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

arXiv: https://arxiv.org/abs/2604.11625 · HTML: https://mlsanity.com/paper/2604.11625/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 17 references that are in the map.
- First posted on arXiv 13 Apr 2026.

## Builds on (most cited first, 9 of 9)

- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators](https://mlsanity.com/paper/1910.03193/) (2019)
- [Overcoming catastrophic forgetting in neural networks](https://mlsanity.com/paper/2507.10485/) (2025)
- [Deep Neural Operator Driven Real Time Inference for Nuclear Systems to Enable Digital Twin Solutions](https://mlsanity.com/paper/2308.07523/) (2023)
- [Spiking Neural Operators for Scientific Machine Learning](https://mlsanity.com/paper/2205.10130/) (2022)
- [Solving Sparse Finite Element Problems on Neuromorphic Hardware](https://mlsanity.com/paper/2501.10526/) (2025)
- [From Proxies to Fields: Spatiotemporal Reconstruction of Global Radiation from Sparse Sensor Sequences](https://mlsanity.com/paper/2506.12045/) (2025)
- [CompNO: A Novel Foundation Model approach for solving Partial Differential Equations](https://mlsanity.com/paper/2601.07384/) (2026)
- [SPINONet: Scalable Spiking Physics-informed Neural Operator for Computational Mechanics Applications](https://mlsanity.com/paper/2603.21674/) (2026)

## Built on by (most cited first, 1 of 1)

- [Targeted search shows that random-device testing underestimates worst-case error in a simulated wave-based neural operator](https://mlsanity.com/paper/2610.07529/) (2026)

## Abstract (arXiv)

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 L2 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.