Fourth-order Runge-Kutta Method Research Articles

Using Short Time Series of Monofractal Synthetic Fluctuations to Estimate the Foreign Exchange Rate: The Case of the US Dollar and the Chilean Peso (USD–CLP)

Short time series are fundamental in the foreign exchange market due to their ability to provide real-time information, allowing traders to react quickly to market movements, thus optimizing profits and mitigating risks. Economic transactions show a strong connection to foreign currencies, making exchange rate prediction challenging. In this study, the exchange rate estimation between the US dollar (USD) and the Chilean peso (CLP) for a short period, from 2 August 2021 to 31 August 2022, is modeled using the nonlinear Schrödinger equation (NLSE) and calculated with the fourth-order Runge–Kutta method, respectively. Additionally, the daily fluctuations of the current exchange rate are characterized using the Hurst exponent, H, and later used to generate short synthetic fluctuations to predict the USD–CLP exchange rate. The results show that the USD–CLP exchange rate can be estimated with an error of less than 5%, while when using short synthetic fluctuations, the exchange rate shows an error of less than 10%.

Stochastic Optimal Control Analysis for HBV Epidemic Model with Vaccination

In this study, we explore the concept of symmetry as it applies to the dynamics of the Hepatitis B Virus (HBV) epidemic model. By incorporating symmetric principles in the stochastic model, we ensure that the control strategies derived are not only effective but also consistent across varying conditions, and ensure the reliability of our predictions. This paper presents a stochastic optimal control analysis of an HBV epidemic model, incorporating vaccination as a pivotal control measure. We formulate a stochastic model to capture the complex dynamics of HBV transmission and its progression to acute and chronic stages. By leveraging stochastic differential equations, we examine the model’s stationary distribution and asymptotic behavior, elucidating the impact of random perturbations on disease dynamics. Optimal control theory is employed to derive control strategies aimed at minimizing the disease burden and vaccination costs. Through rigorous numerical simulations using the fourth-order Runge–Kutta method, we demonstrate the efficacy of the proposed control measures. Our findings highlight the critical role of vaccination in controlling HBV spread and provide insights into the optimization of vaccination strategies under stochastic conditions. The symmetry within the proposed model equations allows for a balanced approach to analyzing both acute and chronic stages of HBV.

Effect of side ratio on the two-degrees-of-freedom vortex-induced vibrations of the rectangular cross section model

The effect of the mutative side ratio (D/B) on the vortex-induced vibration (VIV) characteristic, aerodynamic characteristics, and the surrounding time-averaged and transient flow field of a rectangular cross section model were simulated numerically. Based on Fluent 19.0 platform, overset grid technology and the fourth-order Runge–Kutta method were used at Re 22 000. First, a rectangular cross section model with D/B = 0.25 was selected, and the simulation method and parameter settings were validated against previous literatures. The subsequent analysis compared and evaluated the effect of side ratio on the VIV response by focusing on statistical values of aerodynamic force coefficients, self-spectra, amplitude ratio, motion trajectory, and phase transition changes for stream-wise and cross-flow directions. Moreover, the study examined the influence of different models at different reduced velocities (Ur) on wake vortex-shedding. The findings suggest that, within a fixed cross-sectional area, a smaller side ratio leads to a weaker VIV characteristic and notably lower aerodynamic performance compared to a larger side ratio. The vortex-shedding mode of the rectangular cross section, particularly with a large side ratio, is less sensitive to changes in Ur compared to the standard square cylinder. An examination of the Reynolds number (Re) effect on the minimum and maximum side ratio models reveals that it has a more pronounced impact on the aerodynamic performance and VIV of the cross-flow when compared to in-line flow. In general, it is noted that larger side ratio model exhibits a stronger sensitivity to the variation of Re.

Dynamics of heat transfer in complex fluid systems: Comparative analysis of Jeffrey, Williamson and Maxwell fluids with chemical reactions and mixed convection

