mlsanityData to 14 Oct 2026

Reduced Order Modeling with Shallow Recurrent Decoder Networks

arXiv 2502.10930 ↗First posted 15 Feb 2025cs.LG math.DScited by 24

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Abstract (arXiv)

Reduced Order Modeling is of paramount importance for efficiently inferring high-dimensional spatio-temporal fields in parametric contexts, enabling computationally tractable parametric analyses, uncertainty quantification and control. However, conventional dimensionality reduction techniques are typically limited to known and constant parameters, inefficient for nonlinear and chaotic dynamics, and uninformed to the actual system behavior. In this work, we propose sensor-driven SHallow REcurrent Decoder networks for Reduced Order Modeling (SHRED-ROM). Specifically, we consider the composition of a long short-term memory network, which encodes the temporal dynamics of limited sensor data in multiple scenarios, and a shallow decoder, which reconstructs the corresponding high-dimensional states. SHRED-ROM is a robust decoding-only strategy that circumvents the numerically unstable approximation of an inverse which is required by encoding-decoding schemes. To enhance computational efficiency and memory usage, the full-order state snapshots are reduced by, e.g., proper orthogonal decomposition, allowing for compressive training of the networks with minimal hyperparameter tuning. Through applications on chaotic and nonlinear fluid dynamics, we show that SHRED-ROM (i) accurately reconstructs the state dynamics for new parameter values starting from limited fixed or mobile sensors, independently on sensor placement, (ii) can cope with both physical, geometrical and time-dependent parametric dependencies, while being agnostic to their actual values, (iii) can accurately estimate unknown parameters, and (iv) can deal with different data sources, such as high-fidelity simulations, coupled fields and videos.

Key facts. Cited by 24 papers in the map (data through 14 Oct 2026). Builds on 18 of its 58 references that are in the map. First posted on arXiv 15 Feb 2025.

Builds on

18 of 58 references.

References · 18

  1. 2017Attention Is All You Needcited by 60,361
  2. 2014Empirical Evaluation of Gated Recurrent Neural Networks on Sequence Modelingcited by 2,367
  3. 2019An Introduction to Variational Autoencoderscited by 1,000
  4. 2024The Well: a Large-Scale Collection of Diverse Physics Simulations for Machine Learningcited by 145
  5. 2020A comprehensive deep learning-based approach to reduced order modeling of nonlinear time-dependent parametrized PDEscited by 105
  6. 2018Data Driven Governing Equations Approximation Using Deep Neural Networkscited by 96
  7. 2020Multiscale Simulations of Complex Systems by Learning their Effective Dynamicscited by 86
  8. 2021POD-DL-ROM: enhancing deep learning-based reduced order models for nonlinear parametrized PDEs by proper orthogonal decompositioncited by 79
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  10. 2022Reduced order modeling of parametrized systems through autoencoders and SINDy approach: continuation of periodic solutionscited by 29
  11. 2021A Deep Learning approach to Reduced Order Modelling of Parameter Dependent Partial Differential Equationscited by 28
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6 more
  1. 2025Sparse identification of nonlinear dynamics and Koopman operators with Shallow Recurrent Decoder Networkscited by 20
  2. 2024On latent dynamics learning in nonlinear reduced order modelingcited by 14
  3. 2023Leveraging arbitrary mobile sensor trajectories with shallow recurrent decoder networks for full-state reconstructioncited by 12
  4. 2025Operator Learning for Reconstructing Flow Fields from Sparse Measurements: an Energy Transformer Approachcited by 12
  5. 2022Long-time prediction of nonlinear parametrized dynamical systems by deep learning-based reduced order modelscited by 10
  6. 2024Shallow Recurrent Decoder for Reduced Order Modeling of Plasma Dynamicscited by 8

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Citing papers per year: 2025: 7; 2026: 17.

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  1. 2026MeshGraphNet-Transformer: Scalable Mesh-based Learned Simulation for Solid Mechanicscited by 10
  2. 2025From Models To Experiments: Shallow Recurrent Decoder Networks on the DYNASTY Experimental Facilitycited by 6
  3. 2025Data assimilation and discrepancy modeling with shallow recurrent decoderscited by 6
  4. 2025Towards Efficient Parametric State Estimation in Circulating Fuel Reactors with Shallow Recurrent Decoder Networkscited by 5
  5. 2026CTF4Nuclear: Common Task Framework for Nuclear Fission and Fusion Modelscited by 5
  6. 2025T-SHRED: Symbolic Regression for Regularization and Model Discovery with Transformer Shallow Recurrent Decoderscited by 4
  7. 2025Constrained Sensing and Reliable State Estimation with Shallow Recurrent Decoders on a TRIGA Mark II Reactorcited by 3
  8. 2026Cheap2Rich: A Multi-Fidelity Framework for Data Assimilation and System Identification of Multiscale Physics -- Rotating Detonation Enginescited by 3
  9. 2025PySHRED: A Python package for SHallow REcurrent Decoding for sparse sensing, model reduction and scientific discoverycited by 2
  10. 2026Application of parametric Shallow Recurrent Decoder Network to magnetohydrodynamic flows in liquid metal blankets of fusion reactorscited by 2
  11. 2026Nonlinear model reduction for transport-dominated problemscited by 1
  12. 2026Surrogate models for nuclear fusion with parametric Shallow Recurrent Decoder Networks: applications to magnetohydrodynamicscited by 1
12 more
  1. 2026UQ-SHRED: uncertainty quantification of shallow recurrent decoder networks for sparse sensing via engressioncited by 1
  2. 2026GRIFDIR: Graph Resolution-Invariant FEM Diffusion Models in Function Spaces over Irregular Domainscited by 1
  3. 2025CS-SHRED: Enhancing SHRED for Robust Recovery of Spatiotemporal Dynamicscited by 0
  4. 2026Latent Dynamics Graph Convolutional Networks for model order reduction of parameterized time-dependent PDEscited by 0
  5. 2026Deep Invertible Autoencoders for Dimensionality Reduction of Dynamical Systemscited by 0
  6. 2026GLU: Global-Local-Uncertainty Fusion for Scalable Spatiotemporal Reconstruction and Forecastingcited by 0
  7. 2026LAtent Phase Inference from Short time sequences using SHallow REcurrent Decoders (LAPIS-SHRED)cited by 0
  8. 2026Christoffel-DPS: Optimal sensor placement in diffusion posterior sampling for arbitrary distributionscited by 0
  9. 2026Multi-Fidelity Learning with Shallow Recurrent Decoders for Multi-Physics Applicationscited by 0
  10. 2026Real-time optimal control with shallow recurrent decoder networkscited by 0
  11. 2026Origins and mitigation of double descent in reduced order modelingcited by 0
  12. 2026Real-Time Monitoring of MHD Liquid Metal Flows with Shallow Recurrent Decoderscited by 0