Solving the shallow water equations efficiently is critical to the study of natural hazards induced by tsunami and storm surge, since it provides more response time in an early warning system and allows more runs to be done for probabilistic assessment where thousands of runs may be required. Using adaptive mesh refinement speeds up the process by greatly reducing computational demands while accelerating the code using the graphics processing unit (GPU) does so through using faster hardware. Combining both, we present an efficient CUDA implementation of GeoClaw, an open source Godunov‐type high‐resolution finite volume numerical scheme on adaptive grids for shallow water system with varying topography. The use of adaptive mesh refinement and spherical coordinates allows modeling transoceanic tsunami simulation. Numerical experiments on the 2011 Japan tsunami and a local tsunami triggered by a hypothetical
 NSFPAR ID:
 10372141
 Publisher / Repository:
 DOI PREFIX: 10.1029
 Date Published:
 Journal Name:
 Journal of Advances in Modeling Earth Systems
 Volume:
 11
 Issue:
 8
 ISSN:
 19422466
 Page Range / eLocation ID:
 p. 26062628
 Format(s):
 Medium: X
 Sponsoring Org:
 National Science Foundation
More Like this

Obeid, I. ; Selesnik, I. ; Picone, J. (Ed.)The Neuronix highperformance computing cluster allows us to conduct extensive machine learning experiments on big data [1]. This heterogeneous cluster uses innovative scheduling technology, Slurm [2], that manages a network of CPUs and graphics processing units (GPUs). The GPU farm consists of a variety of processors ranging from lowend consumer grade devices such as the Nvidia GTX 970 to higherend devices such as the GeForce RTX 2080. These GPUs are essential to our research since they allow extremely computeintensive deep learning tasks to be executed on massive data resources such as the TUH EEG Corpus [2]. We use TensorFlow [3] as the core machine learning library for our deep learning systems, and routinely employ multiple GPUs to accelerate the training process. Reproducible results are essential to machine learning research. Reproducibility in this context means the ability to replicate an existing experiment – performance metrics such as error rates should be identical and floatingpoint calculations should match closely. Three examples of ways we typically expect an experiment to be replicable are: (1) The same job run on the same processor should produce the same results each time it is run. (2) A job run on a CPU and GPU should produce identical results. (3) A job should produce comparable results if the data is presented in a different order. System optimization requires an ability to directly compare error rates for algorithms evaluated under comparable operating conditions. However, it is a difficult task to exactly reproduce the results for large, complex deep learning systems that often require more than a trillion calculations per experiment [5]. This is a fairly wellknown issue and one we will explore in this poster. Researchers must be able to replicate results on a specific data set to establish the integrity of an implementation. They can then use that implementation as a baseline for comparison purposes. A lack of reproducibility makes it very difficult to debug algorithms and validate changes to the system. Equally important, since many results in deep learning research are dependent on the order in which the system is exposed to the data, the specific processors used, and even the order in which those processors are accessed, it becomes a challenging problem to compare two algorithms since each system must be individually optimized for a specific data set or processor. This is extremely timeconsuming for algorithm research in which a single run often taxes a computing environment to its limits. Wellknown techniques such as crossvalidation [5,6] can be used to mitigate these effects, but this is also computationally expensive. These issues are further compounded by the fact that most deep learning algorithms are susceptible to the way computational noise propagates through the system. GPUs are particularly notorious for this because, in a clustered environment, it becomes more difficult to control which processors are used at various points in time. Another equally frustrating issue is that upgrades to the deep learning package, such as the transition from TensorFlow v1.9 to v1.13, can also result in large fluctuations in error rates when rerunning the same experiment. Since TensorFlow is constantly updating functions to support GPU use, maintaining an historical archive of experimental results that can be used to calibrate algorithm research is quite a challenge. This makes it very difficult to optimize the system or select the best configurations. The overall impact of all of these issues described above is significant as error rates can fluctuate by as much as 25% due to these types of computational issues. Crossvalidation is one technique used to mitigate this, but that is expensive since you need to do multiple runs over the data, which further taxes a computing infrastructure already running at max capacity. GPUs are preferred when training a large network since these systems train at least two orders of magnitude faster than CPUs [7]. Largescale experiments are simply not feasible without using GPUs. However, there is a tradeoff to gain this performance. Since all our GPUs use the NVIDIA CUDA® Deep Neural Network library (cuDNN) [8], a GPUaccelerated library of primitives for deep neural networks, it adds an element of randomness into the experiment. When a GPU is used to train a network in TensorFlow, it automatically searches for a cuDNN implementation. NVIDIA’s cuDNN implementation provides algorithms that increase the performance and help the model train quicker, but they are nondeterministic algorithms [9,10]. Since our networks have many complex layers, there is no easy way to avoid this randomness. Instead of comparing each epoch, we compare the average performance of the experiment because it gives us a hint of how our model is performing per experiment, and if the changes we make are efficient. In this poster, we will discuss a variety of issues related to reproducibility and introduce ways we mitigate these effects. For example, TensorFlow uses a random number generator (RNG) which is not seeded by default. TensorFlow determines the initialization point and how certain functions execute using the RNG. The solution for this is seeding all the necessary components before training the model. This forces TensorFlow to use the same initialization point and sets how certain layers work (e.g., dropout layers). However, seeding all the RNGs will not guarantee a controlled experiment. Other variables can affect the outcome of the experiment such as training using GPUs, allowing multithreading on CPUs, using certain layers, etc. To mitigate our problems with reproducibility, we first make sure that the data is processed in the same order during training. Therefore, we save the data from the last experiment and to make sure the newer experiment follows the same order. If we allow the data to be shuffled, it can affect the performance due to how the model was exposed to the data. We also specify the float data type to be 32bit since Python defaults to 64bit. We try to avoid using 64bit precision because the numbers produced by a GPU can vary significantly depending on the GPU architecture [1113]. Controlling precision somewhat reduces differences due to computational noise even though technically it increases the amount of computational noise. We are currently developing more advanced techniques for preserving the efficiency of our training process while also maintaining the ability to reproduce models. In our poster presentation we will demonstrate these issues using some novel visualization tools, present several examples of the extent to which these issues influence research results on electroencephalography (EEG) and digital pathology experiments and introduce new ways to manage such computational issues.more » « less

