mlsanityData to 14 Oct 2026

Learning dynamical systems with hit-and-run random feature maps

arXiv 2501.06661 ↗First posted 11 Jan 2025cs.LG physics.data-an stat.MEcited by 8

Not on the map. Why?

Abstract (arXiv)

We show how random feature maps can be used to forecast dynamical systems with excellent forecasting skill. We consider the tanh activation function and judiciously choose the internal weights in a data-driven manner such that the resulting features explore the nonlinear, non-saturated regions of the activation function. We introduce skip connections and construct a deep variant of random feature maps by combining several units. To mitigate the curse of dimensionality, we introduce localization where we learn local maps, employing conditional independence. Our modified random feature maps provide excellent forecasting skill for both single trajectory forecasts as well as long-time estimates of statistical properties, for a range of chaotic dynamical systems with dimensions up to 512. In contrast to other methods such as reservoir computers which require extensive hyperparameter tuning, we effectively need to tune only a single hyperparameter, and are able to achieve state-of-the-art forecast skill with much smaller networks.

Key facts. Cited by 8 papers in the map (data through 14 Oct 2026). Builds on 22 of its 62 references that are in the map. First posted on arXiv 11 Jan 2025.

Builds on

22 of 62 references.

References · 22

  1. 2016Identity Mappings in Deep Residual Networkscited by 1,965
  2. 2021Next Generation Reservoir Computingcited by 160
  3. 2018Data-Driven Forecasting of High-Dimensional Chaotic Systems with Long Short-Term Memory Networkscited by 155
  4. 2019Backpropagation Algorithms and Reservoir Computing in Recurrent Neural Networks for the Forecasting of Complex Spatiotemporal Dynamicscited by 134
  5. 2020The Random Feature Model for Input-Output Maps between Banach Spacescited by 90
  6. 2020Continuous-in-Depth Neural Networkscited by 40
  7. 2021A Framework for Machine Learning of Model Error in Dynamical Systemscited by 38
  8. 2022A Systematic Exploration of Reservoir Computing for Forecasting Complex Spatiotemporal Dynamicscited by 30
  9. 2022Learning continuous models for continuous physicscited by 28
  10. 2020Supervised learning from noisy observations: Combining machine-learning techniques with data assimilationcited by 27
  11. 2023Precise Asymptotic Analysis of Deep Random Feature Modelscited by 22
  12. 2021Combining machine learning and data assimilation to forecast dynamical systems from noisy partial observationscited by 21
10 more
  1. 2021Integrating Recurrent Neural Networks with Data Assimilation for Scalable Data-Driven State Estimationcited by 21
  2. 2019Discovery of Dynamics Using Linear Multistep Methodscited by 17
  3. 2021The Discovery of Dynamics via Linear Multistep Methods and Deep Learning: Error Estimationcited by 14
  4. 2024Scalable Spatiotemporal Prediction with Bayesian Neural Fieldscited by 10
  5. 2020Accuracy of neural networks for the simulation of chaotic dynamics: precision of training data vs precision of the algorithmcited by 7
  6. 2024Hyperparameter Optimization for Randomized Algorithms: A Case Study on Random Featurescited by 7
  7. 2021Robust learning of data anomalies with analytically-solvable entropic outlier sparsificationcited by 5
  8. 2015Representation Learning with Deep Extreme Learning Machines for Efficient Image Set Classificationcited by 3
  9. 2024Localized Schr"odinger Bridge Samplercited by 3
  10. 2024On the choice of the non-trainable internal weights in random feature mapscited by 2

Built on by

Cited by year (2026 to 14 Oct)

Citing papers per year: 2025: 6; 2026: 2.

8 papers.

  1. 2025Dynamic Reservoir Computing with Physical Neuromorphic Networkscited by 3
  2. 2025Learning solution operator of dynamical systems with diffusion maps kernel ridge regressioncited by 3
  3. 2025Adaptive Nonlinear Vector Autoregression: Robust Forecasting for Noisy Chaotic Time Seriescited by 2
  4. 2025Learning Chaotic Dynamics with Neuromorphic Network Dynamicscited by 1
  5. 2025Machine-Precision Prediction of Low-Dimensional Chaotic Systems from Noise-Free Datacited by 1
  6. 2025A Weak Penalty Neural ODE for Learning Chaotic Dynamics from Noisy Time Seriescited by 1
  7. 2026AugRelNet: Relation-Augmented Dynamics for Structure Discovery and Forecasting from Limited Datacited by 0
  8. 2026Learning Closure of Dynamical Systems with Kernel Ridge Regressioncited by 0