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Mathematics
Special Issues
Modeling and Simulation for Optimizing Complex Dynamical Systems
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Modeling and Simulation for Optimizing Complex Dynamical Systems

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "D: Statistics and Operational Research".

Deadline for manuscript submissions: 31 January 2026 | Viewed by 1361

Special Issue Editor

Dr. Seon Han Choi

E-Mail Website
Guest Editor
Department of Electronic and Electrical Engineering, Ewha Womans University, Seoul, Republic of Korea
Interests: modeling and simulation; optimization; artificial intelligence
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

The modeling and simulation (M&S) of dynamical systems are essential for solving problems across various fields of applied mathematics, including physics, biology, engineering, economics, and beyond. By employing diverse mathematical modeling techniques—such as differential equations, discrete-event system specification (DEVS), Petri nets, and cellular automata—practitioners can model complex dynamical systems and simulate (i.e., utilize or analyze) these models to better understand system behavior, improve and optimize performance, and even design new systems. Machine learning techniques, such as recurrent neural networks (RNNs), are an alternative to traditional mathematical modeling methods; recently, they have been effectively implemented when sufficient input–output data are available.

This Special Issue aims to compile the latest research achievements in the field of dynamical system M&S. We particularly seek contributions that not only focus on M&S but also explore the optimization of complex dynamical systems based on M&S. We welcome original research articles and comprehensive review papers on topics including, but not limited to, the following:

  • Mathematical modeling methodologies for dynamical systems (e.g., new modeling formalisms);
  • Efficient and accurate computational simulation methods (e.g., numerical methods, distributed/parallel simulation techniques);
  • Simulation-based optimization techniques (e.g., ranking and selection, metaheuristics);
  • Data-driven and machine learning approaches (e.g., physics-informed neural networks);
  • Applications across various fields.

We look forward to receiving your contributions to this Special Issue.

Thank you for your consideration.

Dr. Seon Han Choi
Guest Editor

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 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 250 words) can be sent to the Editorial Office for assessment.

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. Mathematics is an international peer-reviewed open access semimonthly 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

  • modeling and simulation
  • optimization
  • complex dynamical systems
  • machine learning

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Published Papers (2 papers)

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40 pages, 1118 KB  
Article
FORCE: Fast Outlier-Robust Correlation Estimation via Streaming Quantile Approximation for High-Dimensional Data Streams
by Sooyoung Jang and Changbeom Choi
Mathematics 2026, 14(1), 191; https://doi.org/10.3390/math14010191 - 4 Jan 2026
Viewed by 356
Abstract
The estimation of correlation matrices in high-dimensional data streams presents a fundamental conflict between computational efficiency and statistical robustness. Moment-based estimators, such as Pearson’s correlation, offer linear O(N) complexity but lack robustness. In contrast, high-breakdown methods like the minimum covariance [...] Read more.
The estimation of correlation matrices in high-dimensional data streams presents a fundamental conflict between computational efficiency and statistical robustness. Moment-based estimators, such as Pearson’s correlation, offer linear O(N) complexity but lack robustness. In contrast, high-breakdown methods like the minimum covariance determinant (MCD) are computationally prohibitive (O(Np2+p3)) for real-time applications. This paper introduces Fast Outlier-Robust Correlation Estimation (FORCE), a streaming algorithm that performs adaptive coordinate-wise trimming using the P2 algorithm for streaming quantile approximation, requiring only O(p) memory independent of stream length. We evaluate FORCE against six baseline algorithms—including exact trimmed methods (TP-Exact, TP-TER) that use O(NlogN) sorting with O(Np) storage—across five benchmark datasets spanning synthetic, financial, medical, and genomic domains. FORCE achieves speedups of approximately 470× over FastMCD and 3.9× over Spearman’s rank correlation. On S&P 500 financial data, coordinate-wise trimmed methods substantially outperform FastMCD: TP-Exact achieves the best RMSE (0.0902), followed by TP-TER (0.0909) and FORCE (0.1186), compared to FastMCD’s 0.1606. This result demonstrates that coordinate-wise trimming better accommodates volatility clustering in financial time series than multivariate outlier exclusion. FORCE achieves 76% of TP-Exact’s accuracy while requiring 104× less memory, enabling robust estimation in true streaming environments where data cannot be retained for batch processing. We validate the 25% breakdown point shared by all IQR-based trimmed methods using the ODDS-satellite benchmark (31.7% contamination), confirming identical degradation for FORCE, TP-Exact, and TP-TER. For memory-constrained streaming applications with contamination below 25%, FORCE provides the only viable path to robust correlation estimation with bounded memory. Full article
(This article belongs to the Special Issue Modeling and Simulation for Optimizing Complex Dynamical Systems)
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32 pages, 7952 KB  
Article
Renewable-Integrated Agent-Based Microgrid Model with Grid-Forming Support for Improved Frequency Regulation
by Danyao Peng, Sangyub Lee and Seonhan Choi
Mathematics 2025, 13(19), 3142; https://doi.org/10.3390/math13193142 - 1 Oct 2025
Viewed by 715
Abstract
The increasing penetration of renewable energy presents substantial challenges to frequency stability, particularly in low-inertia microgrids. This study introduces an agent-based microgrid model that integrates generators, loads, an energy storage system (ESS), and renewable sources, mathematically formalized through the discrete-event system specification (DEVS) [...] Read more.
The increasing penetration of renewable energy presents substantial challenges to frequency stability, particularly in low-inertia microgrids. This study introduces an agent-based microgrid model that integrates generators, loads, an energy storage system (ESS), and renewable sources, mathematically formalized through the discrete-event system specification (DEVS) to ensure both structural clarity and extensibility. To dynamically simulate power system behavior, the model incorporates multiple control strategies—including ESS scheduling, automatic generation control (AGC), predictive AGC, and grid-forming (GFM) inverter control—each posed as an mathematically defined control problem. Simulations on the IEEE 13-bus system demonstrates that the coordinated operation of ESS, GFM, and the proposed strategies markedly enhances frequency stability, reducing frequency peaks by 1.14, 1.14, and 0.72 Hz, and shortening the average recovery time by 9.05, 0.15, and 2.58 min, respectively. Collectively, the model provides a systematic representation of grid behavior and frequency regulation mechanisms under high renewable penetration, and establishes a rigorous mathematical framework for advancing microgrid research. Full article
(This article belongs to the Special Issue Modeling and Simulation for Optimizing Complex Dynamical Systems)
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