mlsanityData to 7 Oct 2026

Data-Driven Modeling and Prediction of Non-Linearizable Dynamics via Spectral Submanifolds

arXiv 2201.04976 ↗First posted 13 Jan 2022math.DS cs.LG cs.SYcited by 25

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Abstract (arXiv)

We develop a methodology to construct low-dimensional predictive models from data sets representing essentially nonlinear (or non-linearizable) dynamical systems with a hyperbolic linear part that are subject to external forcing with finitely many frequencies. Our data-driven, sparse, nonlinear models are obtained as extended normal forms of the reduced dynamics on low-dimensional, attracting spectral submanifolds (SSMs) of the dynamical system. We illustrate the power of data-driven SSM reduction on high-dimensional numerical data sets and experimental measurements involving beam oscillations, vortex shedding and sloshing in a water tank. We find that SSM reduction trained on unforced data also predicts nonlinear response accurately under additional external forcing.

Key facts. Cited by 25 papers in the map (data through 7 Oct 2026). Builds on 7 of its 84 references that are in the map. First posted on arXiv 13 Jan 2022.

Builds on

7 of 84 references.

References · 7

  1. 2017Deep learning for universal linear embeddings of nonlinear dynamicscited by 491
  2. 2017Linearly-Recurrent Autoencoder Networks for Learning Dynamicscited by 142
  3. 2017Data-driven discovery of Koopman eigenfunctions for controlcited by 64
  4. 2021How to Compute Invariant Manifolds and their Reduced Dynamics in High-Dimensional Finite-Element Modelscited by 8
  5. 2020Principal component trajectories for modeling spectrally-continuous dynamics as forced linear systemscited by 5
  6. 2021Data-driven Nonlinear Model Reduction to Spectral Submanifolds in Mechanical Systemscited by 3
  7. 2017Exact Nonlinear Model Reduction for a von Karman beam: Slow-Fast Decomposition and Spectral Submanifoldscited by 2

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2022: 2; 2023: 6; 2024: 5; 2025: 7; 2026: 5.

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  1. 2023Discovering Causal Relations and Equations from Datacited by 33
  2. 2023Generative learning for nonlinear dynamicscited by 22
  3. 2023Benchmarking sparse system identification with low-dimensional chaoscited by 19
  4. 2023Learning Nonlinear Projections for Reduced-Order Modeling of Dynamical Systems using Constrained Autoencoderscited by 16
  5. 2023Mori-Zwanzig latent space Koopman closure for nonlinear autoencodercited by 12
  6. 2022Data-driven reduced order models using invariant foliations, manifolds and autoencoderscited by 7
  7. 2024Input-to-State Stable Coupled Oscillator Networks for Closed-form Model-based Control in Latent Spacecited by 7
  8. 2023Latent Dynamics Networks (LDNets): learning the intrinsic dynamics of spatio-temporal processescited by 4
  9. 2024Machine Learning Applications to Computational Plasma Physics and Reduced-Order Plasma Modeling: A Perspectivecited by 4
  10. 2024On the relationship between Koopman operator approximations and neural ordinary differential equations for data-driven time-evolution predictionscited by 3
  11. 2024Distributed computing for physics-based data-driven reduced modeling at scale: Application to a rotating detonation rocket enginecited by 2
  12. 2024Machine-learning invariant foliations in forced systems for reduced order modellingcited by 1
13 more
  1. 2025Invertible Koopman neural operator for data-driven modeling of partial differential equationscited by 1
  2. 2025A discrete physics-informed training for projection-based reduced order models with neural networkscited by 1
  3. 2025RNNs perform task computations by dynamically warping neural representationscited by 1
  4. 2025Data-driven modelling of autonomous and forced dynamical systemscited by 1
  5. 2026Nonlinear model reduction for transport-dominated problemscited by 1
  6. 2022Changes from Classical Statistics to Modern Statistics and Data Sciencecited by 0
  7. 2025Hybrid Time-Domain Behavior Model Based on Neural Differential Equations and RNNscited by 0
  8. 2025SINDy on slow manifoldscited by 0
  9. 2025Blending data and physics for reduced-order modeling of systems with spatiotemporal chaotic dynamicscited by 0
  10. 2026Enhancing sample efficiency in reinforcement-learning-based flow control: replacing the critic with an adaptive reduced-order modelcited by 0
  11. 2026A Deep Learning-based surrogate model for Severe Accidents in nuclear reactors using ASTECcited by 0
  12. 2026Physics-informed reduced-order modelling with equivariant spectral submanifoldscited by 0
  13. 2026Floquet Fibre Geometry and Higher-Order Reduced Coordinates for Off-Manifold Transients near Nonlinear Aeroelastic Fluttercited by 0