GPU fast multipole method with lambda-dynamics features

A significant and computationally most demanding part of molecular dynamics simulations is the calculation of long-range electrostatic interactions. Such interactions can be evaluated directly by the naïve pairwise summation algorithm, which is a ubiquitous showcase example for the compute power of graphics processing units (GPUS). However, the pairwise summation has O(N^2) computational complexity for N interacting particles; thus, an approximation method with a better scaling is required. Today, the prevalent method for such approximation in the field is particle mesh Ewald (PME). PME takes advantage of fast Fourier transforms (FFTS) to approximate the solution efficiently. However, as the underlying FFTS require all-to-all communication between ranks, PME runs into a communication bottleneck. Such communication overhead is negligible only for a moderate parallelization. With increased parallelization, as needed for high-performance applications, the usage of PME becomes unprofitable. Another PME drawback is its inability to perform constant pH simulations efficiently. In such simulations, the protonation states of a protein are allowed to change dynamically during the simulation. The description of this process requires a separate evaluation of the energies for each protonation state. This can not be calculated efficiently with PME as the algorithm requires a repeated FFT for each state, which leads to a linear overhead with respect to the number of states. For a fast approximation of pairwise Coulombic interactions, which does not suffer from PME drawbacks, the Fast Multipole Method (FMM) has been implemented and fully parallelized with CUDA. To assure the optimal FMM performance for diverse MD systems multiple parallelization strategies have been developed. The algorithm has been efficiently incorporated into GROMACS and subsequently tested to determine the optimal FMM parameter set for MD simulations. Finally, the FMM has been incorporated into GROMACS to allow for out-of-the-box electrostatic calculations. The performance of the single-GPU FMM implementation, tested in GROMACS 2019, achieves about a third of highly optimized CUDA PME performance when simulating systems with uniform particle distributions. However, the FMM is expected to outperform PME at high parallelization because the FMM global communication overhead is minimal compared to that of PME. Further, the FMM has been enhanced to provide the energies of an arbitrary number of titratable sites as needed in the constant-pH method. The extension is not fully optimized yet, but the first results show the strength of the FMM for constant pH simulations. For a relatively large system with half a million particles and more than a hundred titratable sites, a straightforward approach to compute alternative energies requires the repetition of a simulation for each state of the sites. The FMM calculates all energy terms only a factor 1.5 slower than a single simulation step. Further improvements of the GPU implementation are expected to yield even more speedup compared to the actual implementation.2021-11-1

Systematically Exploring High-Performance Representations of Vector Fields Through Compile-Time Composition

We present a novel benchmark suite for implementations of vector fields in high-performance computing environments to aid developers in quantifying and ranking their performance. We decompose the design space of such benchmarks into access patterns and storage backends, the latter of which can be further decomposed into components with different functional and non-functional properties. Through compile-time meta-programming, we generate a large number of benchmarks with minimal effort and ensure the extensibility of our suite. Our empirical analysis, based on real-world applications in high-energy physics, demonstrates the feasibility of our approach on CPU and GPU platforms, and highlights that our suite is able to evaluate performance-critical design choices. Finally, we propose that our work towards composing vector fields from elementary components is not only useful for the purposes of benchmarking, but that it naturally gives rise to a novel library for implementing such fields in domain applications.</p

Systematically Exploring High-Performance Representations of Vector Fields Through Compile-Time Composition

We present a novel benchmark suite for implementations of vector fields in high-performance computing environments to aid developers in quantifying and ranking their performance. We decompose the design space of such benchmarks into access patterns and storage backends, the latter of which can be further decomposed into components with different functional and non-functional properties. Through compile-time meta-programming, we generate a large number of benchmarks with minimal effort and ensure the extensibility of our suite. Our empirical analysis, based on real-world applications in high-energy physics, demonstrates the feasibility of our approach on CPU and GPU platforms, and highlights that our suite is able to evaluate performance-critical design choices. Finally, we propose that our work towards composing vector fields from elementary components is not only useful for the purposes of benchmarking, but that it naturally gives rise to a novel library for implementing such fields in domain applications

Computing Double Precision Euclidean Distances using GPU Tensor Cores

Tensor cores (TCs) are a type of Application-Specific Integrated Circuit (ASIC) and are a recent addition to Graphics Processing Unit (GPU) architectures. As such, TCs are purposefully designed to greatly improve the performance of Matrix Multiply-Accumulate (MMA) operations. While TCs are heavily studied for machine learning and closely related fields, where their high efficiency is undeniable, MMA operations are not unique to these fields. More generally, any computation that can be expressed as MMA operations can leverage TCs, and potentially benefit from their higher computational throughput compared to other general-purpose cores, such as CUDA cores on Nvidia GPUs. In this paper, we propose the first double precision (FP64) Euclidean distance calculation algorithm, which is expressed as MMA operations to leverage TCs on Nvidia GPUs, rather than the more commonly used CUDA cores. To show that the Euclidean distance can be accelerated in a real-world application, we evaluate our proposed TC algorithm on the distance similarity self-join problem, as the most computationally intensive part of the algorithm consists of computing distances in a multi-dimensional space. We find that the performance gain from using the tensor core algorithm over the CUDA core algorithm depends weakly on the dataset size and distribution, but is strongly dependent on data dimensionality. Overall, TCs are a compelling alternative to CUDA cores, particularly when the data dimensionality is low ($\leq{4}$), as we achieve an average speedup of $1.28\times$ and up to $2.23\times$ against a state-of-the-art GPU distance similarity self-join algorithm. Furthermore, because this paper is among the first to explore the use of TCs for FP64 general-purpose computation, future research is promising.Comment: Accepted for publicatio

GPU point list generation through histogram pyramids

Image Pyramids are frequently used in porting non-local algorithms to graphics hardware. A Histogram pyramid (short: HistoPyramid), a special version of image pyramid, sums up the number of active entries in a 2D image hierarchically. We show how a HistoPyramid can be utilized as an implicit indexing data structure, allowing us to convert a sparse matrix into a coordinate list of active cell entries (a point list) on graphics hardware . The algorithm reduces a highly sparse matrix with N elements to a list of its M active entries in O(N) + M (log N) steps, despite the restricted graphics hardware architecture. Applications are numerous, including feature detection, pixel classification and binning, conversion of 3D volumes to particle clouds and sparse matrix compression