Complex Dynamic Problems Research Articles

Exploring swirling flow dynamics: Unsupervised machine learning in Maxwell hybrid nanofluid convection over an exponentially stretching cylinder with non-linear radiation effects

This article analyses the flow of Maxwell hybrid nanofluid induced by an exponentially stretching and rotating cylinder. The presence of non-linear convection, non-linear radiation, and magnetic field is also assumed. The factors covered in the study has a wide spectrum of application in various disciplines, and therefore we analyse the influence of different flow parameters after numerically solving the set of modelled differential equations. A data-free physics-informed neural network using a wavelet activation function is used to approximate the numerical solution. The reliability of the used methodology is validated by comparing the results of the limiting case with the available results. The paper demonstrates the effectiveness of using PINN in an unsupervised fashion to tackle fluid flow problems, showcasing their ability to provide reliable and accurate solutions without the need for extensive datasets. This approach highlights the potential of PINN to address complex fluid dynamics problems by utilizing physical laws within the neural network framework. From the numerical study, it is observed that hybrid nanofluid has a better rate of heat transfer compared to the nanofluid. Furthermore, radiation parameter and maxwell flow parameter is seen to exhibit significant impact of the flow profiles.

A comprehensive review of advances in physics-informed neural networks and their applications in complex fluid dynamics

Physics-informed neural networks (PINNs) represent an emerging computational paradigm that incorporates observed data patterns and the fundamental physical laws of a given problem domain. This approach provides significant advantages in addressing diverse difficulties in the field of complex fluid dynamics. We thoroughly investigated the design of the model architecture, the optimization of the convergence rate, and the development of computational modules for PINNs. However, efficiently and accurately utilizing PINNs to resolve complex fluid dynamics problems remain an enormous barrier. For instance, rapidly deriving surrogate models for turbulence from known data and accurately characterizing flow details in multiphase flow fields present substantial difficulties. Additionally, the prediction of parameters in multi-physics coupled models, achieving balance across all scales in multiscale modeling, and developing standardized test sets encompassing complex fluid dynamic problems are urgent technical breakthroughs needed. This paper discusses the latest advancements in PINNs and their potential applications in complex fluid dynamics, including turbulence, multiphase flows, multi-field coupled flows, and multiscale flows. Furthermore, we analyze the challenges that PINNs face in addressing these fluid dynamics problems and outline future trends in their growth. Our objective is to enhance the integration of deep learning and complex fluid dynamics, facilitating the resolution of more realistic and complex flow problems.

Novel approach for precise identification of vibration frequencies and damping ratios from free vibration decay time histories data of nonlinear single degree of freedom models

The significance of Single Degree of Freedom (SDOF) systems lies in their ability to serve as foundational elements for modeling more complex dynamic problems. By capturing essential dynamic behavior with simplicity, SDOF models enable efficient analysis and comprehension of complex systems, justifying the investigation of these simplified models. In nonlinear scenarios, SDOF models result in time series data wherein vibration frequencies vary over time. Classically, time–frequency or Hilbert transforms applied to temporal responses are frequently used to identify the evolution of frequencies and damping ratio over time. These techniques provide results that reflect the spectrum composition achieved for the analyzed time window and present difficulties in precisely determining the magnitude and the exact instant of an effective frequency or damping ratio variation. In this sense, this work introduces a new methodology capable of accurately identifying the vibration frequency as a function of time, i.e., the instantaneous frequency, along with the instantaneous damping ratio. At this initial stage, the focus is on validating the methodology by comparing its performance with the classical approach based on time–frequency transforms. The initial results obtained from synthetic free vibration decay responses of SDOF nonlinear models highlight the accuracy of our findings compared to those obtained from time–frequency transforms. The presented methodology holds promise for further advancement, with potential impacts including structural damage identification, modal identification and nonlinear dynamic analysis.

