Robust and scalable simulation-based inference for gravitational wave signals with gaps

The Laser Interferometer Space Antenna (LISA) data stream will inevitably contain gaps due to maintenance and environmental disturbances, introducing nonstationarities and spectral leakage that compromise standard frequency-domain likelihood evaluations. We present a scalable Simulation-Based Inference (SBI) framework capable of robust parameter estimation directly from gapped time-series data. We employ Flow Matching Posterior Estimation (FMPE) conditioned on a learned summary of the data, optimized through an end-to-end training strategy. To address the computational challenges of long-duration signals, we propose a dual-pathway summarizer architecture: a 1D Convolutional Neural Network (CNN) operating on the time domain for high precision, and a novel wavelet-based 2D CNN utilizing asymmetric, dilated kernels to achieve scalability for datasets spanning months. We demonstrate the efficacy of this framework on simulated Galactic Binary-like signals, showing that our joint training approach yields tighter, unbiased posteriors compared to two-stage reconstruction pipelines. Furthermore, we provide the first systematic comparison showing that FMPE offers superior stability and coverage calibration over conventional Normalizing Flows in the presence of severe data artifacts.