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

2026-04-13

AI Summary

This work addresses the limitations of traditional neural operators in solving partial differential equations (PDEs)—notably model rigidity, high computational cost, and poor generalization—by introducing SCNO, a modular spiking neural operator. SCNO establishes the first composable neuromorphic framework for PDE solving, combining pretrained elementary differential operator blocks with a lightweight conditional aggregator to form its backbone. A residual correction network operating over frozen modules captures coupling effects while mitigating catastrophic forgetting. Evaluated across eight PDEs—including five coupled systems and the neutron diffusion equation—SCNO achieves the lowest L² error on four out of five coupled tasks, surpassing monolithic spiking DeepONet and standard ANN-based DeepONet by up to 62% and 65%, respectively, with only 95K parameters compared to the baselines’ 462K.

Technology Category

• Cognitive Modeling & Cognitive Systems: Neural Spike Coding
• Search and Optimization: Mixed Discrete/Continuous Search
• Machine Learning: Neuro-Symbolic Learning

Application Category

• Search and Retrieval-Augmented AI: Efficiency and scalability of Web search engines
• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems

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.

Problem

• neural operators
• partial differential equations
• modular expansion
• spiking neural networks
• zero-forgetting

Innovation

• Spiking Neural Operator
• Compositional Architecture
• Modular Neuromorphic Computing
• PDE Solving
• Zero-Forgetting Expansion