A comparative study of exact and neural network models for wave‐induced multiphase flow in nonuniform geometries: Application of Levenberg–Marquardt neural networks

AbstractMultiphase fluids exhibit immiscible, heterogeneous structures like emulsions, foams, and suspensions. Their complex rheology arises from relative phase proportions, interfacial interactions, and component properties. Consequently, they demonstrate nonlinear effects—shear‐thinning, viscoelasticity, and yield stress. Peristalsis generates fluid flow by propagating contraction waves along channel walls. This mechanism can effectively transport multiphase and non‐Newtonian fluids in microsystems. Accurate modeling requires considering evolving phase relations, variable viscosity, slip, and particle migration anomalies, using approaches like homogenization theory or volume‐averaging. Applications include peristaltic pumping of emulsified biopharmaceuticals, microscale mixing/separating of multiphase constituents, and enhancing porous media fluid flow in oil reservoirs. Analytical and computational approaches to modeling multiphase fluid flows in peristaltic conduits provide an enhanced understanding of their complex dynamics, toward innovating engineering systems. An analytical approach is taken to model non‐Newtonian Ree‐Eyring fluid flows in asymmetric, peristaltic systems. Governing differential equations incorporate key parameters and yield closed‐form solutions for velocity, flow rate, and permeability. Suitable assumptions of long wavelength, and low Reynolds number provide accuracy. In parallel, an artificial neural network (ANN) is developed using supervised learning to predict permeability. The inputs consist of channel asymmetry, Reynolds number, amplitude ratio, and other physical factors. Outcomes validate both methodologies—analytical equations derive precise relationships from first principles, while ANNs reliably learn the system patterns from input‐output data. Additionally, ANNs can tackle more complex fluid dynamics problems with speed and adaptability. Their promising role is highlighted in developing new fluid models, improving the efficiency of simulations, and designing control systems. Side‐by‐side analytical and ANN simulation plots will further highlight ANN capabilities in emulating the system characteristics. This paves the path for employing machine learning to investigate multifaceted flows in flexible, peristaltic systems at scale. Performing a graphical examination of the engineering skin friction coefficient across a range of parameters, encompassing volume fraction, first and second order slip, Ree–Eyring fluid attributes, and permeability.

Dynamics of ternary nanofluid through radiated sensor surface: Numerical investigation

Application: The impact of flow, heat transfer, and magneto hydrodynamics on sensor surfaces between two parallel compressing plates with porous walls has been examined in this study. This study focuses on understanding unsteady compressed flow in two dimensions, utilizing Aluminum oxide, copper oxide, and titanium dioxide with base fluid polymers as the base fluid. Nanofluids, known as nanometer suspensions in traditional nanoscale fluid transfer, are explored for their potential application in improving lubricative and cooling properties. Purpose and methodology: This study aims to investigate the behavior of a tri-hybrid nanofluid (Aluminum oxide, copper oxide, and titanium dioxide with base fluid polymers) in terms of flow dynamics, heat transfer, and magneto hydrodynamics. Energy and momentum equations, considering magneto hydrodynamic forms and heat transfer, are analyzed. The study employs numerical methods, including similarity transforms and a shooting approach, to solve the governing equations. Core findings: Several parameters, including permeable parameter, magnetic parameter, squeeze flow index parameter, volume fraction by nanoparticles, and radiation parameter, are investigated for their effects on temperature profile and velocity profile. The study illustrates these effects graphically and discusses the influence of these parameters on different components of velocity and temperature fields. Additionally, the impact of the radiation parameter ([Formula: see text] on temperature fields is examined for both positive. Future work: Future research may focus on further optimizing the tri-hybrid nanofluid composition for specific applications, exploring additional parameters that may affect flow behavior, heat transfer, and entropy generation. Additionally, experimental validation of the numerical findings and the development of more advanced numerical techniques for solving complex fluid dynamics problems could be the areas of interest for future work.

Perturbation to Symmetries and Adiabatic Invariants for Generalized Birkhoffian Systems on Time Scales

Time scale is a new and powerful tool for dealing with complex dynamics problems. The main result of this study is the exact invariants and adiabatic invariants of the generalized Birkhoffian system and the constrained Birkhoffian system on time scales. Firstly, we establish the differential equations of motion for the above two systems and give the corresponding Noether symmetries and exact invariants. Then, the perturbation to the Noether symmetries and the adiabatic invariants for the systems mentioned above under the action of slight disturbance are investigated, respectively. Finally, two examples are provided to show the practicality of the findings.

Tipping points of evolving epidemiological networks: Machine learning-assisted, data-driven effective modeling.

