Scalability analysis and performance modelling of layer-parallel training of deep residual networks using a non-linear multigrid-in-time algorithm

Replacing the traditional forward and backward passes in a residual network with a Multigrid-Reduction-in-Time (MGRIT) algorithm paves the way for exploiting parallelism across the layer dimension. In this paper, we evaluate the layer-parallel MGRIT algorithm with respect to convergence, scalability, and performance on regression problems. Specifically, we demonstrate that a few MGRIT iterations solve the systems of equations corresponding to the forward and backward passes in ResNets up to reasonable tolerances. We also demonstrate that the MGRIT algorithm breaks the scalability barrier created by the sequential propagation of data during the forward and backward passes. Moreover, we show that ResNet training using the layer-parallel algorithm significantly reduces the training time compared to the layer-serial algorithm on two non-linear regression tasks. We observe much more efficient training loss curves using layer-parallel ResNets as compared to the layer-serial ResNets on two regression tasks. We hypothesize that the error stemming from approximately solving the forward and backward pass systems using the MGRIT algorithm helps the optimization algorithm escape flat saddle-point-like plateaus or local minima on the optimization landscape. We validate this by illustrating that artificially injecting noise in a typical forward or backward propagation, allows the optimizer to escape a saddle-point-like plateau at network initialization

Hardware-aware block size tailoring on adaptive spacetree grids for shallow water waves.

Spacetrees are a popular formalism to describe dynamically adaptive Cartesian grids. Though they directly yield an adaptive spatial discretisation, i.e. a mesh, it is often more efficient to augment them by regular Cartesian blocks embedded into the spacetree leaves. This facilitates stencil kernels working efficiently on homogeneous data chunks. The choice of a proper block size, however, is delicate. While large block sizes foster simple loop parallelism, vectorisation, and lead to branch-free compute kernels, they bring along disadvantages. Large blocks restrict the granularity of adaptivity and hence increase the memory footprint and lower the numerical-accuracy-per-byte efficiency. Large block sizes also reduce the block-level concurrency that can be used for dynamic load balancing. In the present paper, we therefore propose a spacetree-block coupling that can dynamically tailor the block size to the compute characteristics. For that purpose, we allow different block sizes per spacetree node. Groups of blocks of the same size are identied automatically throughout the simulation iterations, and a predictor function triggers the replacement of these blocks by one huge, regularly rened block. This predictor can pick up hardware characteristics while the dynamic adaptivity of the fine grid mesh is not constrained. We study such characteristics with a state-of-the-art shallow water solver and examine proper block size choices on AMD Bulldozer and Intel Sandy Bridge processors

A Flexible Patch-Based Lattice Boltzmann Parallelization Approach for Heterogeneous GPU-CPU Clusters

Sustaining a large fraction of single GPU performance in parallel computations is considered to be the major problem of GPU-based clusters. In this article, this topic is addressed in the context of a lattice Boltzmann flow solver that is integrated in the WaLBerla software framework. We propose a multi-GPU implementation using a block-structured MPI parallelization, suitable for load balancing and heterogeneous computations on CPUs and GPUs. The overhead required for multi-GPU simulations is discussed in detail and it is demonstrated that the kernel performance can be sustained to a large extent. With our GPU implementation, we achieve nearly perfect weak scalability on InfiniBand clusters. However, in strong scaling scenarios multi-GPUs make less efficient use of the hardware than IBM BG/P and x86 clusters. Hence, a cost analysis must determine the best course of action for a particular simulation task. Additionally, weak scaling results of heterogeneous simulations conducted on CPUs and GPUs simultaneously are presented using clusters equipped with varying node configurations.Comment: 20 pages, 12 figure

AI Driven Near Real-time Locational Marginal Pricing Method: A Feasibility and Robustness Study

Accurate price predictions are essential for market participants in order to optimize their operational schedules and bidding strategies, especially in the current context where electricity prices become more volatile and less predictable using classical approaches. Locational Marginal Pricing (LMP) pricing mechanism is used in many modern power markets, where the traditional approach utilizes optimal power flow (OPF) solvers. However, for large electricity grids this process becomes prohibitively time-consuming and computationally intensive. Machine learning solutions could provide an efficient tool for LMP prediction, especially in energy markets with intermittent sources like renewable energy. The study evaluates the performance of popular machine learning and deep learning models in predicting LMP on multiple electricity grids. The accuracy and robustness of these models in predicting LMP is assessed considering multiple scenarios. The results show that machine learning models can predict LMP 4-5 orders of magnitude faster than traditional OPF solvers with 5-6\% error rate, highlighting the potential of machine learning models in LMP prediction for large-scale power models with the help of hardware solutions like multi-core CPUs and GPUs in modern HPC clusters