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Molecular dynamics (MD) simulation, a computationally intensive method that provides invaluable insights into the behavior of biomolecules, typically requires large-scale parallelization. Implementation of fast parallel MD simulation demands both high bandwidth and low latency for inter-node communication, but in current semiconductor technology, neither of these properties is scaling as quickly as intra-node computational capacity. This disparity in scaling necessitates architectural innovations to maximize the utilization of computational units. For Anton 3, the latest in a family of highly successful special-purpose supercomputers designed for MD simulations, we thus designed and built a completely new specialized network as part of our ASIC. Tightly integrating this network with specialized computation pipelines enables Anton 3 to perform simulations orders of magnitude faster than any general-purpose supercomputer, and to outperform its predecessor, Anton 2 (the state of the art prior to Anton 3), by an order of magnitude. In this paper, we present the three key features of the network that contribute to the high performance of Anton 3. First, through architectural optimizations, the network achieves very low end-to-end inter-node communication latency for fine-grained messages, allowing for better overlap of computation and communication. Second, novel application-specific compression techniques reduce the size of most messages sent between nodes, thereby increasing effective inter-node bandwidth. Lastly, a new hardware synchronization primitive, called a network fence, supports fast fine-grained synchronization tailored to the data flow within a parallel MD application. These application-driven specializations to the network are critical for Anton 3's MD simulation performance advantage over all other machines.