Fast and accurate numerical simulations are crucial for designing large-scale geological carbon storage projects ensuring safe long-term CO2containment as a climate change mitigation strategy. These simulations involve solving numerous large and complex linear systems arising from the implicit Finite Volume (FV) discretization of PDEs governing subsurface fluid flow. Compounded with highly detailed geomodels, solving linear systems is computationally and memory expensive, and accounts for the majority of the simulation time. Modern memory hierarchies are insufficient to meet the latency and bandwidth needs of large-scale numerical simulations. Therefore, exploring algorithms that can leverage alternative and balanced paradigms such as dataflow and in-memory computing is crucial. This work introduces a matrix-free algorithm to solve FV-based linear systems using a dataflow architecture to significantly minimize memory latency and bandwidth bottlenecks. Our implementation achieves two orders of magnitude speedup compared to a GPGPU-based reference implementation, and up to 1.2 PFlops on a single dataflow device.

Finite-difference methods based on high-order stencils are widely used in seismic simulations, weather forecasting, and computational fluid dynamics. Recently, multiple research groups have begun exploring the use of dataflow architectures, such as Cerebras’ wafer-scale engine, to accelerate stencil computations. However, implementations of stencil computations for dataflow architectures must address unique challenges, such as managing the routing of data communications and accommodating a significantly constrained memory footprint. These make hand-crafting code for a dataflow architecture difficult and time-consuming. This paper describes a framework for developing portable, high-performance implementations of stencil computations for modern node architectures. The paper focuses on code generation strategies for the Cerebras wafer-scale engine, including code generation of router configurations and sequencing of communication for high-order stencils. A 25-point starshaped stencil written using our tool is $7 \times$ shorter than handcrafted code written in Cerebras Software Language (CSL), and it delivers comparable performance to manually written code.

Adaptive computing systems automatically monitor their behavior and dynamically adjust their own configuration parameters—or knobs—to ensure that user goals are met despite unpredictable external disturbances to the system. A major limitation of prior adaptation frameworks is that their internal adaptation logic is implemented for a specific, narrow set of goals and knobs, which impedes the development of complex adaptive systems that must meet different goals using different sets of knobs for different deployments, or even change goals during one deployment.

Summary Finite‐difference methods based on high‐order stencils are commonly used for modeling of seismic wave propagation, weather forecasting, computational fluid dynamics, convolutional neural networks, and others. Nowadays, the community commonly employs graphics processing units (GPUs) to accelerate such stencil computations. As a result, knowing how to write efficient stencil computations for GPUs is of significant interest. While high‐performance, low‐order stencils on GPUs have been studied extensively in the literature, not all proposed approaches work well for high‐order stencils. Furthermore, coping with boundary conditions used with stencils for seismic modeling makes it challenging to efficiently exploit thread‐level parallelism on GPUs. In this article, we describe several implementations of a 25‐point stencil. We evaluate our stencil code shapes, memory hierarchy usage, data access patterns, and other performance attributes on several modern GPUs and compare them with machine rooflines. On average, our top‐performing kernels achieve six times the performance of a 25‐point stencil code developed in C and mapped to GPUs using OpenACC. Several of our implementations have excellent performance portability across multiple generations of both NVIDIA and AMD GPUs.

The US Department of Energy’s fastest supercomputers and forthcoming exascale systems employ Graphics Processing Units (GPUs) to increase the computational performance of compute nodes. However, the complexity of GPU architectures makes tailoring sophisticated applications to achieve high performance on GPU-accelerated systems a major challenge. At best, prior performance tools for GPU code only provide coarse-grained tuning advice at the kernel level. In this article, we describe GPA, a performance advisor that suggests potential code optimizations at a hierarchy of levels, including individual lines, loops, and functions. To gather the fine-grained measurements needed to produce such insights, GPA uses instruction sampling and binary instrumentation to monitor execution of GPU code. At the time of this writing, GPU instruction sampling is only available on NVIDIA GPUs. To understand performance losses, GPA uses data flow analysis to approximately attribute measured instruction stalls back to their causes. GPA then analyzes patterns of stalls using information about a program’s structure and the GPU architecture to identify optimization strategies that address inefficiencies observed. GPA then employs detailed performance models to estimate the potential speedup that each optimization might provide. Experiments with benchmarks and applications show that GPA provides useful advice for tuning GPU code. We applied GPA to analyze and tune a collection of codes on NVIDIA V100 and A100 GPUs. GPA suggested optimizations that it estimates will accelerate performance across the set of codes by a geometric mean of 1.21×. Applying these optimizations suggested by GPA accelerated these codes by a geometric mean of 1.19×.

Developing efficient GPU kernels can be difficult because of the complexity of GPU architectures and programming models. Existing performance tools only provide coarse-grained tuning advice at the kernel level, if any. In this paper, we describe GPA, a performance advisor for NVIDIA GPUs that suggests potential code optimizations at a hierarchy of levels, including individual lines, loops, and functions. To relieve users of the burden of interpreting performance counters and analyzing bottlenecks, GPA uses data flow analysis to approximately attribute measured instruction stalls to their root causes and uses information about a program's structure and the GPU to match inefficiency patterns with optimization strategies. To quantify the potential benefits of each optimization strategy, we developed PC sampling-based performance models to estimate its speedup. Our experiments with benchmarks and applications show that GPA provides insightful reports to guide performance optimization. Using GPA, we obtained speedups on a Volta V100 GPU ranging from 1.01 x to 3.58 ×, with a geometric mean of 1.22 x.