflow. We present a time-domain SBI case study that learns the posterior for ringdown waveforms using a normalising flow conditioned on the output from a compact 1-D CNN (Convolutional Neural Network) encoder of the strain time series. The learned posteriors show qualitative agreement with reference time-domain MCMC posteriors. Our emphasis is on developing a robust, extensible time-domain SBI approach with negligible per-event cost once amortised.. We outline design choices like the flow depth and width, structure of the CNN encoder etc., and discuss limitations and next steps. This includes signals with two polarisations, coloured noise, and multiple-mode extensions.