Energy-Efficient Simulation of Non-Homogeneous Turbulent Flows on Neuromorphic Platforms with Custom Neuron Dynamics

  • Taylor, Brady (Sandia National Laboratories)
  • Smith, J Darby (Sandia National Laboratories)
  • Kolla, Hemanth (Sandia National Laboratories)
  • Schmidt, Michael J (Sandia National Laboratories)

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Turbulent flows are inherently chaotic and challenging to simulate numerically. Traditionally, these flows are solved deterministically as a system of discretized partial differential equations (Navier-Stokes), where averaging or filtering operators (e.g., LES, RANS) are introduced to render the problem computationally tractable. Filtering approaches neglect the stochastic fluctuations of the turbulent flow and leave the system unclosed and underdetermined. Modeling heuristics for these stochastic dynamics degrade model fidelity or accuracy compared to the computationally-expensive, brute-force approach of direct numerical simulation (DNS). Alternatively, we may formulate the problem as a stochastic differential equation (SDE) governing the velocity of a fluid particle as it evolves in time. This Lagrangian model can be solved via a random walk over continuous space or approximated as a random walk over a discretized grid constructed from the probability density function described by the SDE. The SDE reformulation achieves closure of Navier-Stokes while maintaining high accuracy. Modern high-performance computing (HPC) platforms face known challenges in adapting to Monte Carlo random sampling algorithms, and as such, these methods are underutilized. However, recent research demonstrates that neuromorphic systems are highly-efficient at implementing random walks by representing walkers as discrete spikes transmitted between neurons. In previous work, we demonstrate the neuromorphic advantage of random walks over a static probability density associated with homogeneous fluid flow, but the case of non-homogeneous flow with non-constant probability denstiy has yet to be implemented. In this lecture, we present novel neuromorphic circuits for simulating non-homogeneous turbulent flow. We consider both standardized leaky-integrate-and-fire (LIF) neurons and neurons with bespoke dynamics. These circuits consume orders-of-magnitude less energy than comparable GPU and CPU implementations without compromising simulation accuracy. SNL is managed and operated by NTESS under DOE NNSA contract DE-NA0003525.