In particular, all our experiments are now in 3D. We also added significantly more results to further explore the behavior of FPSGR in comparison to optimization-based SGR. In particular, we added (a) an example to visualize the performance of regression models and associated quantitative comparisons (Sec. \[sec:regression\_results\]); (b) an analysis of local atrophy score correlated with clinical variables (Sec. \[sec:atrophy\]); (c) correlations within diagnostic groups (Sec. \[sec:atrophy\]); (d) a comparison with pairwise registration (Sec. \[sec:sgr\_justification\]); (e) and experiments on extrapolation on unseen data (Sec. \[sec:forecast\], Sec. \[sec:jacobian\]). 1ex **Organization.** The remainder of this article is organized as follows: Sec. \[sec:method\] describes FPSGR, Sec. \[sec:experimental\_setup\] discusses the experimental setup and the training of the prediction models. In Sec. \[sec:discussion\_of\_experimental\_results\], we present experimental results for 3D MR brain images. The paper concludes with a summary and an outlook on future work.

Fast predictive simple geodesic regression {#sec:method}
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Our fast predictive simple geodesic regression approach is a combination of two methods: *First*, fast predictive image registration (FPIR) and, *second*, integration of FPIR with simple geodesic regression (SGR). Both FPIR and SGR are based on the shooting formulation of LDDMM [@ref:nikhil]; Fig. \[fig:1\] illustrates our overall approach. The individual components are described in 