Gravitational waves (GWs) in the millihertz bands provide are great tools for understanding the cosmological evolution of supermassive black holes (SMBHs) in galactic nuclei. SMBH binaries in high-redshift quasars are expected to be the primarily target of individually identified GW sources. Previous studies mainly considered specific BH seeding models and limited mass ranges in estimating the GW event rate (e.g., light BH seeds originating from Population III remnants vs. heavy BH seeds through direct-collapse of massive pristine gas). Recently, the unprecedented sensitivity of James Webb Space Telescope (JWST) has enabled the discovery of low-mass BHs with masses of 10^6-10^8 Msun at z~4-7, hidden in the pre-JWST era. Combined with known quasars, those newly discovered samples improve understanding of the low-mass end of the BH mass distribution.
In this talk, we present a theoretical model describing BH growth from initial seeding at z>20 to z~2, with an initial seed mass function developed by radiation hydrodynamical simulations, differing from light or heavy seed scenarios. By constraining the model parameters with the up-to-date observed quasar luminosity functions and BH mass functions, we construct the evolution tracks of the BH progenitors. The calibrated model offers a more reliable event rate of GW emission with future space-based GW interferometers, revealing a distinguishable mass distribution for detectable binary BH mergers compared to previous assumptions.