Efficient exploitation of exascale architectures requires rethinking of the numerical algorithms used in many largescale applications. These architectures favor algorithms that expose ultra finegrain parallelism and maximize the ratio of floating point operations to energy intensive data movement. One of the few viable approaches to achieve high efficiency in the area of PDE discretizations on unstructured grids is to use matrixfree/partially assembled highorder finite element methods, since these methods can increase the accuracy and/or lower the computational time due to reduced data motion. In this paper we provide an overview of the research and development activities in the Center for Efficient Exascale Discretizations (CEED), a codesign center in the Exascale Computing Project that is focused on the development of nextgeneration discretization software and algorithms to enable a wide range of finite element applications to run efficiently on future hardware. CEED is a research partnership involving more than 30 computational scientists from two US national labs and five universities, including members of the Nek5000, MFEM, MAGMA and PETSc projects. We discuss the CEED codesign activities based on targeted benchmarks, miniapps and discretization libraries and our work on performance optimizations for largescale GPU architectures. We also provide a broad overview of research and development activities in areas such as unstructured adaptive mesh refinement algorithms, matrixfree linear solvers, highorder data visualization, and list examples of collaborations with several ECP and external applications.more » « less

Abstract This paper documents development of a multiple‐Graphics Processing Unit (GPU) version of FUNWAVE‐Total Variation Diminishing (TVD), an open‐source model for solving the fully nonlinear Boussinesq wave equations using a high‐order TVD solver. The numerical schemes of FUNWAVE‐TVD, including Cartesian and spherical coordinates, are rewritten using CUDA Fortran, with inter‐GPU communication facilitated by the Message Passing Interface. Since FUNWAVE‐TVD involves the discretization of high‐order dispersive derivatives, the on‐chip shared memory is utilized to reduce global memory access. To further optimize performance, the batched tridiagonal solver is scheduled simultaneously in multiple‐GPU streams, which can reduce the GPU execution time by 20–30%. The GPU version is validated through a benchmark test for wave runup on a complex shoreline geometry, as well as a basin‐scale tsunami simulation of the 2011 Tohoku‐oki event. Efficiency evaluation shows that, in comparison with the CPU version running at a 36‐core HPC node, speedup ratios of 4–7 and above 10 can be observed for single‐ and double‐GPU runs, respectively. The performance metrics of multiple‐GPU implementation needs to be further evaluated when appropriate.

Summary This paper studies the performance of different algorithms for solving a dense symmetric indefinite linear system of equations on multicore CPUs with a Graphics Processing Unit (GPU). To ensure the numerical stability of the factorization,
pivoting is required. Obtaining high performance of such algorithms on the GPU is difficult because all the existing pivoting strategies lead to frequent synchronizations and irregular data accesses. Until recently, there has not been any implementation of these algorithms on a hybrid CPU/GPU architecture. To improve their performance on the hybrid architecture, we explore different techniques to reduce the expensive data transfer and synchronization between the CPU and GPU, or on the GPU (e.g., factorizing the matrix entirely on the GPU or in a communication‐avoiding fashion). We also study the performance of the solver using iterative refinements along with the factorization without pivoting combined with the preprocessing technique based on random butterfly transformations, or with the mixed‐precision algorithm where the matrix is factorized in single precision. This randomization algorithm only has a probabilistic proof on the numerical stability, and for this paper, we only focused on the mixed‐precision algorithm without pivoting. However, they demonstrate that we can obtain good performance on the GPU by avoiding the pivoting and using the lower precision arithmetics, respectively. As illustrated with the application in acoustics studied in this paper, in many practical cases, the matrices can be factorized without pivoting. Because the componentwise backward error computed in the iterative refinement signals when the algorithm failed to obtain the desired accuracy, the user can use these potentially unstable but efficient algorithms in most of the cases and fall back to a more stable algorithm with pivoting only in the case of the failure. Copyright © 2017 John Wiley & Sons, Ltd. 
ABSTRACT Magnetic fields provide an important probe of the thermal, material, and structural history of planetary and subplanetary bodies. Core dynamos are a potential source of magnetic fields for differentiated bodies, but evidence of magnetization in undifferentiated bodies requires a different mechanism. Here, we study the amplified field provided by the stellar wind to an initially unmagnetized body using analytic theory and numerical simulations, employing the resistive magnetohydrodynamic AstroBEAR adaptive mesh refinement multiphysics code. We obtain a broadly applicable scaling relation for the peak magnetization achieved once a wind advects, pilesup, and drapes a body with magnetic field, reaching a quasisteady state. We find that the dayside magnetic field for a sufficiently conductive body saturates when it balances the sum of incoming solar wind ram, magnetic, and thermal pressures. Stronger amplification results from pileup by denser and faster winds. Careful quantification of numerical diffusivity is required for accurately interpreting the peak magnetic field strength from simulations, and corroborating with theory. As specifically applied to the Solar system, we find that early solar windinduced field amplification is a viable source of magnetization for observed paleointensities in meteorites from some undifferentiated bodies. This mechanism may also be applicable to other Solar system bodies, including metalrich bodies to be visited in future space missions such as the asteroid (16) Psyche.more » « less