This presentation discusses interpretable, data-driven reduced-order models (ROMs) using kernel methods. While ROMs can significantly reduce the computational cost and runtime of large-scale numerical simulations, many approaches require access to the full-order model (FOM) source code, which is not always feasible. Conversely, non-intrusive ROM approaches like Operator Inference (OpInf) [3, 2] and Latent Space Dynamics Identification (LaSDI) [1] are entirely data-driven and compute ROMs without requiring access to the FOM source code. These approaches first compute reduced-order representations of given snapshot data using, e.g., Proper Orthogonal Decomposition (POD) or a Quadratic Manifold (QM) [4], and learn reduced-order dynamics by solving a least-squares problem to infer reduced-order operators that are optimal in the Frobenius norm. As an alternative to OpInf and LaSDI, our approach uses regularized kernel interpolation to learn the reduced-order dynamics. This approach has the following advantages: (1) the resulting non-intrusive ROM can be imbued with interpretable structure via the choice of kernel; (2) the ROM is optimal in the chosen kernel’s native reproducing kernel Hilbert space (RKHS); and (3) a posteriori error bounds can be derived. We demonstrate the proposed kernel ROM approach on several example problems, including a 2D Euler Riemann problem.