Special Issue "Information Theory, Data Assimilation and Stochastics for Multiscale Nonlinear Systems"

A special issue of Entropy (ISSN 1099-4300). This special issue belongs to the section "Information Theory, Probability and Statistics".

Deadline for manuscript submissions: 30 May 2022.

Special Issue Editors

Dr. Nan Chen
E-Mail Website
Guest Editor
Department of Mathematics, University of Wisconsin-Madison, Madison, WI 53706, USA
Interests: data assimilation; information theory; uncertainty quantification; climate atmosphere and ocean modeling; machine learning
Special Issues, Collections and Topics in MDPI journals
Dr. Honghu Liu
E-Mail Website
Guest Editor
Department of Mathematics, Virginia Tech, Blacksburg, VA 24061, USA
Interests: nonlinear stochastic parameterization; bifurcation and phase transition; reduced-order modeling; geophysical fluid dynamics; delay differential equations; nonlinear optimal control
Dr. Evelyn Lunasin
E-Mail Website
Guest Editor
Department of Mathematics, United States Naval Academy, Annapolis, MD 21402, USA
Interests: turbulence modeling; nonlinear PDE analysis; data assimilation; nonlinear control theory

Special Issue Information

Dear Colleagues, 

Complex multiscale nonlinear stochastic dynamical systems are ubiquitous in geoscience, engineering, and neural and material sciences. For many such systems, due particularly to their high dimensionality and partial observability, it remains a grand challenge in contemporary science and engineering to understand the underlying dynamical mechanisms and to predict their short-term and long-term behaviors. At the same time, cross-disciplinary efforts on various key issues such as coarse-grained dynamics, statistics inference, uncertainty quantification, data assimilation, and extreme-event detection, have collectively led to both more efficient algorithms and improved analytical framework. Moving forward, it is also expected that a judicious use of available data in combination with effective reduced-order models that exploit physics, dynamics as well as statistics constraints will play an increasing role in the theoretic analysis and practical manipulations of such systems. 

The main focus of this Special Issue will be on the state-of-the-art advancements concerning information theory, data assimilation and stochastic/reduced-order modeling of complex multiscale nonlinear systems. We welcome contributions on topics such as Bayesian inferences and sampling, rigorous analysis of the dynamical properties, efficient numerical algorithms, effective low-dimensional surrogate models, and relevant applications. 

Dr. Nan Chen
Dr. Honghu Liu
Dr. Evelyn Lunasin
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com 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 papers will be 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 1800 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 multiscale nonlinear stochastic dynamical systems;
  • uncertainty quantification;
  • data assimilation;
  • reduced-order models;
  • parameterization;
  • extreme events;
  • Bayesian statistics;
  • machine learning;
  • theoretic analysis.

Published Papers (3 papers)

