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On the Feasibility of FPGA Acceleration of Molecular Dynamics Simulations Technical Report (v0.1) Michael Schaffnery, Luca Beniniy yETH Zurich, Integrated Systems Lab IIS, Zurich, Switzerland Abstract—Classical molecular dynamics (MD) simulations are Hence, the core algorithms used in classical MD simulations important tools in life and material sciences since they allow have largely remained in recent years, and most simulation studying chemical and biological processes in detail. However, speed improvements are due to the use of MPI parallelization the inherent scalability problem of particle-particle interactions and the sequential dependency of subsequent time steps render in combination with GPGPUs that handle the computationally MD computationally intensive and difficult to scale. To this dominant parts. Specialized supercomputers such as the Anton end, specialized FPGA-based accelerators have been repeatedly systems are very inaccessible and expensive, and are hence not proposed to ameliorate this problem. However, to date none of the widely used today. leading MD simulation packages fully support FPGA acceleration and a direct comparison of GPU versus FPGA accelerated codes Besides these MPI and GPU-based solutions, FPGA accel- has remained elusive so far. erators have repeatedly been proposed as a viable alternative With this report, we aim at clarifying this issue by comparing to accelerate the compute intensive parts [10–22] . However, measured application performance on GPU-dense compute nodes these studies only show estimated or measured speedup with with performance and cost estimates of a FPGA-based single- respect to older CPU implementations. To date none of the node system. Our results show that an FPGA-based system can leading MD simulation packages fully support FPGA accel- indeed outperform a similarly configured GPU-based system, but the overall application-level speedup remains in the order of 2× eration [23] and a direct comparison of GPU versus FPGA due to software overheads on the host. Considering the price for accelerated codes has remained elusive so far. GPU and FPGA solutions, we observe that GPU-based solutions This report aims at shedding some light onto the questions provide the better cost/performance tradeoff, and hence pure whether and how FPGAs could be used to accelerate classical FPGA-based solutions are likely not going to be commercially viable. However, we also note that scaled multi-node systems MD simulations in the scope of biochemistry, and whether could potentially benefit from a hybrid composition, where GPUs such a solution would be commercially viable. To this end, are used for compute intensive parts and FPGAs for latency and we revisit existing FPGA architectures, model their behavior communication sensitive tasks. on current FPGA technology and estimate the performance and price of an FPGA accelerated system in order to compare I.I NTRODUCTION with GPU accelerated solutions. We focus on single node Classical molecular dynamics (MD) simulations [1] are im- systems in this report (possibly carrying several accelerator portant tools in life and material sciences since they allow cards) since these represent the most common configuration studying chemical and biological processes in detail. For employed today1. Typical MD problems with in the order of example, this enables researchers to study drug-target bindings 100k atoms do not scale well across several nodes, and hence for drug discovery purposes [2] or to analyze protein folding it is most economic to run these simulations on accelerator- processes to understand their biological function [3]. dense single node systems. However, MD is computationally intensive and difficult to Our results show that, in principle, FPGAs can be used to scale due to the sequential dependency between subsequent accelerate MD, and we estimate full application-level speedups timesteps and the many particle-particle interactions. The in the order of 2× with respect to GPU-based solutions. arXiv:1808.04201v1 [cs.DC] 8 Aug 2018 timescales of interest are often orders of magnitude larger than However, our estimates also indicate that this speedup is the simulation time steps (i.e., ns or µs timescales versus fs likely not high enough to compensate for the increased cost time steps), which results in long simulation times even on and reduced flexibility of FPGA-based solutions. Hence we HPC computing infrastructure. conclude that FPGAs are likely not well suited as a replace- To this end, several approaches have been pursued to ment for GPU accelerators. However, we observe that other improve simulation performance, ranging from novel algo- aspects of FPGAs like the low-latency networking capabilities rithms to approximate forces between particles [4] over al- could be leveraged to augment scaled multi-node systems and gorithmic tweaks [5] and biasing methods such as enhanced ameliorate scalability issues by providing