# Neuroscience Inspired Graph Operators Towards Edge-Deployable Virtual Sensing for Irregular Geometries

arXiv: https://arxiv.org/abs/2604.16722 · HTML: https://mlsanity.com/paper/2604.16722/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 4 of its 12 references that are in the map.
- First posted on arXiv 17 Apr 2026.

## Builds on (most cited first, 4 of 4)

- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [Training Spiking Neural Networks Using Lessons From Deep Learning](https://mlsanity.com/paper/2109.12894/) (2021)
- [Virtual Sensing to Enable Real-Time Monitoring of Inaccessible Locations & Unmeasurable Parameters](https://mlsanity.com/paper/2412.00107/) (2024)
- [Real-Time Sensing of Inaccessible Physical Fields via an Edge-Deployable Hardware-Portable Graph Neural Operator](https://mlsanity.com/paper/2604.01802/) (2026)

## Abstract (arXiv)

Predicting full-field physics through the real-time virtual sensing of engineering systems can enhance limited physical sensors but often requires sparse-to-dense reconstruction, complex multiphysics, and highly irregular geometries as well as strict latency and energy constraints for edge-deployability. Neural operators have been presented as a potential candidate for such applications but few architectures exist that explicitly address power consumption. Spiking neuron integration can provide a potential solution when integrated on neuromorphic hardware but the current existing neuron models result in severe performance degradation towards regression-based virtual sensing. To address the performance concerns and edge-constraints, we present the Variable Spiking Graph Neural Operator (VS-GNO) which integrates a sophisticated spectral-spatial convolutional analysis and a previously developed Variable Spiking Neuron (VSN) and energy-error balance loss function. With a non-spiking L2 error baseline of 0.4%, VS-GNO can provide a reconstruction error of 0.71% with 15% average spiking in its spectral-only form and 1.04% with 24.5% spiking in its entire form. These results position VS-GNO as a promising step towards energy-efficient, edge-deployable neural operators for real-time sparse-to-dense virtual sensing in complex, highly irregular engineering environments.