# Sensing Without Colocation: Operator-Based Virtual Instrumentation for Domains Beyond Physical Reach

arXiv: https://arxiv.org/abs/2510.18041 · HTML: https://mlsanity.com/paper/2510.18041/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 15 of its 37 references that are in the map.
- First posted on arXiv 20 Oct 2025.

## Builds on (most cited first, 15 of 15)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [Empirical Evaluation of Gated Recurrent Neural Networks on Sequence Modeling](https://mlsanity.com/paper/1412.3555/) (2014)
- [DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators](https://mlsanity.com/paper/1910.03193/) (2019)
- [FourCastNet: A Global Data-driven High-resolution Weather Model using Adaptive Fourier Neural Operators](https://mlsanity.com/paper/2202.11214/) (2022)
- [Message Passing Neural PDE Solvers](https://mlsanity.com/paper/2202.03376/) (2022)
- [Neural General Circulation Models for Weather and Climate](https://mlsanity.com/paper/2311.07222/) (2023)
- [PDE-Refiner: Achieving Accurate Long Rollouts with Neural PDE Solvers](https://mlsanity.com/paper/2308.05732/) (2023)
- [Towards Multi-spatiotemporal-scale Generalized PDE Modeling](https://mlsanity.com/paper/2209.15616/) (2022)
- [Sequential Deep Operator Networks (S-DeepONet) for Predicting Full-field Solutions Under Time-dependent Loads](https://mlsanity.com/paper/2306.08218/) (2023)
- [Deep Neural Operator Driven Real Time Inference for Nuclear Systems to Enable Digital Twin Solutions](https://mlsanity.com/paper/2308.07523/) (2023)
- [Improved generalization with deep neural operators for engineering systems: Path towards digital twin](https://mlsanity.com/paper/2301.06701/) (2023)
- [TI-DeepONet: Learnable Time Integration for Stable Long-Term Extrapolation](https://mlsanity.com/paper/2505.17341/) (2025)
- [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)

## Abstract (arXiv)

Classical sensing rests on one foundational assumption: the quantity of interest must be colocated with the measurement device. This is not an engineering convenience. It is the organizing principle of every instrumentation standard developed over the past century, and it fails completely at aviation altitude, where no physical sensor can survive long enough to monitor the cosmic radiation field that irradiates millions of aircrew annually. We establish that this barrier is resolved by a new sensing principle: when the sensor manifold and the target field manifold are physically disjoint, a learned operator bridging them is the instrument. We term this operator-theoretic virtual sensing and instantiate it in STONe, which maps twelve ground-based neutron monitors (sparse, indirect, surface-bound) to the complete global dose field at 10,000,m across 180-day horizons, achieving sub-millisecond inference where Monte Carlo transport requires hours. Deployed without modification on an NVIDIA Jetson Orin Nano embedded AI platform at 7.3,W average system power and 143.3,MB GPU memory footprint; within the envelope of photovoltaic-powered field hardware co-locatable with existing neutron monitor stations, STONe constitutes a physically realizable sensing device of a new category: an instrument whose measurement principle is operator-theoretic and whose deployment constraint is the power budget of remote environmental monitoring infrastructure, not the accessibility of the target domain.