network-compute sampling methods [6], to custom hardware solutions, such as capabilities in addition to GPU acceleration. the MDGRAPE systems from Riken [7] and the Anton-1/2 This report is structured in three main sections: Sec.II supercomputers developed by D.E. Shaw Research LLC [3], summarizes background and related work, performance bench- [8], [9]. However, we observe that algorithmic improvements marks of two widely used software packages are given in are often very problem specific, and it often takes a long time Sec. III, and in Sec.IV we provide the FPGA estimates and until they are adopted by major production software packages. comparisons with GPU-based systems. II.B ACKGROUND AND RELATED WORK the equations of motion have to be integrated, and additional 2 A. Classical MD constraints have to be applied before restarting the loop. This section gives a brief overview of MD, for more details 2) Evaluation of Non-bonded Interactions we refer to [1], [2], [24], [25]. The first term with 1=r12 and 1=r6 modelling the Van der 1) Simulation Loop and Force-Fields Waals interaction decays very quickly. Therefore, a cutoff radius r can be used (usually in the order of 8-16 Angstroms), A typical biomolecular MD simulation consists of a macro- and only neighboring particles within the spanned sphere are molecule that is immersed in a solvent (e.g., water). Each atom considered during the evaluation of this term. in the system is assigned a coordinate x , velocity v and i i The Coulomb interaction on the other hand is more difficult acceleration a . The aim of MD is to simulate the individual i to handle, as it decays relatively slowly (1=r). Earlier methods trajectories of the atoms, and this is done by integrating the also just used a cutoff radius, but this may introduce significant forces acting on each particle. The integration is carried out in errors. To this end, different algorithms that leverage the peri- discrete timesteps, with a resolution in the order of 2 fs, and odic arrangement have been introduced. The most prominent the forces are calculated by taking the negative derivative of one is the Ewald sum method (and variations thereof). This is a potential function V w.r.t. to each particle coordinate x : i basically a mathematical trick to split the Coulomb interaction @V (x (t)) into two separate terms: a localized term that is evaluated fi (t) = miai (t) = − (1) @(xi (t) in space-domain, and a non-local term that is evaluated in where the potential function is based on classical Newtonian the inverse space (i.e., in the spatial frequency domain / k- mechanics. The potential typically comprises the following space). This decomposition enables efficient approximation terms: methods that have computational complexity O(N log(N)) bonds angles instead of O(N 2). One such method that is widely used X kl;i 2 X kα,i 2 V = (li − l0;i) + (αi − α0;i) together with PBC today is called Particle-Mesh Ewald (PME) 2 2 i i [29–32]. Basically, the spatial term is handled locally with a torsions M ! cutoff radius (same as for the Van der Waals term above), X X Vik + cos (n · θ − θ ) 2 ik ik 0;ik and the second is approximated using a gridded interpolation i k (2) method combined with 3D FFTs (hence the O(N log(N))) pairs 12 6! X r0;ij r0;ij complexity). The spatial term is sometimes also called the + ij − 2 short-range interaction part, whereas the inverse space term is rij rij i;j called the long-range interaction part. pairs X qiqj In terms of computation and communication, the non- + bonded terms are the heavy ones, and consist of two cutoff- 4π0rrij i;j radius limited PP problems, and two 3D FFT problems. As Such a set of functions and the corresponding parameteriza- we shall see later in Sec. III, these non-bonded forces account tion is often also called a force-field (examples for specific for more than 90% of the compute time in an unparallelized force field instances are CHARMM36m, GROMOS36 or AM- MD simulation. Moreover, an intrinsic problem of MD is that BERff99). The first three terms in (2) cover the interactions the simulation time steps are sequentially dependent, which due to bonding relationships and are hence also called the inherently limits the parallelizability, and means that we have bonded terms. The last two terms cover the van der Waals to parallelize a single time step as good as possible (which and electrostatic (Coulomb) interactions, and are hence called essentially creates a communication problem). Note that the the non-bonded terms. We can already anticipate from these dataset sizes are very manageable and only in the order of a equations that the non-bonded terms will play a dominant couple of MBytes. role during force calculation since it is a particle-particle (PP) problem with O(N 2). The bonded terms are usually much 3) Other Approaches less intensive (O(N)) since we do not have bonds among all Today, the most serious contenders for replacing PME elec- particles in the system.
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