Embedding-based placement of processing element networks on FPGAs for physical model simulation

Abstract

Physical models utilize mathematical equations to model physical systems like airway mechanics, neuron networks, or chemical reactions. Previous work has shown that physical models can execute fast on FPGAs (field-programmable gate arrays). We introduce an approach for implementing physical models on FPGAs that applies graph theoretic techniques to make use of a physical model's natural structure--tree, ring, chain, etc.--resulting in model execution speedups. A first phase of the approach maps physical model equations to a structured virtual PE (processing element) graph using graph theoretic folding techniques. A second phase maps the structured virtual PE graph to physical PE regions on an FPGA using graph embedding theory. We also present a simulated annealing approach with custom cost and neighbor functions that can map any physical model onto an FPGA with low wire costs. Average circuit speedup improvements over previous works for various physical models are 65% using the graph embedding and 35% using the simulated annealing approach. Each approach's more efficient use of FPGA resources also enables larger models to be implemented on an FPGA device.