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AI-Based and Data-Driven Modeling and Control: Mathematical Methods and Industrial...
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AI-Based and Data-Driven Modeling and Control: Mathematical Methods and Industrial Applications

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "E2: Control Theory and Mechanics".

Deadline for manuscript submissions: 31 January 2027 | Viewed by 3231

Editor

Dr. Yuyang Zhou

E-Mail Website
Guest Editor
School of Computing Engineering and Built Environment, Edinburgh Napier University, Edinburgh EH10 5DT, UK
Interests: stochastic system control; robabilistic control; probability density function (PDF) control strategy; minimum entropy control; decentralized control
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

The integration of artificial intelligence and data-driven methodologies into control system design is rapidly transforming how we model, analyze, and regulate complex industrial processes. This Special Issue aims to gather cutting-edge research at the intersection of mathematics, control theory, and AI-enabled modeling, focusing on both theoretical foundations and real-world implementations.

As traditional model-based approaches face limitations in high-dimensional, nonlinear, or uncertain environments, AI-based and data-driven frameworks offer promising alternatives. However, their success in safety-critical and industrial applications relies on solid mathematical underpinnings, including interpretability, stability, and robustness guarantees.

For this issue, we welcome original research and surveys that advance the understanding of

  • Data-driven modeling and identification of dynamical systems;
  • Reinforcement learning/machine learning-based control and optimization;
  • AI-integrated predictive and adaptive control strategies;
  • Scheduling and resource optimization under network constraints;
  • Hybrid modeling combining physical laws and learning components (e.g., physics-informed ML);
  • Distributional and probabilistic control in uncertain environments;
  • Stability, convergence, and performance analysis for learning-based controllers;
  • Applications in industrial transportation, energy systems, autonomous platforms, and logistics.

This Special Issue will provide a platform on which researchers and practitioners may explore how intelligent modeling and control methods—rooted in mathematical principles—can drive innovation in complex engineered systems. Contributions that demonstrate rigorous analysis alongside practical relevance are especially encouraged.

Dr. Yuyang Zhou
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-anonymized 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

  • AI-based optimization
  • industrial process control
  • data-driven modeling and control
  • model-based reinforcement learning
  • AI-integrated control frameworks
  • network-constrained systems
  • physics-informed neural networks
  • uncertainty quantification and propagation
  • nonlinear and complex system modeling and control
  • real-time optimization and control

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Published Papers (5 papers)

