Synthesis of custom networks of heterogeneous processing elements for complex physical system emulation

Physical system models that consist of thousands of ordinary differential equations can be synthesized to field-programmable gate arrays (FPGAs) for highly-parallelized, real-time physical system emulation. Previous work introduced synthesis of custom networks of homogeneous processing elements, consisting of processing elements that are either all general differential equation solvers or are all custom solvers tailored to solve specific equations. However, a complex physical system model may contain different types of equations such that using only general solvers or only custom solvers does not provide all of the possible speedup. We introduce methods to synthesize a custom network of heterogeneous processing elements for emulating physical systems, where each element is either a general or custom differential equation solver. We show average speedups of 45x over a 3 GHz single-core desktop processor, and of 11x and 20x over a 3 GHz four-core desktop and a 763 MHz NVIDIA graphical processing unit, respectively. Compared to a commercial high-level synthesis tool including regularity extraction, the networks of heterogeneous processing elements were on average 10.8x faster. Compared to homogeneous networks of general and single-type custom processing elements, heterogeneous networks were on average 7x and 6x faster, respectively.