[@hong2017fast] achieves $\approx 16$ times speed-up compared with SGR [@ref:hong] for the same setting (parallel computing with the same number of cores). In our case, we achieve a more than 40 times speed-up compared with SGR for the same setting (a single GPU).

Experimental results for 3D ADNI data {#sec:discussion_of_experimental_results}
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![Region of Interest (ROI) significantly associated with atrophy in AD used to compute atrophy scores.[]{data-label="fig:ROI"}](image/ROI_refine.png){width="50.00000%"}

For our experiments, we created 10 different (dataset, registration approach) combinations, each combination specifically designed to assess certain properties of our proposed strategy. These combinations are described next.

-   All subjects from the `ADNI-1` dataset in combination with optimization-based LDDMM.

-   Two subgroups of `ADNI-1` (i.e., different training data portions) in combination with FPSGR *without* a correction network.

-   The same two subgroups as in 2), but in combination with FPSGR *with* a correction network.

-   The same five groups of 1-3, but for `ADNI-2`.

Our general hypothesis is that the prediction models (for `ADNI-1/2`) show similar performance to optimization-based LDDMM and that using the correction network for the predictions improves results. To assess differences, we compare differences in deformations. Specifically, for every deformation produced by the different approaches, we compute its Jacobian determinant 