# LAtent Phase Inference from Short time sequences using SHallow REcurrent Decoders (LAPIS-SHRED)

arXiv: https://arxiv.org/abs/2604.01216 · HTML: https://mlsanity.com/paper/2604.01216/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 19 of its 72 references that are in the map.
- First posted on arXiv 1 Apr 2026.

## Builds on (most cited first, 19 of 19)

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- [Data-Driven Forecasting of High-Dimensional Chaotic Systems with Long Short-Term Memory Networks](https://mlsanity.com/paper/1802.07486/) (2018)
- [Multiple Physics Pretraining for Physical Surrogate Models](https://mlsanity.com/paper/2310.02994/) (2023)
- [Data-Driven Sparse Sensor Placement for Reconstruction](https://mlsanity.com/paper/1701.07569/) (2017)
- [Engression: Extrapolation through the Lens of Distributional Regression](https://mlsanity.com/paper/2307.00835/) (2023)
- [Sequential Deep Operator Networks (S-DeepONet) for Predicting Full-field Solutions Under Time-dependent Loads](https://mlsanity.com/paper/2306.08218/) (2023)
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- [Sparse identification of nonlinear dynamics and Koopman operators with Shallow Recurrent Decoder Networks](https://mlsanity.com/paper/2501.13329/) (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)
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- [Data assimilation and discrepancy modeling with shallow recurrent decoders](https://mlsanity.com/paper/2512.01170/) (2025)
- [T-SHRED: Symbolic Regression for Regularization and Model Discovery with Transformer Shallow Recurrent Decoders](https://mlsanity.com/paper/2506.15881/) (2025)
- [Cheap2Rich: A Multi-Fidelity Framework for Data Assimilation and System Identification of Multiscale Physics -- Rotating Detonation Engines](https://mlsanity.com/paper/2601.20295/) (2026)
- [SENDAI: A Hierarchical Sparse-measurement, EfficieNt Data AssImilation Framework](https://mlsanity.com/paper/2601.21664/) (2026)

## Abstract (arXiv)

Reconstructing full spatio-temporal dynamics from sparse observations in both space and time remains a central challenge in complex systems, as measurements can be spatially incomplete and can be also limited to narrow temporal windows. Yet approximating the complete spatio-temporal trajectory is essential for mechanistic insight and understanding, model calibration, and operational decision-making. We introduce LAPIS-SHRED (LAtent Phase Inference from Short time sequence using SHallow REcurrent Decoders), a modular architecture that reconstructs and/or forecasts complete spatiotemporal dynamics from sparse sensor observations confined to short temporal windows. LAPIS-SHRED operates through a three-stage pipeline: (i) a SHRED model is pre-trained entirely on simulation data to map sensor time-histories into a structured latent space, (ii) a temporal sequence model, trained on simulation-derived latent trajectories, learns to propagate latent states forward or backward in time to span unobserved temporal regions from short observational time windows, and (iii) at deployment, only a short observation window of hyper-sparse sensor measurements from the true system is provided, from which the frozen SHRED model and the temporal model jointly reconstruct or forecast the complete spatiotemporal trajectory. The framework supports bidirectional inference, inherits data assimilation and multiscale reconstruction capabilities from its modular structure, and accommodates extreme observational constraints including single-frame terminal inputs. We evaluate LAPIS-SHRED on six experiments spanning complex spatio-temporal physics: turbulent flows, multiscale propulsion physics, volatile combustion transients, and satellite-derived environmental fields, highlighting a lightweight, modular architecture suited for operational settings where observation is constrained by physical or logistical limitations.