Lisa Gaedke-Merzhäuser

Afif Boudaoud, Lisa Gaedke-Merzhäuser, Alexandros Nikolaos Ziogas et al.

Spatio-temporal Bayesian inference drives environmental and health sciences using latent Gaussian models. Integrated Nested Laplace Approximations (INLA) enable inference for these models at HPC scale but rely on derivative-based optimization over $d$ hyperparameters. State-of-the-art INLA implementations approximate derivatives via central finite differences (FD), requiring $2d{+}1$ evaluations. These evaluations are embarrassingly parallel, but total work and energy grow with $d$, limiting time-to-solution under fixed budgets. Reverse-mode automatic differentiation (AD) computes exact gradients independently of $d$, but its efficient application to INLA's structured-sparse kernels is an open challenge. We present ADELIA, the first AD-enabled INLA implementation with a structure-exploiting multi-GPU backward pass leveraging model sparsity. We evaluate ADELIA on ten benchmark models, including real-world air-pollution monitoring. We achieve $4.2$--$7.9\times$ per-gradient speedups and reliable convergence on production-scale models with up to 1.9M latent variables, where FD struggles. Even when scaled to 16--32 GPUs to match ADELIA's wall-clock time, FD consumes $5$--$8\times$ more energy.

Lisa Gaedke-Merzhäuser, Alena Kopaničáková, Rolf Krause

We present a new multilevel minimization framework for the training of deep residual networks (ResNets), which has the potential to significantly reduce training time and effort. Our framework is based on the dynamical system's viewpoint, which formulates a ResNet as the discretization of an initial value problem. The training process is then formulated as a time-dependent optimal control problem, which we discretize using different time-discretization parameters, eventually generating multilevel-hierarchy of auxiliary networks with different resolutions. The training of the original ResNet is then enhanced by training the auxiliary networks with reduced resolutions. By design, our framework is conveniently independent of the choice of the training strategy chosen on each level of the multilevel hierarchy. By means of numerical examples, we analyze the convergence behavior of the proposed method and demonstrate its robustness. For our examples we employ a multilevel gradient-based methods. Comparisons with standard single level methods show a speedup of more than factor three while achieving the same validation accuracy.