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Research

Article
Estimating Distributions of Parameters in Nonlinear State Space Models with Replica Exchange Particle Marginal Metropolis–Hastings Method
Entropy 2022, 24(1), 115; https://0-doi-org.brum.beds.ac.uk/10.3390/e24010115 - 12 Jan 2022
Viewed by 138
Abstract
Extracting latent nonlinear dynamics from observed time-series data is important for understanding a dynamic system against the background of the observed data. A state space model is a probabilistic graphical model for time-series data, which describes the probabilistic dependence between latent variables at [...] Read more.
Extracting latent nonlinear dynamics from observed time-series data is important for understanding a dynamic system against the background of the observed data. A state space model is a probabilistic graphical model for time-series data, which describes the probabilistic dependence between latent variables at subsequent times and between latent variables and observations. Since, in many situations, the values of the parameters in the state space model are unknown, estimating the parameters from observations is an important task. The particle marginal Metropolis–Hastings (PMMH) method is a method for estimating the marginal posterior distribution of parameters obtained by marginalization over the distribution of latent variables in the state space model. Although, in principle, we can estimate the marginal posterior distribution of parameters by iterating this method infinitely, the estimated result depends on the initial values for a finite number of times in practice. In this paper, we propose a replica exchange particle marginal Metropolis–Hastings (REPMMH) method as a method to improve this problem by combining the PMMH method with the replica exchange method. By using the proposed method, we simultaneously realize a global search at a high temperature and a local fine search at a low temperature. We evaluate the proposed method using simulated data obtained from the Izhikevich neuron model and Lévy-driven stochastic volatility model, and we show that the proposed REPMMH method improves the problem of the initial value dependence in the PMMH method, and realizes efficient sampling of parameters in the state space models compared with existing methods. Full article
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Article
An Adaptive Rank Aggregation-Based Ensemble Multi-Filter Feature Selection Method in Software Defect Prediction
Entropy 2021, 23(10), 1274; https://0-doi-org.brum.beds.ac.uk/10.3390/e23101274 - 29 Sep 2021
Cited by 2 | Viewed by 433
Abstract
Feature selection is known to be an applicable solution to address the problem of high dimensionality in software defect prediction (SDP). However, choosing an appropriate filter feature selection (FFS) method that will generate and guarantee optimal features in SDP is an open research [...] Read more.
Feature selection is known to be an applicable solution to address the problem of high dimensionality in software defect prediction (SDP). However, choosing an appropriate filter feature selection (FFS) method that will generate and guarantee optimal features in SDP is an open research issue, known as the filter rank selection problem. As a solution, the combination of multiple filter methods can alleviate the filter rank selection problem. In this study, a novel adaptive rank aggregation-based ensemble multi-filter feature selection (AREMFFS) method is proposed to resolve high dimensionality and filter rank selection problems in SDP. Specifically, the proposed AREMFFS method is based on assessing and combining the strengths of individual FFS methods by aggregating multiple rank lists in the generation and subsequent selection of top-ranked features to be used in the SDP process. The efficacy of the proposed AREMFFS method is evaluated with decision tree (DT) and naïve Bayes (NB) models on defect datasets from different repositories with diverse defect granularities. Findings from the experimental results indicated the superiority of AREMFFS over other baseline FFS methods that were evaluated, existing rank aggregation based multi-filter FS methods, and variants of AREMFFS as developed in this study. That is, the proposed AREMFFS method not only had a superior effect on prediction performances of SDP models but also outperformed baseline FS methods and existing rank aggregation based multi-filter FS methods. Therefore, this study recommends the combination of multiple FFS methods to utilize the strength of respective FFS methods and take advantage of filter–filter relationships in selecting optimal features for SDP processes. Full article
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Article
Data-Driven Analysis of Nonlinear Heterogeneous Reactions through Sparse Modeling and Bayesian Statistical Approaches
Entropy 2021, 23(7), 824; https://0-doi-org.brum.beds.ac.uk/10.3390/e23070824 - 28 Jun 2021
Viewed by 1111
Abstract
Heterogeneous reactions are chemical reactions that occur at the interfaces of multiple phases, and often show a nonlinear dynamical behavior due to the effect of the time-variant surface area with complex reaction mechanisms. It is important to specify the kinetics of heterogeneous reactions [...] Read more.
Heterogeneous reactions are chemical reactions that occur at the interfaces of multiple phases, and often show a nonlinear dynamical behavior due to the effect of the time-variant surface area with complex reaction mechanisms. It is important to specify the kinetics of heterogeneous reactions in order to elucidate the microscopic elementary processes and predict the macroscopic future evolution of the system. In this study, we propose a data-driven method based on a sparse modeling algorithm and sequential Monte Carlo algorithm for simultaneously extracting substantial reaction terms and surface models from a number of candidates by using partial observation data. We introduce a sparse modeling approach with non-uniform sparsity levels in order to accurately estimate rate constants, and the sequential Monte Carlo algorithm is employed to estimate time courses of multi-dimensional hidden variables. The results estimated using the proposed method show that the rate constants of dissolution and precipitation reactions that are typical examples of surface heterogeneous reactions, necessary surface models, and reaction terms underlying observable data were successfully estimated from only observable temporal changes in the concentration of the dissolved intermediate products. Full article
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Planned Papers

The below list represents only planned manuscripts. Some of these manuscripts have not been received by the Editorial Office yet. Papers submitted to MDPI journals are subject to peer-review.

Title: Replica Exchange Particle Marginal Metropolis-Hastings Method
Authors:
Hiroaki Inoue1, Koji Hukushima2, Toshiaki Omori1
Author Affiliations:
1. Kobe University, 2. The University of Tokyo
Abstract:
To elucidate the latent dynamics underlying multidimensional time-series data, the state-space models have been utilized in the field of data assimilation. Since the values of parameters in the state-space model are unknown in many situations, it is important to establish a data-driven method for estimating the parameters in the state-space model from the observations. The particle marginal Metropolis-Hastings (PMMH) method is a framework to estimate the marginal posterior distribution of parameters by marginalization over the distribution of latent variables in the state-space model. Even though the marginal posterior distribution of parameters can be estimated by iterating this method infinitely, the estimated result depends on the initial values for a finite number of times in practice. In this paper, we propose the replica-exchange particle marginal Metropolis-Hastings (REPMMH) method as a method to improve this problem by combining the PMMH method with the replica-exchange method. We evaluate the proposed method using simulated data obtained from the Izhikevich neuron model and L\'{e}vy-driven stochastic volatility model, and we show that it is possible to improve the problem of the initial value dependency in the PMMH method by the proposed REPMMH method.

Title: Shocks Prediction by Reduced Models for Stochastic Burgers Equations
Authors: Dr. Fei Lu
Affiliation: John Hopkins University
Abstract: Shocks are extreme events of stochastic Burgers. They are challenging to predict by a coarse reduced model due to the need of fine scales. We introduce a data-driven multiscale reduced model to address the challenge.

Authors: Dr. Yoonsang Lee 
Affiliation: Department of Mathematics at Dartmouth College

 

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