We study the tipping point collective dynamics of an adaptive susceptible-infected-susceptible (SIS) epidemiological network in a data-driven, machine learning-assisted manner. We identify a parameter-dependent effective stochastic differential equation (eSDE) in terms of physically meaningful coarse mean-field variables through a deep-learning ResNet architecture inspired by numerical stochastic integrators. We construct an approximate effective bifurcation diagram based on the identified drift term of the eSDE and contrast it with the mean-field SIS model bifurcation diagram. We observe a subcritical Hopf bifurcation in the evolving network's effective SIS dynamics that causes the tipping point behavior; this takes the form of large amplitude collective oscillations that spontaneously-yet rarely-arise from the neighborhood of a (noisy) stationary state. We study the statistics of these rare events both through repeated brute force simulations and by using established mathematical/computational tools exploiting the right-hand side of the identified SDE. We demonstrate that such a collective SDE can also be identified (and the rare event computations also performed) in terms of data-driven coarse observables, obtained here via manifold learning techniques, in particular, Diffusion Maps. The workflow of our study is straightforwardly applicable to other complex dynamic problems exhibiting tipping point dynamics.

Dynamic optimization on quantum hardware: Feasibility for a process industry use case

The quest for real-time dynamic optimization solutions in the process industry represents a formidable computational challenge, particularly within the realm of applications like model-predictive control, where rapid and reliable computations are critical. Conventional methods can struggle to surmount the complexities of such tasks. Quantum computing and quantum annealing emerge as avant-garde contenders to transcend conventional computational constraints. We convert a dynamic optimization problem, characterized by an optimization problem with a system of differential–algebraic equations embedded, into a Quadratic Unconstrained Binary Optimization problem, enabling quantum computational approaches. The empirical findings synthesized from classical methods, simulated annealing, quantum annealing via D-Wave’s quantum annealer, and hybrid solver methodologies, illuminate the intricate landscape of computational prowess essential for tackling complex and high-dimensional dynamic optimization problems. Our findings suggest that while quantum annealing is a maturing technology that currently does not outperform state-of-the-art classical solvers, continuous improvements could eventually aid in increasing efficiency within the chemical process industry.

Bayesian reinforcement learning reliability analysis

A Bayesian reinforcement learning reliability method that combines Bayesian inference for the failure probability estimation and reinforcement learning-guided sequential experimental design is proposed. The reliability-oriented sequential experimental design is framed as a finite-horizon Markov decision process (MDP), with the associated utility function defined by a measure of epistemic uncertainty about Kriging-estimated failure probability, referred to as integrated probability of misclassification (IPM). On this basis, a one-step Bayes optimal learning function termed integrated probability of misclassification reduction (IPMR), along with a compatible convergence criterion, is defined. Three effective strategies are implemented to accelerate IPMR-informed sequential experimental design: (i) Analytical derivation of the inner expectation in IPMR, simplifying it to a single expectation. (ii) Substitution of IPMR with its upper bound IPMRU to avoid element-wise computation of its integrand. (iii) Rational pruning of both quadrature set and candidate pool in IPMRU to alleviate computer memory constraint. The efficacy of the proposed approach is demonstrated on two benchmark examples and two numerical examples. Results indicate that IPMRU facilitates a much more rapid reduction of IPM compared to other existing learning functions, while requiring much less computational time than IPMR itself. Therefore, the proposed reliability method offers a substantial advantage in both computational efficiency and accuracy, especially in complex dynamic reliability problems.

Multi-Objective Stochastic Paint Optimizer for Solving Dynamic Economic Emission Dispatch with Transmission Loss Prediction Using Random Forest Machine Learning Model

