# GLU: Global-Local-Uncertainty Fusion for Scalable Spatiotemporal Reconstruction and Forecasting

arXiv: https://arxiv.org/abs/2603.26023 · HTML: https://mlsanity.com/paper/2603.26023/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 25 of its 51 references that are in the map.
- First posted on arXiv 27 Mar 2026.

## Builds on (most cited first, 25 of 25)

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- [On Over-Squashing in Message Passing Neural Networks: The Impact of Width, Depth, and Topology](https://mlsanity.com/paper/2302.02941/) (2023)
- [NeRP: Implicit Neural Representation Learning with Prior Embedding for Sparsely Sampled Image Reconstruction](https://mlsanity.com/paper/2108.10991/) (2021)
- [Implicit Reparameterization Gradients](https://mlsanity.com/paper/1805.08498/) (2018)
- [β-Variational autoencoders and transformers for reduced-order modelling of fluid flows](https://mlsanity.com/paper/2304.03571/) (2023)
- [Combining data assimilation and machine learning to emulate a dynamical model from sparse and noisy observations: a case study with the Lorenz 96 model](https://mlsanity.com/paper/2001.01520/) (2020)
- [Generalized Jensen-Shannon Divergence Loss for Learning with Noisy Labels](https://mlsanity.com/paper/2105.04522/) (2021)
- [Learning to Reconstruct Missing Data from Spatiotemporal Graphs with Sparse Observations](https://mlsanity.com/paper/2205.13479/) (2022)
- [Encoding physics to learn reaction-diffusion processes](https://mlsanity.com/paper/2106.04781/) (2021)
- [Global field reconstruction from sparse sensors with Voronoi tessellation-assisted deep learning](https://mlsanity.com/paper/2101.00554/) (2021)
- [Mitigating Spectral Bias in Neural Operators via High-Frequency Scaling for Physical Systems](https://mlsanity.com/paper/2503.13695/) (2025)
- [Amortized Variational Inference: When and Why?](https://mlsanity.com/paper/2307.11018/) (2023)
- [Reduced Order Modeling with Shallow Recurrent Decoder Networks](https://mlsanity.com/paper/2502.10930/) (2025)
- [Neural Chaos: A Spectral Stochastic Neural Operator](https://mlsanity.com/paper/2502.11835/) (2025)
- [RecFNO: a resolution-invariant flow and heat field reconstruction method from sparse observations via Fourier neural operator](https://mlsanity.com/paper/2302.09808/) (2023)
- [Graph Convolutional Neural Networks for Body Force Prediction](https://mlsanity.com/paper/2012.02232/) (2020)
- [Efficient deep data assimilation with sparse observations and time-varying sensors](https://mlsanity.com/paper/2310.16187/) (2023)
- [Spatially-Aware Diffusion Models with Cross-Attention for Global Field Reconstruction with Sparse Observations](https://mlsanity.com/paper/2409.00230/) (2024)
- [EnvPoser: Environment-aware Realistic Human Motion Estimation from Sparse Observations with Uncertainty Modeling](https://mlsanity.com/paper/2412.10235/) (2024)
- [Representation Learning for Spatiotemporal Physical Systems](https://mlsanity.com/paper/2603.13227/) (2026)
- [Machine learning for industrial sensing and control: A survey and practical perspective](https://mlsanity.com/paper/2401.13836/) (2024)
- [Jointly spatial-temporal representation learning for individual trajectories](https://mlsanity.com/paper/2312.04055/) (2023)
- [RainScaleGAN: a Conditional Generative Adversarial Network for Rainfall Downscaling](https://mlsanity.com/paper/2503.13316/) (2025)

## Abstract (arXiv)

Digital twins of complex physical systems are expected to infer unobserved states from sparse measurements and predict their evolution in time, yet these two functions are typically treated as separate tasks. Here we present GLU, a Global-Local-Uncertainty framework that formulates sparse reconstruction and dynamic forecasting as a unified state-representation problem and introduces a structured latent assembly to both tasks. The central idea is to build a structured latent state that combines a global summary of system-level organization, local tokens anchored to available measurements, and an uncertainty-driven importance field that weights observations according to the physical informativeness. For reconstruction, GLU uses importance-aware adaptive neighborhood selection to retrieve locally relevant information while preserving global consistency and allowing flexible query resolution on arbitrary geometries. Across a suite of challenging benchmarks, GLU consistently improves reconstruction fidelity over reduced-order, convolutional, neural operator, and attention-based baselines, better preserving multi-scale structures. For forecasting, a hierarchical Leader-Follower Dynamics module evolves the latent state with substantially reduced memory growth, maintains stable rollout behavior and delays error accumulation in nonlinear dynamics. On a realistic turbulent combustion dataset, it further preserves not only sharp fronts and broadband structures in multiple physical fields, but also their cross-channel thermo-chemical couplings. Scalability tests show that these gains are achieved with substantially lower memory growth than comparable attention-based baselines. Together, these results establish GLU as a flexible and computationally practical paradigm for sparse digital twins.