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. 2025 Sep 1;18(17):4112. doi: 10.3390/ma18174112

AI and Computational Methods for Modelling, Simulations and Optimizing of Advanced Systems: Innovations in Complexity

Marcin Sosnowski 1,*, Jaroslaw Krzywanski 1, Karolina Grabowska 1, Dorian Skrobek 1, Ghulam Moeen Uddin 2, Cezary Kozlowski 1, Jacek Przybylski 1, Malgorzata Deska 1
PMCID: PMC12430230  PMID: 40942538

The rapid evolution of artificial intelligence (AI) and computational methods has transformed the landscape of modeling, simulation, and optimization, particularly for complex, interdisciplinary systems. As scientific challenges grow increasingly multifaceted—from energy systems to advanced engineered materials, and from multi-scale biological phenomena to data-driven industrial solutions—the integration of AI with traditional and novel computational approaches continues to produce breakthrough advances.

The presented MDPI Topic “AI and Computational Methods for Modelling, Simulations and Optimizing of Advanced Systems: Innovations in Complexity” brings together 40 original research articles that span foundational algorithmic innovations to impactful case studies in science and engineering. This Topic responds to the growing demand for robust, adaptable, and interpretable computational methods capable of addressing real-world, high-dimensional, and nonlinear problems. Here, we present a brief overview of recent advances, persistent knowledge gaps, the contributions of this Topic, and future research directions.

Recent years have seen remarkable synergies between physics-based modeling, traditional numerical methods (FEM, FDM, etc.), and data-driven or hybrid AI approaches. Physics-guided and domain-informed machine learning has substantially improved the interpretability and accuracy of models for complex, chaotic, or data-scarce systems. AI-enhanced solvers and hybrid frameworks demonstrably outperform classical techniques in predicting nonlinear dynamics, optimizing system performance, and discovering new physical laws [1,2,3]. Generative AI and reinforcement learning are beginning to revolutionize optimization in engineering design, energy management, and manufacturing through the capacity for on-the-fly adaptation and real-time learning [4]. Surrogate modeling, hyper-heuristics, and neural-based metaheuristics (evolutionary algorithms hybridized with ML) now enable tractable optimization of previously intractable, high-dimensional design spaces [5,6].

The field of complexity science has profoundly benefited from data-driven methods that can extract hidden patterns and guide systemic interventions across scales. Advances in knowledge graph construction, multi-scale simulation, and agent-based modeling directly address pressing challenges in fields such as healthcare, logistics, and environmental management [7,8].

Despite remarkable progress, the community faces several inherent challenges:

  • Interpretability and Transparency: As models grow in sophistication and autonomy, ensuring their interpretability, especially in critical domains (energy, health, finance), is necessary for trust and regulatory acceptance [6].

  • Robustness and Scalability: Many AI-enhanced optimization tools excel on test cases but struggle with generalization, transferability, and scaling to industrially relevant, real-world problems [8,9].

  • Integration with Domain Knowledge: It remains challenging to systematically incorporate physical laws, constraints, and expert insights directly into learning architectures without loss of flexibility [2,7,9].

  • Benchmarking and Reproducibility: A proliferation of methods and benchmarks complicates fair comparisons, reproducibility, and consistent progress assessment across domains [3,10,11].

This Topic, “AI and Computational Methods for Modelling, Simulations and Optimizing of Advanced Systems: Innovations in Complexity”, addresses multiple facets of these knowledge gaps through research that proposes and validates novel hybrid algorithms uniting classical optimization (GA, PSO, ACO) with neural, evolutionary, or reinforcement learning components; presents case studies of real-world applications (e.g., material design, smart grid optimization, energy storage, process control) where advanced AI-based simulation and modeling drive measurable improvements; demonstrates approaches for explainability and physical interpretability in deep learning for dynamical and multi-scale systems; advances the theoretical underpinnings of network science, multifractal analysis, and information-theoretic methods with computational innovation; and benchmarks and evaluates emerging methods with careful attention to open-source data availability and reproducible research practices. The published articles are distributed among the journals as indicated in Table 1.

Table 1.

The distribution of articles among the journals.

Journal No. of Papers
Energies 11
Entropy 9
Materials 9
Fractal and Fractional 4
Machine Learning & Knowledge Extraction (MAKE) 4
Algorithms 3
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The contributions to the Topic “AI and Computational Methods for Modelling, Simulations and Optimizing of Advanced Systems: Innovations in Complexity” are listed below:

Conflicts of Interest

The authors declare no conflicts of interest.

List of Contributions

  1. Bashishtha, T.; Singh, V.; Yadav, U.; Varshney, T. Reaction Curve-Assisted Rule-Based PID Control Design for Islanded Microgrid. Energies 2024, 17, 1110. https://doi.org/10.3390/en17051110.

  2. Tian, F.; Wang, Y.; Li, Z. Numerical Simulation of Soliton Propagation Behavior for the Fractional-in-Space NLSE with Variable Coefficients on Unbounded Domain. Fractal Fract. 2024, 8, 163. https://doi.org/10.3390/fractalfract8030163.

