Enhanced long short-term memory architectures for chaotic systems modeling: An extensive study on the Lorenz system

Area of Science:

• * Computational Science and Engineering
• * Applied Mathematics
• * Artificial Intelligence

Background:

• * Long Short-Term Memory (LSTM) networks are established machine learning models for time-series data.
• * Chaotic systems present complex modeling challenges due to their sensitivity to initial conditions and dynamic behavior.
• * Existing deep learning methodologies may be overly complex for certain modeling tasks.

Purpose of the Study:

• * To introduce and evaluate an enhanced Long Short-Term Memory (LSTM) variant for chaotic system modeling.
• * To analyze the performance of a simplified LSTM architecture in handling noise, non-stationarity, and parameter drifts.
• * To assess the model's efficacy in both short- and long-term forecasting of chaotic systems.

Main Methods:

• * Development of a modified LSTM architecture incorporating three standard gates and feedback adjustments.
• * Simulation of the Lorenz and Rössler chaotic systems using MATLAB to generate experimental datasets.
• * Large-scale analysis focusing on LSTM gate-level architecture, noise effects, and dynamic behavior modeling.

Main Results:

• * The enhanced LSTM model demonstrated accurate performance in modeling chaotic systems.
• * A simplified LSTM architecture proved sufficient for complex tasks, negating the need for intricate deep learning approaches.
• * The model effectively handled noisy data, non-stationary behavior, and system parameter drifts.

Conclusions:

• * A simplified, three-gate LSTM architecture is a viable and effective tool for chaotic system modeling.
• * Complex deep learning methodologies are not always necessary for accurate chaotic system analysis and forecasting.
• * The proposed enhanced LSTM offers a computationally efficient alternative for modeling dynamic systems.