Three-dimensional Ground Penetrating Radar (3D GPR) data offer comprehensive views of the subsurface, yet identifying and classifying underground anomalies from this data is challenging due to limitations like scarce training data and variable underground environments. In response, we introduce learning in the Cube Reservoir Network (CubeRes) model space for efficient and accurate subsurface anomaly detection. CubeRes, incorporating three reservoirs, captures the dynamics in both horizontal and vertical directions inherent in the 3D GPR data. Fitting the data with CubeRes, representing the data with the compact fitted model, and measuring the difference between models by a proposed parameterized model metric, the original data is transformed from the data space to the CubeRes model space. Subsequently, we introduce an optimization strategy in this model space, aimed at bolstering fitting accuracy and improving category discrimination. This enhancement facilitates a more nuanced differentiation of dynamics across various GPR data categories, thereby enabling effective classification on the models rather than the original data. Experiments on real-world data validate our method's effectiveness and superiority, particularly in data-limited scenarios.