Dynamic economic emission dispatch problems are complex optimization tasks in power systems that aim to simultaneously minimize both fuel costs and pollutant emissions while satisfying various system constraints. Traditional methods often involve solving intricate nonlinear load flow equations or employing approximate loss formulas to account for transmission losses. These methods can be computationally expensive and may not accurately represent the actual transmission losses, affecting the overall optimization results. To address these limitations, this study proposes a novel approach that integrates transmission loss prediction into the dynamic economic emission dispatch (DEED) problem. A Random Forest machine learning model was offline-trained to predict transmission losses accurately, eliminating the need for repeated calculations during each iteration of the optimization process. This significantly reduced the computational burden of the algorithm and improved its efficiency. The proposed method utilizes a powerful multi-objective stochastic paint optimizer to solve the highly constrained and complex dynamic economic emission dispatch problem integrated with random forest-based loss prediction. A fuzzy membership-based approach was employed to determine the best compromise Pareto-optimal solution. The proposed algorithm integrated with loss prediction was validated on widely used five and ten-unit power systems with B-loss coefficients. The results obtained using the proposed algorithm were compared with seventeen algorithms available in the literature, demonstrating that the multi-objective stochastic paint optimizer (MOSPO) outperforms most existing algorithms. Notably, for the Institute of Electrical and Electronics Engineers (IEEE) thirty bus system, the proposed algorithm achieves yearly fuel cost savings of USD 37,339.5 and USD 3423.7 compared to the existing group search optimizer algorithm with multiple producers (GSOMP) and multi-objective multi-verse optimization (MOMVO) algorithms.

Emulator of PR‐DNS: Accelerating Dynamical Fields With Neural Operators in Particle‐Resolved Direct Numerical Simulation

AbstractParticle‐resolved direct numerical simulations (PR‐DNS) play an increasing role in investigating aerosol‐cloud‐turbulence interactions at the most fundamental level of processes. However, the high computational cost associated with high resolution simulations poses considerable challenges for large domain or long duration simulation using PR‐DNS. To address these issues, here we present an emulator of the complex physics‐based PR‐DNS developed by use of the data‐driven Fourier Neural Operator (FNO) method. The effectiveness of the method is showcased by presenting turbulence and temperature fields in a two‐dimensional space. The results demonstrate high accuracy at various resolutions and the emulator is two orders of magnitude cheaper in terms of computational demand compared to the physics‐based PR‐DNS model. Furthermore, the FNO emulator exhibits strong generalization capabilities for different initial conditions and ultra‐high‐resolution without the need to retrain models. These findings highlight the potential of the FNO method as a promising tool to simulate complex fluid dynamics problems with high accuracy, computational efficiency, and generalization capabilities, enhancing our understanding of the aerosol‐cloud‐precipitation system.

Structural reliability analysis based on probability density evolution method and stepwise truncated variance reduction

To address the substantial computational burden associated with probability density evolution method (PDEM) in structural reliability analysis, this study proposes a novel look-ahead learning function named stepwise truncated variance reduction (STVR), integrating polynomial chaos Kriging (PCK) and PDEM. Three key features of STVR are highlighted. First, it enables quantifying the maximum reduction in predictive errors of PCK within the regions of interest (ROI) when adding a new point. Second, closed-form expression for STVR is derived through Kriging update formulas, eliminating the need for computationally intensive Gauss–Hermite quadrature or extensive conditional simulations of PCK. Third, a dynamic adjustment procedure is proposed for the probability level-related parameter in STVR, with the aim of achieving a good balance between the exploitation and exploration of ROI during the sequential experimental design process. The performance of STVR is demonstrated through two benchmark analytical functions and three numerical examples of varying complexity. Results indicate that the dynamic adjustment procedure for the probability level-related parameter in STVR outperforms the empirical setting of a minor value. Then, STVR proves more advantageous than existing pointwise and look-ahead learning functions, particularly in addressing complex dynamic reliability problems.

Homogeneous-heterogeneous reactions on Darcy-Forchheimer nanofluid flow system

The use of artificial neural networks (ANNs) to solve complex fluid dynamics problems has revolutionized computational approaches. This article explores novel ANN solutions for fluid problems. ANNs have demonstrated unmatched effectiveness in comprehending and forecasting fluidic behaviors, from mimicking complex fluid flow trends to optimizing structures for dynamics. This study emphasizes the significance of neural networks in revolutionizing our understanding and control of fluidic systems by using ANNs and Bayesian Regularization. This study examined the 3D Darcy-Forchheimer stretching flow (TDDFSF) of nanofluid under convective conditions along with homogeneous and heterogeneous reactions by employing the scheme of Bayesian Regularization with the procedure of backpropagation in neural networks (SBR-BNNs). The flow is influenced by Brownian diffusion, thermophoresis and zero nanoparticles mass flux condition. The PDEs given in this model are converted into nonlinear ODEs. Results from MSE, regression analysis, and error histogram are used to verify the performance of SBR-BNNs. The absolute errors lie in the ranges up to 10−9, which depict the worth of the solver SBR-BNNs. The absolute error measures the discrepancy between the values actually observed and those predicted by the SBR-BNNs model. SBR-BNNs' high precision in TDDFSF models can lead to more effective and reliable solutions.

