NeuroPDE+: A Scalable Neuromorphic PDE Accelerator Based on Spintronic and Ferroelectric Devices

Abstract

The pursuit of high-performance PDE solvers rests on three fundamental challenges: (i) the curse of dimensionality in kinetic and financial equations, (ii) the poor extrapolation of purely data-driven surrogates, and (iii) the widening gap between algorithm design and hardware specialization. To overcome these challenges, we present NeuroPDE+, a scalable neuromorphic PDE solver design based on spintronic and ferroelectric devices for accelerating PDE solutions. NeuroPDE+ consists of two dedicated units: a diffusion tracking unit (DTU), which emulates random walks on Markov chains through activations between hardware neurons, and a scattering tracking unit (STU), which samples non-local jumps via a multi-level probability tree. System-level simulations suggest that NeuroPDE+ achieves a squared error below 1e-2 in steady-state heat equation and particle transport problems. Simulation results further indicate that the DTU achieves up to a 315x performance gain over previous neuromorphic processors, and that the STU achieves a 1000x speedup compared to a general-purpose CPU. Co-designing algorithm and hardware with intrinsic stochasticity and non-volatile in-memory computing, NeuroPDE+ preliminarily explores a new paradigm for efficient and scalable neuromorphic PDE solvers. This approach could pave the way for probabilistic computing architectures in large-scale scientific simulations.

14 pages, 24 figures