Rapid parameter estimation with the full symphony of compact binary mergers using meshfree approximation

We present a fast Bayesian inference framework to address the growing computational cost of gravitational-wave parameter estimation. The increased cost is driven by improved broadband detector sensitivity, particularly at low frequencies due to advances in detector commissioning, resulting in longer in-band signals and a higher detection rate. Waveform models now incorporate features like higher-order modes, further increasing the complexity of standard inference methods. Our framework employs meshfree likelihood interpolation with radial basis functions to accelerate Bayesian inference using the IMRPhenomXHM waveform model that incorporates higher modes of the gravitational-wave signal. In the initial start-up stage, interpolation nodes are placed within a constant-match metric ellipsoid in the intrinsic parameter space. During sampling, likelihood is evaluated directly using the precomputed interpolants, bypassing the costly steps of on-the-fly waveform generation and overlap-integral computation. We improve efficiency by sampling in a rotated parameter space aligned with the eigenbasis of the metric ellipsoid, where parameters are uncorrelated by construction. This speeds up sampler convergence. This method yields unbiased parameter recovery when applied to 100 simulated neutron-star-black-hole signals (NSBH) in LIGO-Virgo data, while reducing computational cost by up to an order of magnitude for the longest-duration signal. The meshfree framework equally applies to symmetric compact binary systems dominated by the quadrupole mode, supporting parameter estimation across a broad range of sources. Applied to a simulated NSBH signal in Einstein Telescope data, where the effects of Earth's rotation are neglected for simplicity, our method achieves an O(10^4) speed-up, demonstrating its potential use in the third-generation (3G) era.