# Data assimilation and discrepancy modeling with shallow recurrent decoders

arXiv: https://arxiv.org/abs/2512.01170 · HTML: https://mlsanity.com/paper/2512.01170/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 60 references that are in the map.
- First posted on arXiv 1 Dec 2025.

## Builds on (most cited first, 11 of 11)

- [Ensemble-SINDy: Robust sparse model discovery in the low-data, high-noise limit, with active learning and control](https://mlsanity.com/paper/2111.10992/) (2021)
- [Modeling the Dynamics of PDE Systems with Physics-Constrained Deep Auto-Regressive Networks](https://mlsanity.com/paper/1906.05747/) (2019)
- [Sparse learning of stochastic dynamic equations](https://mlsanity.com/paper/1712.02432/) (2017)
- [A Framework for Machine Learning of Model Error in Dynamical Systems](https://mlsanity.com/paper/2107.06658/) (2021)
- [Reduced Order Modeling with Shallow Recurrent Decoder Networks](https://mlsanity.com/paper/2502.10930/) (2025)
- [Sparse identification of nonlinear dynamics and Koopman operators with Shallow Recurrent Decoder Networks](https://mlsanity.com/paper/2501.13329/) (2025)
- [Learning Discrepancy Models From Experimental Data](https://mlsanity.com/paper/1909.08574/) (2019)
- [Discrepancy Modeling Framework: Learning missing physics, modeling systematic residuals, and disambiguating between deterministic and random effects](https://mlsanity.com/paper/2203.05164/) (2022)
- [Interconnections of input-output Hamiltonian systems with dissipation](https://mlsanity.com/paper/1603.04019/) (2016)
- [Port-Hamiltonian formulation of nonlinear electrical circuits](https://mlsanity.com/paper/2004.10821/) (2020)
- [A port-Hamiltonian approach to modeling the structural dynamics of complex systems](https://mlsanity.com/paper/2008.07985/) (2020)

## Built on by (most cited first, 6 of 6)

- [Information theory and discriminative sampling for model discovery](https://mlsanity.com/paper/2512.16000/) (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)
- [UQ-SHRED: uncertainty quantification of shallow recurrent decoder networks for sparse sensing via engression](https://mlsanity.com/paper/2604.01305/) (2026)
- [LAtent Phase Inference from Short time sequences using SHallow REcurrent Decoders (LAPIS-SHRED)](https://mlsanity.com/paper/2604.01216/) (2026)
- [Real-time optimal control with shallow recurrent decoder networks](https://mlsanity.com/paper/2607.19302/) (2026)

## Abstract (arXiv)

The requirements of modern sensing are rapidly evolving, driven by increasing demands for data efficiency, real-time processing, and deployment under limited sensing coverage. Complex physical systems are often characterized through the integration of a limited number of point sensors in combination with scientific computations which approximate the dominant, full-state dynamics. Simulation models, however, inevitably neglect small-scale or hidden processes, are sensitive to perturbations, or oversimplify parameter correlations, leading to reconstructions that often diverge from the reality measured by sensors. This creates a critical need for data assimilation, the process of integrating observational data with predictive simulation models to produce coherent and accurate estimates of the full state of complex physical systems. We propose a machine learning framework for Data Assimilation with a SHallow REcurrent Decoder (DA-SHRED) which bridges the simulation-to-real (SIM2REAL) gap between computational modeling and experimental sensor data. For real-world physics systems modeling high-dimensional spatiotemporal fields, where the full state cannot be directly observed and must be inferred from sparse sensor measurements, we leverage the latent space learned from a reduced simulation model via SHRED, and update these latent variables using real sensor data to accurately reconstruct the full system state. Furthermore, our algorithm incorporates a sparse identification of nonlinear dynamics based regression model in the latent space to identify functionals corresponding to missing dynamics in the simulation model. We demonstrate that DA-SHRED successfully closes the SIM2REAL gap and additionally recovers missing dynamics in highly complex systems, demonstrating that the combination of efficient temporal encoding and physics-informed correction enables robust data assimilation.