# Real-Time Sensing of Inaccessible Physical Fields via an Edge-Deployable Hardware-Portable Graph Neural Operator

arXiv: https://arxiv.org/abs/2604.01802 · HTML: https://mlsanity.com/paper/2604.01802/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 29 of its 63 references that are in the map.
- First posted on arXiv 2 Apr 2026.

## Builds on (most cited first, 29 of 29)

- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering](https://mlsanity.com/paper/1606.09375/) (2016)
- [DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators](https://mlsanity.com/paper/1910.03193/) (2019)
- [Spectral Networks and Locally Connected Networks on Graphs](https://mlsanity.com/paper/1312.6203/) (2013)
- [Neural Operator: Graph Kernel Network for Partial Differential Equations](https://mlsanity.com/paper/2003.03485/) (2020)
- [Physics-informed neural networks (PINNs) for fluid mechanics: A review](https://mlsanity.com/paper/2105.09506/) (2021)
- [Fourier Neural Operator with Learned Deformations for PDEs on General Geometries](https://mlsanity.com/paper/2207.05209/) (2022)
- [Understanding LSTM -- a tutorial into Long Short-Term Memory Recurrent Neural Networks](https://mlsanity.com/paper/1909.09586/) (2019)
- [Wavelet neural operator: a neural operator for parametric partial differential equations](https://mlsanity.com/paper/2205.02191/) (2022)
- [Neural Integral Equations](https://mlsanity.com/paper/2209.15190/) (2022)
- [Deep Neural Operator Driven Real Time Inference for Nuclear Systems to Enable Digital Twin Solutions](https://mlsanity.com/paper/2308.07523/) (2023)
- [Explainable, Interpretable & Trustworthy AI for Intelligent Digital Twin: Case Study on Remaining Useful Life](https://mlsanity.com/paper/2301.06676/) (2023)
- [Improved generalization with deep neural operators for engineering systems: Path towards digital twin](https://mlsanity.com/paper/2301.06701/) (2023)
- [Structure and Performance of Fully Connected Neural Networks: Emerging Complex Network Properties](https://mlsanity.com/paper/2107.14062/) (2021)
- [Virtual Sensing-Enabled Digital Twin Framework for Real-Time Monitoring of Nuclear Systems Leveraging Deep Neural Operators](https://mlsanity.com/paper/2410.13762/) (2024)
- [From Proxies to Fields: Spatiotemporal Reconstruction of Global Radiation from Sparse Sensor Sequences](https://mlsanity.com/paper/2506.12045/) (2025)
- [Digital Twin-Centered Hybrid Data-Driven Multi-Stage Deep Learning Framework for Enhanced Nuclear Reactor Power Prediction](https://mlsanity.com/paper/2211.13157/) (2022)
- [Neuroscience inspired scientific machine learning (Part-1): Variable spiking neuron for regression](https://mlsanity.com/paper/2311.09267/) (2023)
- [Spatio-spectral graph neural operator for solving computational mechanics problems on irregular domain and unstructured grid](https://mlsanity.com/paper/2409.00604/) (2024)
- [From Theory to Application: A Practical Introduction to Neural Operators in Scientific Computing](https://mlsanity.com/paper/2503.05598/) (2025)
- [Adversarial Vulnerabilities in Neural Operator Digital Twins: Gradient-Free Attacks on Nuclear Thermal-Hydraulic Surrogates](https://mlsanity.com/paper/2603.22525/) (2026)
- [A Fourier Neural Operator Approach for Modelling Exciton-Polariton Condensate Systems](https://mlsanity.com/paper/2309.15593/) (2023)
- [PDE Traffic Observer Validated on Freeway Data](https://mlsanity.com/paper/1906.04012/) (2019)
- [Single vs. Multiple Branches in DeepONet and S-DeepONet: Network Architecture Follows Coupling in Multiphysics Systems](https://mlsanity.com/paper/2507.03660/) (2025)
- [Bridging Sequential Deep Operator Network and Video Diffusion: Residual Refinement of Spatio-Temporal PDE Solutions](https://mlsanity.com/paper/2507.06133/) (2025)
- [Neuroscience inspired scientific machine learning (Part-2): Variable spiking wavelet neural operator](https://mlsanity.com/paper/2311.14710/) (2023)
- [Nonlinear moving horizon estimation for robust state and parameter estimation -- extended version](https://mlsanity.com/paper/2312.13175/) (2023)
- [Digital-analog hybrid matrix multiplication processor for optical neural networks](https://mlsanity.com/paper/2401.15061/) (2024)
- [Continuous Monitoring of Large-Scale Generative AI via Deterministic Knowledge Graph Structures](https://mlsanity.com/paper/2509.03857/) (2025)

## Built on by (most cited first, 4 of 4)

- [When Spike Sparsity Does Not Translate to Deployed Cost: VS-WNO on Jetson Orin Nano](https://mlsanity.com/paper/2604.17040/) (2026)
- [Operator Boosting Produces Pareto-Efficient PDE Surrogates](https://mlsanity.com/paper/2606.17460/) (2026)
- [Low-Latency Activation-Regularized Sparse Neural Operators with Distillation Assistance Towards Real-Time Neuromorphic Virtual Sensing](https://mlsanity.com/paper/2608.23987/) (2026)
- [Neuroscience Inspired Graph Operators Towards Edge-Deployable Virtual Sensing for Irregular Geometries](https://mlsanity.com/paper/2604.16722/) (2026)

## Abstract (arXiv)

Real-time inference of inaccessible interior physical fields from sparse boundary observations is a fundamental but unresolved problem in scientific machine learning, with direct relevance to safety-critical monitoring across many engineering applications. Existing neural operators achieve high accuracy but leave deployment to embedded edge platforms unaddressed. Here we introduce VIRSO (Virtual Irregular Real-Time Sparse Operator), the first neural operator with a unique spatial-spectral architecture that explicitly addresses edge-deployment hardware. VIRSO learns a nonlinear mapping from sparse, geometrically disjoint boundary inputs to spatially continuous interior multiphysics fields on irregular unstructured meshes through a spectral-spatial decomposition explicitly aligned with hardware execution: a compute-bound graph spectral pathway and a memory-bandwidth-bound spatial-aggregation pathway, each independently characterized on datacenter and embedded accelerators. The design reduces the inference energy-delay product by 29× relative to the vanilla graph-operator baseline (206 J·ms → 7.0 J·ms on an NVIDIA H200) and enables 17.0 samples/s embedded inference on an NVIDIA Jetson Orin Nano within 7.06 W board-level power, without modification. A mesh-density-adaptive graph construction strategy (V-KNN) simultaneously improves accuracy and reduces graph edge count by 34%. Across three benchmarks with reconstruction ratios from 47:1 to 156:1, VIRSO achieves mean relative L2 errors below 1% with fewer parameters than operator baselines and delivers an inference speedup of ≈ 104 times over the high-fidelity reference solver. To our knowledge, this is the first demonstration of a single-digit-watt neural operator, establishing hardware co-design as a missing ingredient in operator-based inference and a tractable path to real-time deployment.