The core-surface flow is crucial for understanding the dynamics of the Earth’s outer core and geomagnetic secular variations. Conventional core flow models often use a single set of spherical harmonic coefficients to represent the flow both inside and outside the tangent cylinder, inherently imposing continuity across the tangent cylinder around the solid inner core. To address this limitation, we present a core-surface flow inversion framework based on physics-informed neural networks. This framework employs distinct neural network representations for the flow inside and outside the tangent cylinder, allowing for discontinuities as the flow crosses the tangent cylinder. Additionally, it incorporates secular acceleration data to constrain the temporal evolution of the core flow. Using this inversion framework, we derive a new core-surface flow model spanning 2001 to 2024 from a geomagnetic model, incorporating the latest magnetic data from Swarm satellites and Macau Science Satellite-1. The recovered model reveals persistent large-scale circulation linked to westward drift, significant temporal variations in the equatorial Pacific, and distinct jet-like structures at the poles. The inversion also reveals a large-scale wave pattern in equatorial azimuthal flow acceleration, corresponding to observed geomagnetic jerks and likely resulting from quasi-geostrophic magneto-Coriolis waves. Additionally, the framework infers small-scale magnetic fields at the core-mantle boundary, highlighting split flux concentrations and localized high-latitude patches.