This study addresses the complex dynamics of heat transfer in magnetohydrodynamic (MHD) systems involving Jeffrey, Williamson, Maxwell, and Newtonian fluids, focusing on how chemical reactions, activation energy, porosity, and mixed convection impact fluid behavior. The problem is critical due to the significant influence these factors have on industrial processes and applications involving non-Newtonian fluids. The developed a mathematical model represented by partial differential equations (PDEs), which were solved using similarity transformations and the fourth order Runge-Kutta (R-K) method combined with shooting technique, with MATLAB software facilitating the solution process. The results reveal that variations in magnetic field strength, porosity, and buoyancy force significantly affect fluid velocities, while radiation, Brownian motion, and thermophoresis alter temperature profiles. Furthermore, chemical reaction rates, Schmidt number, relaxation constant, and activation energy influence fluid concentrations. Key findings include that increasing porosity and magnetic field strength generally decreases fluid velocity, while higher radiation and Prandtl numbers reduce temperature. Chemical reactions and activation energy decrease fluid concentrations, with non-Newtonian fluids showing more pronounced effects compared to Newtonian fluids. The novelty of this work lies in its comprehensive analysis of multiple interacting parameters and their combined effects on heat transfer in MHD systems, providing insights that extend beyond previous studies in the literature. This research offers valuable implications for optimizing fluid dynamics in various industrial applications, including food processing, ink formulation, and friction reduction.

A study on the fractional-order COVID-19 SEIQR model and parameter analysis using homotopy perturbation method

In this article, we present a fractional-order susceptible-exposed-infected-quarantine-recovered (SEIQR) model to analyze the dynamics of the COVID-19 pandemic. The model includes susceptible (S), exposed (E), infected (I), quarantined (Q), and recovered (R) populations and uses a fractional-order differential equation to provide a further accurate representation of the disease's progression. We employ the homotopy perturbation method (HPM) to derive analytical solutions and the Runge-Kutta fourth-order (RK4) method to obtain numerical solutions. The results indicate that the fractional-order model, particularly for a fractional parameter α = 0.40, provides better accuracy and stability compared to the classical integer-order model. This study highlights the importance of fractional-order modeling in understanding the spread of COVID-19 and suggests its potential application in predicting and controlling future epidemics.

A model of racing kayak surge motion a numerical approach with realistic oscillating propulsion forces

This study presents a novel forward dynamics model of racing kayak surge motion. The model, driven by adjustable oscillating propulsion forces, replicates true paddle stroke forces. It is based on Newton’s second law of motion, with the net force comprising of propulsion force, skin friction drag, wave-making drag, form drag, and air drag. The total mass includes the kayak, paddler, and added mass. The fourth-order Runge–Kutta method is used to solve for speed and distance. The model incorporates a unique hull formulation for wetted surface area estimation, Michell’s integral for wave-making drag, and a log wind profile with allometric scaling for air drag. It accounts for varying stature height, body mass, kayak dimensions, wind speed, and stroke propulsion profiles. The model is a significant advancement in its domain, with broad applicability for the future. It aligns with existing data and analyses, but validation data is limited.

Stability and Control of Car Dynamics with a Quarter Model via a Novel Simple Harmonic Hump under External Force

Effects of the road, such as speed bumps, can significantly affect a car’s stability. This study focuses on how a quarter-car model is affected by a basic harmonic speed hump and how Cubic Negative Velocity Control (CNVC) is used to control the amplitude of disturbances. This study differs from earlier research in considering various control and force kinds that impact the system. The external forces in this context are a component of a non-linear dynamic system. Two-degree-of-freedom (2DOF) differential coupled equations describe the system’s equation. Numerous numerical experiments have been conducted, including proportional derivative (PD), negative derivative feedback (NDF), positive position feedback (PPF), linear negative velocity control (LNVC), and CNVC; the results show that when the hump is represented as a simple harmonic hump, CNVC has the best effect and can regulate vibrations more precisely than the other approaches on this system. Subsequently, the vibration value of the system was numerically analyzed both before and after the control was implemented. Using the frequency response equation and phase plane approaches in conjunction with the Runge–Kutta fourth order method (RK-4) in the context of resonance situation analysis, the stability of the numerical solution has been evaluated.

Mpsqd: A matrix product state based Python package to simulate closed and open system quantum dynamics.

We introduce a Python package based on matrix product states (MPS) to simulate both the time-dependent Schrödinger equation (TDSE) and the hierarchical equations of motion (HEOM). The wave function in the TDSE or the reduced density operator/auxiliary density operators in the HEOM are represented using MPS. A matrix product operator (MPO) is then constructed to represent the Hamiltonian in the TDSE or the generalized Liouvillian in the HEOM. The fourth-order Runge-Kutta method and the time-dependent variational principle are used to propagate the MPS. Several examples, including the nonadiabatic interconversion dynamics of the pyrazine molecule, excitation energy transfer dynamics in molecular aggregates and photosynthetic light-harvesting complexes, the spin-boson model, a laser driven two-state model, the Holstein model, and charge transport in the Anderson impurity model, are presented to demonstrate the capability of the package.

