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Related Experiment Video

Updated: Oct 15, 2025

Constructing and Visualizing Models using Mime-based Machine-learning Framework

Constructing and Visualizing Models using Mime-based Machine-learning Framework

Published on: July 22, 2025

Combining machine learning and data assimilation to forecast dynamical systems from noisy partial observations.

Georg A Gottwald¹, Sebastian Reich²

¹School of Mathematics and Statistics, The University of Sydney, Sydney, NSW 2006, Australia.

Chaos (Woodbury, N.Y.)

|October 31, 2021

Summary

This summary is machine-generated.

We developed a fast, easy method using neural networks and data assimilation to learn dynamical system behavior from incomplete, noisy data. This approach, called RAFDA, improves upon standard methods by training sequentially on observations.

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Last Updated: Oct 15, 2025

Constructing and Visualizing Models using Mime-based Machine-learning Framework

Constructing and Visualizing Models using Mime-based Machine-learning Framework

Published on: July 22, 2025

Area of Science:

Dynamical Systems
Machine Learning
Data Assimilation

Background:

Learning the propagator map of dynamical systems is crucial for prediction and control.
Traditional methods often struggle with partial and noisy observational data.
Supervised learning offers a potential avenue for improving propagator map estimation.

Purpose of the Study:

To present a novel supervised learning method for learning the propagator map of dynamical systems.
To develop a computationally efficient and easy-to-implement framework.
To enhance the accuracy of learning from partial and noisy observations.

Main Methods:

A neural network utilizing random feature maps is sequentially trained.
Data assimilation procedures are integrated for sequential training.
Takens's embedding theorem is employed to train the network on delay coordinates.

Main Results:

The proposed method, RAFDA (Random Feature Maps and Data Assimilation), demonstrates superior performance.
RAFDA outperforms standard random feature maps trained on batch data.
The framework is computationally cheap and easy to implement.

Conclusions:

RAFDA offers an effective approach for learning dynamical system propagators from observational data.
Sequential training within a data assimilation framework enhances learning accuracy.
The method provides a practical solution for real-world applications with limited data.