SCNO: Spiking Compositional Neural Operator -- Towards a Neuromorphic Foundation Model for Nuclear PDE Solving

TL;DR

The paper introduces SCNO, a modular neuromorphic neural operator architecture that efficiently solves coupled PDEs, outperforming traditional models and enabling zero-forgetting expansion for nuclear PDE applications.

Contribution

SCNO is the first compositional spiking neural operator, combining modular blocks and a correction network for efficient, expandable PDE solving, especially in nuclear physics.

Findings

SCNO outperforms monolithic DeepONet models on multiple PDEs.

SCNO requires significantly fewer trainable parameters.

SCNO achieves the lowest relative L2 error on several coupled PDEs.

Abstract

Neural operators have emerged as powerful surrogates for partial differential equation (PDE) solvers, yet they are typically trained as monolithic models for individual PDEs, require energy-intensive GPU hardware, and must be retrained from scratch when new physics emerge. We introduce the Spiking Compositional Neural Operator (SCNO), a modular architecture combining spiking and conventional components that addresses all three limitations. SCNO maintains a library of small spiking neural operator blocks, each trained on a single elementary differential operator (convection, diffusion, reaction), and composes them through a lightweight input-conditioned aggregator to solve coupled PDEs not seen during block training. A small correction network learns cross-coupling residuals while keeping all blocks and the aggregator frozen, preserving zero-forgetting modular expansion by construction. We evaluate SCNO on eight PDE families including five coupled systems and a nuclear-relevant 1-group neutron diffusion equation. SCNO with correction achieves the lowest relative $L^2$ error on four of five coupled PDEs, outperforming both a monolithic spiking DeepONet (by up to 62%, mean over 3 seeds) and a standard ANN DeepONet (by up to 65%), while requiring only 95K trainable parameters versus 462K for the monolithic baseline. To our knowledge, this is the first compositional spiking neural operator and the first proof-of-concept for modular neuromorphic PDE solving with built-in forgetting-free expansion.