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Synthesize physical models on FPGAs fully utilizes FPGA's parallel computation feature, thus improves simulation speed and enables real-time simulation of complex physical models. We proposed a custom network of processing elements to automate the synthesis process. Following figure shows a mapping of a 4 generation weibel lung into a PE network, where each PE solves the ODEs (ordinary differential equation) of each branch.

We developed a PE compiler to automatically map a physical model into a PE network and provide a design space.

General PE: Contains a general ALU component. A general PE can solve any types of ODEs, but is slower than a custom PE
Custom PE: Contains a (or a few) custom ODE datapath. A custom PE can only solve one or a few types of ODEs, but is 5~20 faster than a general PE

Following figure shows the results (for five different physiology models) of the network of processing elements compare to other common approaches. Results show the simulation runtime of Euler solver at 0.01 ms step. The networks of PEs are fully synthesized and implemented on a Xilinx Virtex6 240T-2 FPGA. (note 1000 ms is the real-time constraint).

PC: C code on a 3.06 GHz Intel I7-950 quad-core processor with 16G DDR3 RAM, compiled with Microsoft VS2010 with –O3 flag. (PC(1): single thread, PC(4): multi-thread, estimated with PC(1) / 4)
GPU: CUDA C code on a 763 MHz NVIDIA GTX460 Fermi GPU with 336 CUDA cores, compiled using nvcc with –O3 flag
HLS: High-level synthesis with regularity extraction
General PEs: network of general PEs
Custom PEs: network of custom PEs
Heterogeneous PEs: network of heterogeneous PEs (with both general PEs and custom PEs).