  3. Shen, H.; Shan, X. An Efficient Image Cryptosystem Utilizing Difference Matrix and Genetic Algorithm. Entropy 2024, 26, 351. https://doi.org/10.3390/e26050351.

  4. Zhang, J.; Shi, B.; Wang, B.; Yu, G. Crushing Response and Optimization of a Modified 3D Re-Entrant Honeycomb. Materials 2024, 17, 2083. https://doi.org/10.3390/ma17092083.

  5. Du, X.; Salasakar, S.; Thakur, G. A Comprehensive Summary of the Application of Machine Learning Techniques for CO2-Enhanced Oil Recovery Projects. Mach. Learn. Knowl. Extr. 2024, 6, 917–943. https://doi.org/10.3390/make6020043.

  6. El Sayed, A.; Poyrazoglu, G. Analysis of Grid Performance with Diversified Distributed Resources and Storage Integration: A Bilevel Approach with Network-Oriented PSO. Energies 2024, 17, 2270. https://doi.org/10.3390/en17102270.

  7. Belhaiza, S.; Al-Abdallah, S. A Neural Network Forecasting Approach for the Smart Grid Demand Response Management Problem. Energies 2024, 17, 2329. https://doi.org/10.3390/en17102329.

  8. Zhang, T.; Mo, H. Towards Multi-Objective Object Push-Grasp Policy Based on Maximum Entropy Deep Reinforcement Learning under Sparse Rewards. Entropy 2024, 26, 416. https://doi.org/10.3390/e26050416.

  9. Hamidpour, P.; Araee, A.; Baniassadi, M.; Garmestani, H. Multiphase Reconstruction of Heterogeneous Materials Using Machine Learning and Quality of Connection Function. Materials 2024, 17, 3049. https://doi.org/10.3390/ma17133049.

  10. Neugebauer, M.; d’Obyrn, J.; Sołowiej, P. Economic Analysis of Profitability of Using Energy Storage with Photovoltaic Installation in Conditions of Northeast Poland. Energies 2024, 17, 3075. https://doi.org/10.3390/en17133075.

  11. Liu, M.; Cao, Y.; Nie, C.; Wang, Z.; Zhang, Y. Finite Element Analysis of Densification Process in High Velocity Compaction of Iron-Based Powder. Materials 2024, 17, 3085. https://doi.org/10.3390/ma17133085.

  12. De-la-Mata-Moratilla, S.; Gutierrez-Martinez, J.; Castillo-Martinez, A.; Caro-Alvaro, S. Prediction of the Behaviour from Discharge Points for Solid Waste Management. Mach. Learn. Knowl. Extr. 2024, 6, 1389–1412. https://doi.org/10.3390/make6030066.

  13. Bassetti, D.; Pospíšil, L.; Horenko, I. On Entropic Learning from Noisy Time Series in the Small Data Regime. Entropy 2024, 26, 553. https://doi.org/10.3390/e26070553.

  14. Shiryayeva, O.; Suleimenov, B.; Kulakova, Y. Optimal Design of I-PD and PI-D Industrial Controllers Based on Artificial Intelligence Algorithm. Algorithms 2024, 17, 288. https://doi.org/10.3390/a17070288.

  15. Mahammedi, A.; Kouider, R.; Tayeb, N.; Kassir Al-Karany, R.; Cuerda-Correa, E.; Al-Kassir, A. Thermal and Hydrodynamic Measurements of a Novel Chaotic Micromixer to Enhance Mixing Performance. Energies 2024, 17, 3248. https://doi.org/10.3390/en17133248.

  16. Maciorowski, D.; Spychala, M.; Miedzinska, D. An Experimental and Numerical Investigation of a Heat Exchanger for Showers. Energies 2024, 17, 3641. https://doi.org/10.3390/en17153641.

  17. Ktari, A.; Ghauch, H.; Rekaya-Ben Othman, G. Machine Learning Techniques for Blind Beam Alignment in mmWave Massive MIMO. Entropy 2024, 26, 626. https://doi.org/10.3390/e26080626.

  18. López, J.; Vásquez-Coronel, J. Analyzing Monofractal Short and Very Short Time Series: A Comparison of Detrended Fluctuation Analysis and Convolutional Neural Networks as Classifiers. Fractal Fract. 2024, 8, 460. https://doi.org/10.3390/fractalfract8080460.

  19. Ren, Y.; Zhang, Z.; He, G.; Zhang, Y.; Zhang, Z. Hierarchical Significance of Environment Impact Factor on the Sand Erosion Performance of Lightweight Alloys. Materials 2024, 17, 3890. https://doi.org/10.3390/ma17163890.

  20. Shen, H.; Kulasegaram, S.; Brousseau, E. On the Aptness of Material Constitutive Models for Simulating Nano-Scratching Processes. Materials 2024, 17, 4208. https://doi.org/10.3390/ma17174208.

  21. Yu, Y.; Zhou, D.; Qiao, L.; Feng, P.; Kang, X.; Yang, C. Highly Porous Co-Al Intermetallic Created by Thermal Explosion Using NaCl as a Space Retainer. Materials 2024, 17, 4380. https://doi.org/10.3390/ma17174380.

