mlsanityData to 14 Oct 2026

Deep KKL: Data-driven Output Prediction for Non-Linear Systems

arXiv 2103.12443 ↗First posted 23 Mar 2021cs.LG cs.SY eess.SYcited by 10

Not on the map. Why?

Abstract (arXiv)

We address the problem of output prediction, ie. designing a model for autonomous nonlinear systems capable of forecasting their future observations. We first define a general framework bringing together the necessary properties for the development of such an output predictor. In particular, we look at this problem from two different viewpoints, control theory and data-driven techniques (machine learning), and try to formulate it in a consistent way, reducing the gap between the two fields. Building on this formulation and problem definition, we propose a predictor structure based on the Kazantzis-Kravaris/Luenberger (KKL) observer and we show that KKL fits well into our general framework. Finally, we propose a constructive solution for this predictor that solely relies on a small set of trajectories measured from the system. Our experiments show that our solution allows to obtain an efficient predictor over a subset of the observation space.

Key facts. Cited by 10 papers in the map (data through 14 Oct 2026). Builds on 12 of its 41 references that are in the map. First posted on arXiv 23 Mar 2021.

Builds on

12 of 41 references.

References · 12

  1. 2014Learning Phrase Representations using RNN Encoder-Decoder for Statistical Machine Translationcited by 4,057
  2. 2017Spectrally-normalized margin bounds for neural networkscited by 686
  3. 2017Deep learning for universal linear embeddings of nonlinear dynamicscited by 494
  4. 2018Lipschitz regularity of deep neural networks: analysis and efficient estimationcited by 415
  5. 2017The Expressive Power of Neural Networks: A View from the Widthcited by 320
  6. 2017Deep Learning for Physical Processes: Incorporating Prior Scientific Knowledgecited by 96
  7. 2020Augmenting Physical Models with Deep Networks for Complex Dynamics Forecastingcited by 95
  8. 2018Neural Lander: Stable Drone Landing Control using Learned Dynamicscited by 85
  9. 2019A survey on intrinsic motivation in reinforcement learningcited by 81
  10. 2019CoPhy: Counterfactual Learning of Physical Dynamicscited by 81
  11. 2020EgoMap: Projective mapping and structured egocentric memory for Deep RLcited by 23
  12. 2019Visual Reaction: Learning to Play Catch with Your Dronecited by 6

Built on by

Cited by year (2026 to 14 Oct)

Citing papers per year: 2022: 3; 2023: 1; 2024: 1; 2025: 1; 2026: 4.

10 papers.

  1. 2022Filtered-CoPhy: Unsupervised Learning of Counterfactual Physics in Pixel Spacecited by 14
  2. 2022Recognition Models to Learn Dynamics from Partial Observations with Neural ODEscited by 8
  3. 2024Nonlinear Discrete-Time Observers with Physics-Informed Neural Networkscited by 8
  4. 2025Reasoning in visual navigation of end-to-end trained agents: a dynamical systems approachcited by 4
  5. 2022Learning Reduced Nonlinear State-Space Models: an Output-Error Based Canonical Approachcited by 1
  6. 2023Learning Hybrid Dynamics Models With Simulator-Informed Latent Statescited by 1
  7. 2026HyperKKL: Enabling Non-Autonomous State Estimation through Dynamic Weight Conditioningcited by 0
  8. 2026A mathematical framework for time-delay reservoir computing analysiscited by 0
  9. 2026HyperKKL: Learning KKL Observers for Non-Autonomous Nonlinear Systems via Hypernetwork-Based Input Conditioningcited by 0
  10. 2026A KKL Observer Perspective on Reservoir Computingcited by 0