A modified adaptive beluga whale optimization based on spiral search and elitist strategy for short-term hydrothermal scheduling

Short-term hydrothermal scheduling is a complex dynamic nonlinear optimization problem which considers various hydropower constraints. In this study, an adaptive beluga whale optimization method based on a spiral search and elitist strategy is proposed to solve this complex problem. The proposed method has three main advantages: First, an adaptive parameter strategy based on a cosine function achieves a better balance between exploration and exploitation. Second, the spiral search and elite strategy guides search agents to search for focused areas and effectively narrows the scope of the invalid search space. Third, instead of the penalty function method, a feasibility-based selection comparison technique and heuristic strategy are adopted to address complex constraints in STHS. In comparison to the results of benchmark functions from CEC 2015, ASEBWO generally demonstrates superior convergence accuracy when compared to the other seven algorithms. Additionally, the feasibility and effectiveness of ASEBWO are verified using two hydrothermal scheduling systems and compared with those of more than 10 algorithms. The comparison results demonstrate that ASEBWO achieves the best solution quality.

Optimizing Operations Management and Business Analytics Strategies under Uncertainty: Dynamic Programming

Dynamic programming is a method used in mathematics, management science, computer science, economics, and bioinformatics to solve complex problems by decomposing the original problem into relatively simple sub-problems. Dynamic programming is often applicable to problems with overlapping subproblems and optimal substructure properties. This paper employs a comprehensive research approach of literature review, as well as empirical analysis and case studies to investigate the topic and demonstrate the practicality and effectiveness of dynamic programming in solving complex decision-making problems. However, the curse of dimensionality poses challenges when dealing with high-dimensional decision spaces, requiring approximate dynamic programming methods, including reinforcement learning algorithms. Therefore, when dealing with more complex dynamic programming problems, it is also essential to use program construction tools such as Python to help design a program that can optimize the problem. Therefore, in the learning of dynamic programming, in addition to the correct understanding of basic concepts and methods, specific problems must be analyzed and dealt with in detail, models should be built with rich imagination, and solutions should be solved with creative skills.

Spatiotemporal Relationship Cognitive Learning for Multirobot Air Combat

Relationship cognition is crucial to learning-based Multi-Robot Systems (MRSs). As an advanced application of MRSs for fierce confrontation, the relationships among autonomous air combat robots inherently present complex time-varying characteristics, which makes relationship cognition even more difficult. However, previous studies have only focused on spatial cooperative relationships, thus ignoring the potential impact of the temporal dynamics of relationships on long-term cooperative behaviors. To tackle this drawback, we propose a novel Multi-Agent Deep Reinforcement Learning (MADRL) based autonomous air combat robots collaboration algorithm, called Spatio-Temporal Aerial robots Relationship Co-Optimization (STARCO). STARCO formulates the complex dynamic relationship cognition problem into a spatio-temporal deep Graph Neural Network (GNN) learning problem. On this basis, we overcome the limitations of previous methods, by accurately capturing the key spatio-temporal patterns from aggressive air combat, and enable global collaborative decision-making through joint strategy optimization. An empirical study shows that STARCO outperforms several state-of-the-art MARL baselines by 24.6% in learning performance. We also demonstrate that STARCO is capable of evolving various cooperative strategies comparable to human expert knowledge.

Investigation of the Rock-Breaking Mechanism of Drilling under Different Conditions Using Numerical Simulation

The interaction between the drill bit and rock is a complex dynamic problem in the process of drilling and breaking rock. In this paper, the dynamic process of drilling and breaking rock is analyzed using ABAQUS software. The rock-breaking mechanism of drilling is revealed according to the stress–strain state of the rock and the force of the drill bit. The effect of the size of the drill bit and the characteristics of the rock mass on the drilling parameters is studied during the drilling process. The results show that both thrust force and torque show a linear increase with the increasing drilling speed under each fixed rotational speed. The drill bit size has minimal impact on the correlation coefficient of the relationship curves between thrust force, torque, and rotation speed. The drilling results in a soft–hard interlayered rock formation show that there are significant differences in thrust force and torque during the drilling process of different rock types. Whether transitioning from a soft rock layer to a hard rock layer or vice versa, the relationship between thrust force and torque is distinctly manifested whenever there is a change in rock quality. The thrust force and torque increase correspondingly with the increase in confining pressure. When subjected to lateral pressure, thrust force and torque gradually increase with the rising confining pressure. Vertical drilling exhibits a larger increase in thrust force and torque compared to horizontal drilling. The thrust force and torque increase more significantly with the rise in confining pressure compared to lateral pressure.