  22. Lee, M. Fractal Self-Similarity in Semantic Convergence: Gradient of Embedding Similarity across Transformer Layers. Fractal Fract. 2024, 8, 552. https://doi.org/10.3390/fractalfract8100552.

  23. Fernández Valderrama, D.; Guerrero Alonso, J.; León de Mora, C.; Robba, M. Scenario Generation Based on Ant Colony Optimization for Modelling Stochastic Variables in Power Systems. Energies 2024, 17, 5293. https://doi.org/10.3390/en17215293.

  24. Cai, W.; Di, X.; Wang, X.; Gao, W.; Jia, H. Stealthy Vehicle Adversarial Camouflage Texture Generation Based on Neural Style Transfer. Entropy 2024, 26, 903. https://doi.org/10.3390/e26110903.

  25. Hui, P.; Zhao, J.; Li, C.; Zhu, Q. Quotient Network-A Network Similar to ResNet but Learning Quotients. Algorithms 2024, 17, 521. https://doi.org/10.3390/a17110521.

  26. Kantamneni, S.; Liu, Z.; Tegmark, M. How Do Transformers Model Physics? Investigating the Simple Harmonic Oscillator. Entropy 2024, 26, 997. https://doi.org/10.3390/e26110997.

  27. Lee, M.; Lee, S. Box-Counting Dimension Sequences of Level Sets in AI-Generated Fractals. Fractal Fract. 2024, 8, 730. https://doi.org/10.3390/fractalfract8120730.

  28. Belfekih, T.; Fitas, R.; Schaffrath, H.; Schabel, S. Graph-Based Analysis for the Characterization of Corrugated Board Compression. Materials 2024, 17, 6083. https://doi.org/10.3390/ma17246083.

  29. Kang, S.; Choi, D.; Son, S.; Choi, C. Generation and Validation of CFD-Based ROMs for Real-Time Temperature Control in the Main Control Room of Nuclear Power Plants. Energies 2024, 17, 6406. https://doi.org/10.3390/en17246406.

  30. Benaissa, B.; Kobayashi, M.; Takenouchi, H. Enhancing Consumer Agent Modeling Through Openness-Based Consumer Traits and Inverse Clustering. Mach. Learn. Knowl. Extr. 2025, 7, 9. https://doi.org/10.3390/make7010009.

  31. Vaiyapuri, T. Optimizing Hydrogen Production in the Co-Gasification Process: Comparison of Explainable Regression Models Using Shapley Additive Explanations. Entropy 2025, 27, 83. https://doi.org/10.3390/e27010083.

  32. Huang, L.; Cao, Y.; Zhang, M.; Meng, Z.; Wang, T.; Zhu, X. Optimization Design of Casting Process for Large Long Lead Cylinder of Aluminum Alloy. Materials 2025, 18, 531. https://doi.org/10.3390/ma18030531.

  33. Zhang, H.; Liu, H. Real-Time Power System Optimization Under Typhoon Weather Using the Smart “Predict, Then Optimize” Framework. Energies 2025, 18, 615. https://doi.org/10.3390/en18030615.

  34. Zhang, E.; Chen, X.; Zhou, J.; Wu, H.; Chen, Y.; Huang, H.; Li, J.; Yang, Q. Modeling the Carbothermal Chlorination Mechanism of Titanium Dioxide in Molten Salt Using a Deep Neural Network Potential. Materials 2025, 18, 659. https://doi.org/10.3390/ma18030659.

  35. Soto Calvo, M.; Lee, H. Electrical Storm Optimization (ESO) Algorithm: Theoretical Foundations, Analysis, and Application to Engineering Problems. Mach. Learn. Knowl. Extr. 2025, 7, 24. https://doi.org/10.3390/make7010024.

  36. Xu, X.; Lu, X.; Wang, J. DeeWaNA: An Unsupervised Network Representation Learning Framework Integrating Deepwalk and Neighborhood Aggregation for Node Classification. Entropy 2025, 27, 322. https://doi.org/10.3390/e27030322.

  37. Tijani, O.; Serra, S.; Lanusse, P.; Malti, R.; Viot, H.; Reneaume, J. Grey-Box Modelling of District Heating Networks Using Modified LPV Models. Energies 2025, 18, 1626. https://doi.org/10.3390/en18071626.

  38. Ugwumadu, C.; Tabarez, J.; Drabold, D.; Pandey, A. PowerModel-AI: A First On-the-Fly Machine-Learning Predictor for AC Power Flow Solutions. Energies 2025, 18, 1968. https://doi.org/10.3390/en18081968.

  39. Rivera Torres, P.; Chen, C.; Rodríguez González, S.; Llanes Santiago, O. A Learning Probabilistic Boolean Network Model of a Manufacturing Process with Applications in System Asset Maintenance. Entropy 2025, 27, 463. https://doi.org/10.3390/e27050463.

  40. Levner, E.; Kriheli, B. Analysis of Reliability and Efficiency of Information Extraction Using AI-Based Chatbot: The More-for-Less Paradox. Algorithms 2025, 18, 412. https://doi.org/10.3390/a18070412.

Footnotes

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