The widely parallel, spiking neural networks of neuromorphic processors can enable computationally powerful formulations. While recent interest has focused on primarily machine learning tasks, the space of appropriate applications is wide and continually expanding. Here, we leverage the parallel and event-driven structure to solve a steady state heat equation using a random walk method. The random walk can be executed fully within a spiking neural network using stochastic neuron behavior, and we provide results from both IBM TrueNorth and Intel Loihi implementations. Additionally, we position this algorithm as a potential scalable benchmark for neuromorphic systems.
The rise of low-power neuromorphic hardware has the potential to change high-performance computing; however much of the focus on brain-inspired hardware has been on machine learning applications. A low-power solution for solving partial differential equations could radically change how we approach large-scale computing in the future. The random walk is a fundamental stochastic process that underlies many numerical tasks in scientific computing applications. We consider here two neural algorithms that can be used to efficiently implement random walks on spiking neuromorphic hardware. The first method tracks the positions of individual walkers independently by using a modular code inspired by grid cells in the brain. The second method tracks the densities of random walkers at each spatial location directly. We present the scaling complexity of each of these methods and illustrate their ability to model random walkers under different probabilistic conditions. Finally, we present implementations of these algorithms on neuromorphic hardware.