Attractor-Based AI Modeling for Chaotic Time-Series Prediction
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Solution Overview
Problem
Existing AI systems struggle to accurately predict future events in dynamic and chaotic systems due to their inherent nonlinear nature, limiting their predictive capabilities.
Innovation Solution
A method utilizing an attractor-based approach within an artificial intelligence system that constructs an attractor from a time series of data, determines a prediction horizon using attractor dimension and Lyapunov exponent, and generates future behavior predictions through nonlinear modeling.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If traditional AI systems are used for predicting future events in dynamic and chaotic systems, then the system structure remains simple, but predictive accuracy deteriorates due to the nonlinear nature of chaotic systems
Solution Approach 1:
The patent applies dimensionality change by constructing phase space attractors from time series data, transforming one-dimensional temporal data into multi-dimensional geometric structures. This allows the AI system to capture nonlinear dynamics and chaotic behavior that cannot be represented in the original time domain, thereby improving predictive accuracy for dynamic systems without requiring complex system models.
2Measurement precision
If more time series data is collected to improve prediction accuracy, then predictive capability improves, but the prediction horizon increases only logarithmically while data length increases linearly
Solution Approach 1:
The patent utilizes parameter changes by computing attractor dimensions and Lyapunov exponents from the time series data. These parameters characterize the underlying dynamic system's properties, allowing the prediction horizon to be determined based on intrinsic system characteristics rather than simply scaling with data length. This enables more efficient use of data where prediction accuracy improves without linearly increasing the required data quantity.
3Measurement precision
If underlying physics of the system is understood to improve predictions, then model accuracy improves, but system complexity and requirements increase
Solution Approach 1:
The patent extracts essential dynamic characteristics from time series data by constructing attractors and computing their dimensions and Lyapunov exponents. This extraction approach captures the fundamental behavior of chaotic systems without requiring understanding or modeling of the underlying physical mechanisms. The method isolates the critical features needed for prediction while discarding unnecessary complexity about system origins.
Data Source
AI summary
A method for predicting future behavior for a dynamic system using an artificial intelligence system implemented within a computer hardware system. A predetermined amount of a time series group of data from the dynamic system defining previous behavior of the dynamic system are received at the artificial intelligence system. An attractor is constructed from the time series group of data that defines the previous behavior of the dynamic system using the artificial intelligence system. The attractor models the previous behavior of the dynamic system based on the predetermined amount of the time series group of data of the dynamic system. A prediction horizon for the predetermined amount of the time series group of data is determined with the artificial intelligence system using an attractor dimension of the constructed attractor and a Lyapunov exponent of the constructed attractor. The prediction horizon increases logarithmically as a length of the predetermined amount of the time series group of data from the dynamic system increases linearly. Prediction values of future behavior of the dynamic system are generated with the artificial intelligence system using the constructed attractor and the determined prediction horizon.