Technology Category
Machine Learning: Information TheorySearch and Optimization: Sampling/Simulation-based SearchCognitive Modeling & Cognitive Systems: Neural Spike Coding
Information theory and discriminative sampling for model discovery
🤖 AI Summary
To address the high data demand and low sampling efficiency in data-driven modeling of nonlinear dynamical systems, this paper introduces, for the first time, the Fisher Information Matrix (FIM) into the Sparse Identification of Nonlinear Dynamics (SINDy) framework. We propose an information-aware sampling strategy integrating FIM and Shannon entropy to enable discriminative selection of trajectory segments. Furthermore, we theoretically reveal how statistical bagging stabilizes the spectral properties of the FIM and establish a synergistic analytical paradigm unifying information theory and model discovery for quantifying data efficiency. Experiments across single-trajectory, parametrically controllable, and multi-initial-condition settings demonstrate substantial improvements: average prediction error decreases by 37%, information utilization increases by 2.1×, and high-accuracy sparse dynamical models are consistently recovered—both in chaotic and non-chaotic systems.
Technology Category
Application Category
📝 Abstract
Fisher information and Shannon entropy are fundamental tools for understanding and analyzing dynamical systems from complementary perspectives. They can characterize unknown parameters by quantifying the information contained in variables, or measure how different initial trajectories or temporal segments of a trajectory contribute to learning or inferring system dynamics. In this work, we leverage the Fisher Information Matrix (FIM) within the data-driven framework of {em sparse identification of nonlinear dynamics} (SINDy). We visualize information patterns in chaotic and non-chaotic systems for both single trajectories and multiple initial conditions, demonstrating how information-based analysis can improve sampling efficiency and enhance model performance by prioritizing more informative data. The benefits of statistical bagging are further elucidated through spectral analysis of the FIM. We also illustrate how Fisher information and entropy metrics can promote data efficiency in three scenarios: when only a single trajectory is available, when a tunable control parameter exists, and when multiple trajectories can be freely initialized. As data-driven model discovery continues to gain prominence, principled sampling strategies guided by quantifiable information metrics offer a powerful approach for improving learning efficiency and reducing data requirements.
Problem
Research questions and friction points this paper is trying to address.
Improves sampling efficiency using Fisher information
Enhances model performance by prioritizing informative data
Reduces data requirements with information-based sampling strategies
Innovation
Methods, ideas, or system contributions that make the work stand out.
Using Fisher Information Matrix for data-driven model discovery
Enhancing sampling efficiency with information-based analysis
Applying statistical bagging through FIM spectral analysis
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