This paper presents a scalable approach for large-scale Adaptive Mesh Refinement (AMR) time series interactive visualization. We can define AMR data as a dynamic gridding format of cells hierarchically refined from a computational domain described in this study as a regular Cartesian grid. This adaptive feature is essential for tracking time-dependent evolutionary phenomena and makes the AMR format an essential representation for 3D numerical simulations. However, the visualization of numerical simulation data highlights one critical issue: the significant increases in generated data memory footprint reaching petabytes, thus greatly exceeding the memory capabilities of the most recent graphics hardware. Therefore, the question is how to access this massive data - AMR time series in particular - for interactive visualization on a simple workstation. To overcome this main problem, we present an out-of-core GPU-based architecture. Our proposal is a cache system based on an ad-hoc bricking identified by a Space-Filling Curve (SFC) indexing and managed by a GPU-based page table that loads required AMR data on-the-fly from disk to GPU memory.