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

Abstract

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.

Figures (17)

• Figure 1: Overview of the LAPIS-SHRED architecture. Stage i (SHRED): Sparse sensor observations $\mathbf{S} = [\mathbf{s}_0, \ldots, \mathbf{s}_T] \in \mathbb{R}^{p \times (T+1)}$ from simulation ensembles are processed via a pre-trained SHRED model into latent representations $\mathbf{z}_0, \ldots, \mathbf{z}_T$, which are decoded to reconstruct the full spatiotemporal trajectory. A short window of latent codes---from either the initial or terminal phase---is extracted for temporal model training. Stage ii (Temporal Model): Trained on simulation-derived latent trajectories, a BiLSTM architecture learns to map short-window latent codes (augmented with positional encodings) to the unobserved portion of the latent trajectory. Stage iii (LAPIS Inference): At test time, only the short observation window from the ground truth system (reality) is available. The frozen SHRED model extracts the observed-window latent codes, the temporal model infers the unobserved latent trajectory, and the frozen decoder reconstructs the complete spatiotemporal evolution. The architecture shown depicts backward inference from a terminal time window; forward inference from an initial time window proceeds analogously.
• Figure 2: LAPIS-SHRED backward reconstruction on the 2D Kuramoto--Sivashinsky system. Ground truth (top row), LAPIS-SHRED reconstruction from the terminal 10% of the trajectory (second row), and SHRED baseline using the full sensor time-series (third row), shown at selected time steps.
• Figure 3: LAPIS-SHRED backward reconstruction on 2D Kolmogorov flow: vorticity field. Ground truth (top row), LAPIS-SHRED reconstruction from the terminal 10% of the trajectory (second row), and SHRED baseline using the full sensor time-series (third row), shown at selected time steps.
• Figure 4: LAPIS-SHRED forward prediction on the 2D von Karman vortex street. Ground truth (top row), LAPIS-SHRED prediction from the initial $10\%$ of the trajectory (second row), and SHRED baseline using the full sensor time-series (third row), shown at selected time steps.
• Figure 5: Forward-LAPIS-SHRED inference with multi-scale architecture on the 1D rotating detonation engine (RDE) dataset. Top row: spatiotemporal field of the high-fidelity data (left), multi-scale reconstruction (center), and the Forward-LAPIS-SHRED inference (right), which concatenates the training window, a held-out test region, and a 200-step autoregressive forward rollout into the unobserved regime. The purple dashed line marks the training data boundary and the green dashed line marks the observation boundary. Bottom row: spatial snapshots at selected time steps comparing the ground truth, Forward-LAPIS-SHRED inference, and the low-fidelity-only baseline.

Theorems & Definitions (10)

• Remark 2.1: Spatial module Interchangeability
• Remark 3.1: Extreme Data Constraint
• Remark 3.2: Seq2Seq vs. Autoregressive Temporal Models
• Definition B.3: Dissipative system with stable equilibrium
• Proposition B.4: Backward sensitivity for linear dissipative systems
• Remark B.5: Role of the simulation prior
• Proposition B.6: Error bound with simulation prior
• Theorem B.7: LAPIS-SHRED error bound for nonlinear dissipative systems
• proof : Proof sketch
• Remark B.8: Backward sensitivity and the role of the simulation prior