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Research

28 pages, 4040 KB  
Article
DEVS-Based Simulation of Cube-Shaped AS/RS: Demand-Driven Digging Minimization and Cooperative Multi-AGV Predictive Staging
by Chan-Woo Kim, Ji-Min Woo and Kyung-Min Seo
Mathematics 2026, 14(13), 2414; https://doi.org/10.3390/math14132414 - 6 Jul 2026
Abstract
Cube-shaped automated storage and retrieval systems (AS/RS) enhance storage density by organizing inventory in a three-dimensional grid. However, they face two operational bottlenecks: (1) digging—the temporary removal and restacking of upper bins to access a target bin—and (2) inefficient idle staging and return [...] Read more.
Cube-shaped automated storage and retrieval systems (AS/RS) enhance storage density by organizing inventory in a three-dimensional grid. However, they face two operational bottlenecks: (1) digging—the temporary removal and restacking of upper bins to access a target bin—and (2) inefficient idle staging and return policies in multi-AGV operations. We proposed a demand-based digging and bin-placement strategy and a waiting-point (staging) selection policy that considers AGV positions and remaining task times. These control policies are implemented in both rule-based and multi-agent reinforcement learning (MARL) variants. Their performance is evaluated using a Discrete Event System Specification (DEVS) simulation framework. In a 30 × 30 × 4 grid, three experiments demonstrated that deploying five AGVs achieved the best performance within the tested configuration; the demand-based digging and placement strategy achieved a 6.2% reduction in makespan, and the rule-based and MARL staging policies achieved additional reductions of 2.5% and 1.1%, respectively. These results highlight the benefits of jointly optimizing digging and multi-AGV staging and provide practical guidance for control-policy design in cube-shaped AS/RS. Full article
(This article belongs to the Special Issue AI-Based and Data-Driven Modeling and Control: Mathematical Methods and Industrial Applications)
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26 pages, 966 KB  
Article
A Statistical Modeling and Monitoring Framework for Dynamic Processes Based on Knowledge Graph and Dissimilarity Analysis
by Yunhan Hao and Shanliang Zhu
Mathematics 2026, 14(12), 2047; https://doi.org/10.3390/math14122047 - 8 Jun 2026
Viewed by 161
Abstract
Dynamic industrial processes often exhibit complex variable interactions, and time-varying behaviors, which pose significant challenges to conventional multivariate statistical monitoring methods. To address these issues, this paper proposes a novel data-driven monitoring framework that integrates knowledge-informed bipartite graph embedding with multi-scale dissimilarity analysis. [...] Read more.
Dynamic industrial processes often exhibit complex variable interactions, and time-varying behaviors, which pose significant challenges to conventional multivariate statistical monitoring methods. To address these issues, this paper proposes a novel data-driven monitoring framework that integrates knowledge-informed bipartite graph embedding with multi-scale dissimilarity analysis. First, a bipartite graph-embedding strategy is developed to incorporate mechanistic knowledge into the modeling process, enabling a more interpretable representation of dynamic relationships among process variables. On this basis, a multi-scale recursive dissimilarity monitoring method is further designed to enhance detection performance by capturing process variations across different temporal scales while reducing sensitivity to sliding window selection. The effectiveness of the proposed framework is validated through a numerical example and a benchmark simulation process. The results demonstrate that the proposed method achieves improved fault detection performance and robustness compared with conventional approaches. Full article
(This article belongs to the Special Issue AI-Based and Data-Driven Modeling and Control: Mathematical Methods and Industrial Applications)
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22 pages, 866 KB  
Article
Improving PINN Convergence in Nonlinear Multiphase Flow Problems Through Weight Gradient Consistency Analysis
by Damir Aminev, Marina Kravchenko and Nikolay Smirnov
Mathematics 2026, 14(11), 1832; https://doi.org/10.3390/math14111832 - 25 May 2026
Viewed by 315
Abstract
The training of physics-informed neural networks (PINNs) for nonlinear multiphase flow in porous media is hampered by gradient conflicts between the individual components of the composite loss function. To address this problem, we propose a weighted gradient consistency metric that jointly accounts for [...] Read more.
The training of physics-informed neural networks (PINNs) for nonlinear multiphase flow in porous media is hampered by gradient conflicts between the individual components of the composite loss function. To address this problem, we propose a weighted gradient consistency metric that jointly accounts for the magnitudes and directions of the gradients of each loss term. Theoretical estimates of the convergence rate are derived, relating the proposed metric to the spectral properties of the preconditioner. The method is evaluated through a comparative study of optimizers—Adam, L-BFGS, and self-scaled Broyden—applied to three formulations of increasing complexity: a linear Buckley–Leverett model, a compressible two-phase model, and a fully nonlinear model with non-Newtonian rheology. The experiments demonstrate that self-scaled methods consistently achieve higher gradient alignment, faster loss reduction, and improved approximation accuracy compared to standard quasi-Newton and first-order baselines. Full article
(This article belongs to the Special Issue AI-Based and Data-Driven Modeling and Control: Mathematical Methods and Industrial Applications)
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24 pages, 3016 KB  
Article
Data-Driven Computation Scheme for Duncan–Chang EB Model
by Chaojun Han, Qianhui Liu, Xiaohang Li and Hezuo Zhang
Mathematics 2026, 14(5), 751; https://doi.org/10.3390/math14050751 - 24 Feb 2026
Viewed by 612
Abstract
This paper extends the data-driven computational mechanics paradigm to nonlinear materials characterized by the Duncan–Chang Elastic-Bulk (E-B) constitutive model. Unlike in linear elastic systems, geotechnical media exhibit stress-dependent tangent moduli and non-convex constitutive manifolds. We propose a recursive nested data-driven solver that dynamically [...] Read more.
This paper extends the data-driven computational mechanics paradigm to nonlinear materials characterized by the Duncan–Chang Elastic-Bulk (E-B) constitutive model. Unlike in linear elastic systems, geotechnical media exhibit stress-dependent tangent moduli and non-convex constitutive manifolds. We propose a recursive nested data-driven solver that dynamically adapts the phase-space distance metric to account for pressure-dependent hardening. A rigorous mathematical analysis of convergence is provided, demonstrating that the solver’s performance is governed by the local transversality between the conservation law constraint set and the nonlinear material manifold. We derive explicit error bounds that couple spatial discretization resolution with material data density. Numerical experiments using triaxial test data from a high-altitude region validate the theoretical predictions, showing that the proposed scheme demonstrates convergence in single-element tests. Full article
(This article belongs to the Special Issue AI-Based and Data-Driven Modeling and Control: Mathematical Methods and Industrial Applications)
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18 pages, 1084 KB  
Article
Tractor and Semitrailer Scheduling with Time Windows in Highway Ports with Unbalanced Demand Under Network Conditions
by Hongxia Guo, Fengjun Wang, Yuyan He and Yuyang Zhou
Mathematics 2025, 13(17), 2881; https://doi.org/10.3390/math13172881 - 6 Sep 2025
Viewed by 1202
Abstract
To address the challenges of unbalanced demand and high operational costs in highway port logistics, this study investigates the scheduling of tractors and semitrailers under time window constraints in a networked environment, where geographically distributed ports are interconnected by fixed routes, and tractors [...] Read more.
To address the challenges of unbalanced demand and high operational costs in highway port logistics, this study investigates the scheduling of tractors and semitrailers under time window constraints in a networked environment, where geographically distributed ports are interconnected by fixed routes, and tractors dynamically transport semitrailers between ports to balance asymmetric demands. A mathematical optimization model is developed, incorporating multiple car yards, diverse transport demands, and temporal constraints. To solve the model efficiently, an Adaptive Large Neighborhood Search (ALNS) algorithm is proposed and benchmarked against an improved Ant Colony System (IACS). Simulation results show that, compared to traditional scheduling methods, the proposed approach reduces the number of required tractors by up to 61% and operational costs by up to 21%, depending on tractor working hours. The tractor-to-semitrailer ratio improves from 1.00:1.10 to 1.00:2.59, demonstrating the enhanced resource utilization enabled by the ALNS algorithm. These findings offer practical guidance for optimizing tractor and semitrailer configurations in highway port operations under varying conditions. Full article
(This article belongs to the Special Issue AI-Based and Data-Driven Modeling and Control: Mathematical Methods and Industrial Applications)
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