Differential equation-driven intelligent control: Integrating AI, Quantum computing, and adaptive strategies for next-generation industrial automation DOI
Ji‐Huan He, Yue Cheng, Ceng Luo

et al.

Advances in Differential Equations and Control Processes, Journal Year: 2025, Volume and Issue: 32(1), P. 3096 - 3096

Published: April 24, 2025

The increasing intricacy of industrial systems highlights the inadequacies conventional control theories in management high-dimensional nonlinear dynamics, real-time coupling, and multi-scale modelling. This article introduces a transformative paradigm—differential equation-driven intelligent control—that synergizes artificial intelligence (AI), quantum computing, adaptive strategies to redefine next-generation automation. following innovations are at core this paradigm: Physics-informed neural networks (PINNs) for solving partial differential equations (PDEs), Quantum-enhanced linear algebra stochastic equation (SDE) optimization, symbolic regression automated discovery fractional-order dynamic models. A case study on flexible robotic arm dynamics demonstrates tunability hybrid rigid-flexible via parameters Lyapunov-based control. concept Equations as Service (EaaS) is proposed democratize access distributed computational solvers, enabling optimization applications such drone swarm coordination carbon-neutral manufacturing. number critical challenges addressed text, including interpretability AI (for example, through use SHAP-based explainability tools), reliability quantum-classical ethical governance frameworks. Through interdisciplinary collaboration, vision self-evolving factories by 2030 outlined—where autonomously refine using sensor data. Examples include smart grids adapting renewable energy fluctuations millisecond scales assembly lines recalibrating mitigate material defects. overarching objective paradigm shift, termed EaaS, transition from their traditional role static descriptors that self-optimizing assets. expected lay foundation resilient, explainable, sustainable ecosystems era Industry 5.0.

Language: Английский

A novel hybrid framework for efficient higher order ODE solvers using neural networks and block methods DOI Creative Commons

V. Murugesh,

M. Priyadharshini,

Yogesh Kumar Sharma

et al.

Scientific Reports, Journal Year: 2025, Volume and Issue: 15(1)

Published: March 12, 2025

Abstract In this paper, the author introduces Neural-ODE Hybrid Block Method, which serves as a direct solution for solving higher-order ODEs. Many single and multi-step methods employed in numerical approximations lose their stability when applied of ODEs with oscillatory and/or exponential features, case. A new hybrid approach is formulated implemented, incorporates both approximate power neural networks robustness block methods. particular, it uses ability to spaces, utilizes method avoids conversion these equations into system first-order If used analysis, capable dealing several dynamic behaviors, such stiff boundary conditions. This paper presents mathematical formulation, architecture network choice its parameters proposed model. addition, results derived from convergence analysis agree that suggested technique more accurate compared existing solvers can handle effectively. Numerical experiments ordinary differential indicate fast has high accuracy linear nonlinear problems, including simple harmonic oscillators, damped systems like Van der Pol equation. The advantages are thought be generalized all scientific engineering disciplines, physics, biology, finance, other areas demand precise solutions. following also suggests potential research avenues future studies well: prospects model multi-dimensional systems, application partial (PDEs), appropriate higher efficiency.

Language: Английский

Citations

0
He’s frequency formulation for fractal-fractional nonlinear oscillators: a comprehensive analysis DOI Creative Commons
Li Zhang, Khaled A. Gepreel, Jiahui Yu

et al.

Frontiers in Physics, Journal Year: 2025, Volume and Issue: 13

Published: March 20, 2025

This mini-review focuses on He’s frequency formulation for fractal-fractional nonlinear oscillators. It examines the significance and applications of this in understanding analyzing frequency-amplitude relationship within a fractal space. The review analyses key features advantages formulation, highlighting its role providing straightforward approach to vibration systems compared traditional methods. Furthermore, it discusses an open problem future research.

Language: Английский

Citations

0
Mathematical approach for rapid determination of pull-in displacement in MEMS devices DOI Creative Commons
Shao Yan,

Yutong Cui

Frontiers in Physics, Journal Year: 2025, Volume and Issue: 13

Published: April 7, 2025

Introduction Microelectromechanical systems (MEMS) are pivotal in diverse fields such as telecommunications, healthcare, and aerospace. A critical challenge MEMS devices is accurately determining the pull-in displacement voltage, which significantly impacts device performance. Existing methods, including variational iteration method homotopy perturbation method, often fall short providing precise estimations of these parameters. Methods This study introduces a novel mathematical approach that combines physical insights into phenomenon with theory. The begins definition device's model. By uniquely applying principle incorporating custom-designed functional, set equations derived. These transformed an iterative algorithm for calculating displacement, nonlinear terms addressed through approximation techniques tailored to system’s characteristics. Results Validation using specific examples demonstrates method's accuracy voltage. For instance, oscillator case, exact results were achieved computation time 0.015 s. Compared traditional this yields values rather than approximations, showcasing superior precision efficiency. Discussion proposed offers significant advantages, enhanced accuracy, reduced computational time, minimized error accumulation by solving algebraic instead iterating differential equations. It also exhibits robustness variations initial conditions system Limitations include need modifying criterion when formulation unattainable exclusion environmental factors like temperature pressure fluctuations. Future research should focus on refining models incorporate integrating Galerkin technology. Conclusion advances understanding behavior holds substantial potential design optimization across various applications, further driving progression

Language: Английский

Citations

0
Deep learning-based Adam optimization for magnetohydrodynamics radiative thin film flow of ternary hybrid nanofluid with oscillatory boundary conditions DOI
Jian Wang, Maddina Dinesh Kumar, S. Mamatha Upadhya

et al.

Chaos Solitons & Fractals, Journal Year: 2025, Volume and Issue: 196, P. 116448 - 116448

Published: April 19, 2025

Language: Английский

Citations

0
Differential equation-driven intelligent control: Integrating AI, Quantum computing, and adaptive strategies for next-generation industrial automation DOI
Ji‐Huan He, Yue Cheng, Ceng Luo

et al.

Advances in Differential Equations and Control Processes, Journal Year: 2025, Volume and Issue: 32(1), P. 3096 - 3096

Published: April 24, 2025

The increasing intricacy of industrial systems highlights the inadequacies conventional control theories in management high-dimensional nonlinear dynamics, real-time coupling, and multi-scale modelling. This article introduces a transformative paradigm—differential equation-driven intelligent control—that synergizes artificial intelligence (AI), quantum computing, adaptive strategies to redefine next-generation automation. following innovations are at core this paradigm: Physics-informed neural networks (PINNs) for solving partial differential equations (PDEs), Quantum-enhanced linear algebra stochastic equation (SDE) optimization, symbolic regression automated discovery fractional-order dynamic models. A case study on flexible robotic arm dynamics demonstrates tunability hybrid rigid-flexible via parameters Lyapunov-based control. concept Equations as Service (EaaS) is proposed democratize access distributed computational solvers, enabling optimization applications such drone swarm coordination carbon-neutral manufacturing. number critical challenges addressed text, including interpretability AI (for example, through use SHAP-based explainability tools), reliability quantum-classical ethical governance frameworks. Through interdisciplinary collaboration, vision self-evolving factories by 2030 outlined—where autonomously refine using sensor data. Examples include smart grids adapting renewable energy fluctuations millisecond scales assembly lines recalibrating mitigate material defects. overarching objective paradigm shift, termed EaaS, transition from their traditional role static descriptors that self-optimizing assets. expected lay foundation resilient, explainable, sustainable ecosystems era Industry 5.0.

Language: Английский

Citations

0