# From Proxies to Fields: Spatiotemporal Reconstruction of Global Radiation from Sparse Sensor Sequences

arXiv: https://arxiv.org/abs/2506.12045 · HTML: https://mlsanity.com/paper/2506.12045/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 54 references that are in the map.
- First posted on arXiv 24 May 2025.

## Builds on (most cited first, 10 of 10)

- [DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators](https://mlsanity.com/paper/1910.03193/) (2019)
- [Neural Operator: Graph Kernel Network for Partial Differential Equations](https://mlsanity.com/paper/2003.03485/) (2020)
- [Fourier Neural Operator with Learned Deformations for PDEs on General Geometries](https://mlsanity.com/paper/2207.05209/) (2022)
- [Skillful Precipitation Nowcasting using Deep Generative Models of Radar](https://mlsanity.com/paper/2104.00954/) (2021)
- [Neural General Circulation Models for Weather and Climate](https://mlsanity.com/paper/2311.07222/) (2023)
- [Deep learning to represent sub-grid processes in climate models](https://mlsanity.com/paper/1806.04731/) (2018)
- [Novel DeepONet architecture to predict stresses in elastoplastic structures with variable complex geometries and loads](https://mlsanity.com/paper/2306.03645/) (2023)
- [Deep Neural Operator Driven Real Time Inference for Nuclear Systems to Enable Digital Twin Solutions](https://mlsanity.com/paper/2308.07523/) (2023)
- [Advanced Deep Operator Networks to Predict Multiphysics Solution Fields in Materials Processing and Additive Manufacturing](https://mlsanity.com/paper/2403.14795/) (2024)
- [Predictions of Transient Vector Solution Fields with Sequential Deep Operator Network](https://mlsanity.com/paper/2311.11500/) (2023)

## Built on by (most cited first, 7 of 7)

- [Real-Time Sensing of Inaccessible Physical Fields via an Edge-Deployable Hardware-Portable Graph Neural Operator](https://mlsanity.com/paper/2604.01802/) (2026)
- [Distribution-Free Uncertainty-Aware Virtual Sensing via Conformalized Neural Operators](https://mlsanity.com/paper/2507.11574/) (2025)
- [Single vs. Multiple Branches in DeepONet and S-DeepONet: Network Architecture Follows Coupling in Multiphysics Systems](https://mlsanity.com/paper/2507.03660/) (2025)
- [Beyond Uniform Sampling: Synergistic Active Learning and Input Denoising for Robust Neural Operators](https://mlsanity.com/paper/2604.13316/) (2026)
- [SCNO: Spiking Compositional Neural Operator -- Towards a Neuromorphic Foundation Model for Nuclear PDE Solving](https://mlsanity.com/paper/2604.11625/) (2026)
- [Sensing Without Colocation: Operator-Based Virtual Instrumentation for Domains Beyond Physical Reach](https://mlsanity.com/paper/2510.18041/) (2025)
- [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)

Accurate reconstruction of latent environmental fields from sparse, indirect observations is a fundamental challenge across scientific domains, from atmospheric science and geophysics to public health and aerospace safety. Existing approaches typically rely on physics-based simulations or dense sensor networks; however, these methods are hampered by high computational cost, latency, and limited spatial coverage. Here we introduce the Temporal Radiation Operator Network (TRON), a spatiotemporal neural operator architecture that infers continuous global scalar fields solely from sequences of sparse, non-uniform proxy measurements. Unlike recent prediction models that require dense, gridded inputs to predict system states, TRON tackles sparse-to-dense, cross-domain field reconstruction. It reconstructs the current global field in real time from sparse, temporally evolving sensor data, without access to any future observations or dense ground-truth fields. We demonstrate this approach on global cosmic radiation dose mapping: TRON, trained on daily reference fields spanning 2001 to 2023, generalizes across 65,341 spatial locations with input sequences ranging from 7 to 90 days. It achieves sub-second inference with relative L2 errors below 0.1%, representing over a 58,000× speedup compared to physics-based estimators. Although showcased in the radiation application, TRON provides a domain-agnostic framework for continuous field reconstruction from sparse data, with broad applications in atmospheric modeling, geophysical hazard monitoring, and real-time environmental risk prediction.