DRL-Based Secure Aggregation and Resource Orchestration in MEC-Enabled Hierarchical Federated Learning

Federated learning (FL) provides a new paradigm for protecting data privacy by enabling model training at devices and model aggregation at servers. However, data information may be leaked to honest-but-curious aggregation servers by updated model parameters. The existing secure methods do not fully exploit the potentiality of data characteristics in enhancing security, which makes it impossible to optimize limited system resources overall to achieve secure, fair and efficient FL systems. In this paper, a DRL-based joint secure aggregation and resource orchestration scheme is proposed to guarantee security and fairness, and improve efficiency for hierarchical FL assisted by untrusted mobile-edge computing (MEC) servers. We formulate a joint optimization problem of data size, payment and resource orchestration, to maximize the long-term social welfare subject to secure aggregation and limited resources. Since the formulated problem is a complex mixed integer dynamic optimization problem with NP-hardness, where multiple mixed integer optimization variables are highly coupled in time-varying constraints and objective function, it is difficult to obtain its optimal solution via traditional optimization methods. Thus, we propose a hierarchical reward function-based DRL algorithm (MATD3) to guide the agents to approach the optimal policy of secure aggregation and resource orchestration. Simulation results show that the proposed algorithm MATD3 can achieve superior performance over comparison algorithms and the MEC-enabled HFL framework outperforms two-layer FL frameworks.

Higher order dynamic mode decomposition beyond aerospace engineering

It is a well known fact that fluid dynamics play a crucial rule in countless fields in scientific and industrial applications, including nature and medicine (ocean currents, fluid motion around jellyfish, blood circulation...), in energy production (wind turbines, tidal energy, combustion...) and of course in transportation and aerospace (trains, automobiles, aerospace shape optimization, cross-flow instability...). Understanding all these complex fluid dynamics problems is not an easy task and it requires a routinely description and quantification. Data-science and its diverse technique have arisen as a powerful tool to tackle these fluid dynamics problems, techniques such as machine learning and artificial intelligence, data processing and decision making, modeling and simulations are but a few of the promising tools described so far. In this work, we focus on data-driven techniques. In particular, we are introducing the fully data-driven technique, the higher order dynamic mode decomposition (HODMD). This technique was originally developed for the fluid mechanics field, but rapidly grew and covered several other fields and applications. A short review comparing two different applications will be shown in this contribution. We will first present our proposed technique, explain its solid mathematical foundations and highlight its capabilities (robustness, denoising properties, efficiency regardless of the amounts of data...). Next, we show the applicability of the HODMD technique to two, very different and quite complex problems: (i) a compressible, turbulent jet and (ii) pattern identification in medical dataset, consisting of echocardiography images.

Dynamic and adaptive mesh-based graph neural network framework for simulating displacement and crack fields in phase field models

Fracture is one of the main causes of failure in engineering structures. Phase field methods coupled with adaptive mesh refinement (AMR) techniques have been widely used to model crack propagation due to their ease of implementation and scalability. However, phase field methods can still be computationally demanding making them unfeasible for high-throughput design applications. Machine learning (ML) models such as Graph Neural Networks (GNNs) have shown their ability to emulate complex dynamic problems with speed-ups orders of magnitude faster compared to high-fidelity simulators. In this work, we present a dynamic mesh-based GNN framework for emulating phase field simulations of single-edge crack propagation with AMR for different crack configurations. The developed framework – ADAPTive mesh-based graph neural network (ADAPT-GNN) – exploits the benefits of both ML methods and AMR by describing the graph representation at each time step as the refined mesh itself. Using ADAPT-GNN, we predict the evolution of displacement fields and scalar damage field (or phase field) with good accuracy compared to the conventional phase-field fracture model. We also compute crack stress fields with good accuracy using the predicted displacements and phase field parameter.