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Entropy
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An Information-Theoretical Perspective on Complex Dynamical Systems
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An Information-Theoretical Perspective on Complex Dynamical Systems

A special issue of Entropy (ISSN 1099-4300). This special issue belongs to the section "Complexity".

Deadline for manuscript submissions: 30 November 2024 | Viewed by 799

Special Issue Editors

Dr. Di Qi

E-Mail Website
Guest Editor
Department of Mathematics, Purdue University, West Lafayette, IN 47907, USA
Interests: filtering; multiscale data assimilation; statistical control; data-driven models for turbulent systems
Prof. Dr. José F. F. Mendes

E-Mail Website
Guest Editor
Department of Physics & I3N, University of Aveiro, 3810-193 Aveiro, Portugal
Interests: network theory; theoretical neuroscience; statistical mechanics; complex systems; percolation theory

Special Issue Information

Dear Colleagues,

Complex dynamical systems are ubiquitous in various science and engineering fields. Key issues to consider include their basic mathematical structural properties and qualitative features, their statistical prediction, uncertainty quantification (UQ) and sensitivity, their data assimilation/filtering, and the inevitable model errors that arise in approximating such complex systems. These model errors arise through both the curse of small ensemble size for large systems and the lack of physical understanding. Information theory provides an objective, unbiased way to evaluate model errors. Strategies for effective modeling and prediction require blending ideas from information theory, Bayesian statistics, and statistical physics in an emerging paradigm for these grand challenges, including extreme event prediction.

 This Special Issue aims at introducing new insights and approaches for advancing the study of general complex systems. Topics of interest for this Special Issue include, but are not limited to, the following themes:

  1. Building suitable unambiguous mathematical models for statistical/stochastic prediction, parameter estimation, and uncertainty quantification;
  2. Improved understanding of model-based ensemble forecast using information theory and judicious comprehensive mathematical tools;
  3. New data-driven and machine learning strategies to characterize the dynamical and statistical features of high-dimensional complex systems;
  4. Emerging development of multiscale algorithms for filtering/data assimilation and state estimation for complex systems and real-world applications;
  5. Information barriers and improving the skill with model errors for state estimation and prediction.

Dr. Di Qi
Prof. Dr. José F. F. Mendes
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at mdpi.longhoe.net by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Entropy is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • complex dynamical systems
  • stochastic modeling
  • data assimilation
  • information theory
  • data-driven methods
  • extreme events

Published Papers (2 papers)

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Research

27 pages, 11309 KiB  
Article
Efficient and Flexible Method for Reducing Moderate-Size Deep Neural Networks with Condensation
by Tianyi Chen and Zhi-Qin John Xu
Entropy 2024, 26(7), 567; https://doi.org/10.3390/e26070567 - 30 Jun 2024
Viewed by 174
Abstract
Neural networks have been extensively applied to a variety of tasks, achieving astounding results. Applying neural networks in the scientific field is an important research direction that is gaining increasing attention. In scientific applications, the scale of neural networks is generally moderate size, [...] Read more.
Neural networks have been extensively applied to a variety of tasks, achieving astounding results. Applying neural networks in the scientific field is an important research direction that is gaining increasing attention. In scientific applications, the scale of neural networks is generally moderate size, mainly to ensure the speed of inference during application. Additionally, comparing neural networks to traditional algorithms in scientific applications is inevitable. These applications often require rapid computations, making the reduction in neural network sizes increasingly important. Existing work has found that the powerful capabilities of neural networks are primarily due to their nonlinearity. Theoretical work has discovered that under strong nonlinearity, neurons in the same layer tend to behave similarly, a phenomenon known as condensation. Condensation offers an opportunity to reduce the scale of neural networks to a smaller subnetwork with a similar performance. In this article, we propose a condensation reduction method to verify the feasibility of this idea in practical problems, thereby validating existing theories. Our reduction method can currently be applied to both fully connected networks and convolutional networks, achieving positive results. In complex combustion acceleration tasks, we reduced the size of the neural network to 41.7% of its original scale while maintaining prediction accuracy. In the CIFAR10 image classification task, we reduced the network size to 11.5% of the original scale, still maintaining a satisfactory validation accuracy. Our method can be applied to most trained neural networks, reducing computational pressure and improving inference speed. Full article
(This article belongs to the Special Issue An Information-Theoretical Perspective on Complex Dynamical Systems)
34 pages, 10834 KiB  
Article
Unambiguous Models and Machine Learning Strategies for Anomalous Extreme Events in Turbulent Dynamical System
by Di Qi
Entropy 2024, 26(6), 522; https://doi.org/10.3390/e26060522 - 17 Jun 2024
Viewed by 272
Abstract
Data-driven modeling methods are studied for turbulent dynamical systems with extreme events under an unambiguous model framework. New neural network architectures are proposed to effectively learn the key dynamical mechanisms including the multiscale coupling and strong instability, and gain robust skill for long-time [...] Read more.
Data-driven modeling methods are studied for turbulent dynamical systems with extreme events under an unambiguous model framework. New neural network architectures are proposed to effectively learn the key dynamical mechanisms including the multiscale coupling and strong instability, and gain robust skill for long-time prediction resistive to the accumulated model errors from the data-driven approximation. The machine learning model overcomes the inherent limitations in traditional long short-time memory networks by exploiting a conditional Gaussian structure informed of the essential physical dynamics. The model performance is demonstrated under a prototype model from idealized geophysical flow and passive tracers, which exhibits analytical solutions with representative statistical features. Many attractive properties are found in the trained model in recovering the hidden dynamics using a limited dataset and sparse observation time, showing uniformly high skill with persistent numerical stability in predicting both the trajectory and statistical solutions among different statistical regimes away from the training regime. The model framework is promising to be applied to a wider class of turbulent systems with complex structures. Full article
(This article belongs to the Special Issue An Information-Theoretical Perspective on Complex Dynamical Systems)
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