Stability analysis of electrorheological (ER) lubricant operated multilobe hydrodynamic journal bearing

Purpose An electrorheological (ER) fluid consists of dielectric particles blended in a nonconducting oil. ER lubricants are often considered smart lubricants. This paper aims to examine the steady state and dynamic response of multilobe journal bearings using an ER lubricant. Design/methodology/approach Reynold’s equation has been used to describe the lubricant flow in the journal-bearing clearance space. The Bingham model is used to characterize the nonlinear behavior of the lubricant. The solution of the Reynolds equation is obtained using the Newton–Raphson method, with gaseous cavitation in the fluid film numerically addressed by applying a mass-conserving algorithm. The effects of lobe geometry and the applied electric field are investigated on film pressure profile, fluid film thickness, direct stiffness and damping parameters. The equation of motion for journal center coordinates is solved using the fourth-order Runge–Kutta method, to predict journal center motion trajectories. Findings Using ER lubricant combined with two-lobe journal bearing significantly improved the minimum film thickness by 49.75%, the direct stiffness parameter by 132.18% and the damping parameter by 206.3%. However, the multilobe configuration was found to negatively impact the frictional powerloss of the bearing system. In the case of multilobe configurations of journal bearings using ER lubricant, linear motion journal trajectories are observed to be reduced and exhibit increased stability. Originality/value This study presents the effect of an ER lubricant and multilobe configuration on the rotor-dynamic performance and stability analysis of hydrodynamic journal bearings. Peer review The peer review history for this article is available at: https://publons.com/publon/10.1108/ILT-06-2024-0201/

Characteristics of discharge of skew side sluice gate

The present study is aimed to assess discharge characteristics of skew side sluice gate. It is determined to develop equations for elementary discharge coefficient, Ce when a side sluice gate is placed at an angle with the main channel. Also, the present study is undertaken to develop generalized equations for elementary discharge coefficient of skew side sluice gate both for free and submerged flow conditions. Solving governing flow equations and further numerical integration by using fourth order Runge–Kutta method are used to find computed discharge. Error between observed and computed discharge is found and it is minimized to obtain optimum set of constants to develop Ce. Equations for Ce when the side sluice gate is placed at various angles are developed both for free and submerged flow conditions. Also, generalized equations for elementary discharge coefficient are developed. Further, Kling-Gupta Efficiency, KGE and validation of generalized equations for elementary discharge coefficient both for free and submerged flow conditions have indicated that there is an agreement between observed and computed discharges and thus shown accuracy. The findings of the present study are useful to study further on flow characteristics of skew side sluice gate which has vital practical significance.

Studies on drug delivery from dissolving microneedle and its uptake in tissue

Abstract In this study, a mathematical model for transdermal drug administration using a dissolving conical microneedle (MN) is developed. The drug is absorbed in the blood compartment after passing through the skin's viable epidermis. Reversible reaction kinetics then allow the drug to enter the tissue compartment. An unsteady reaction equation is used to predict the drug's distribution into the skin following MN's dissolution. An unsteady reaction mechanism is used to determine the concentrations in the blood and tissue compartments. Using the fourth-order Runge-Kutta method, the governing equations with their initial conditions are solved numerically. The MN is expected to dissolve completely in 108.1 seconds, according to the predicted results, while the concentration in the skin peaks at 94.4 seconds. The concentrations in the tissue and blood compartments, however, reach their respective maximal amounts later on. In this investigation, the impacts of the drug's mass fraction, volume fraction, and penetration rate cannot be completely ruled out. A thorough sensitivity analysis has been carried out for some of the parameters involved. Our findings closely align with the findings reported in the literature.

Seismic response prediction for buildings with sliding live loads using neural networks

The seismic response of primary structures (PS) can be significantly influenced by live loads, particularly when these loads consist of stacked bodies that are capable of sliding during seismic events. Conventional design methods often fail to account for the energy dissipation resulting from such sliding, leading to overly conservative structural estimates. This study examines the effects of sliding live loads on the seismic response of a PS, where two rigid bodies, referred to as secondary bodies (SBs), are stacked as live loads on a PS. The interaction between the lower SB and the PS, as well as between the SBs, is modelled using Coulomb's friction model. The governing equations are solved using the fourth-order Runge-Kutta method. Seismic Zones III and V from IS 1893:2016 are considered as hazard levels. A parametric investigation explores the impact of varying dynamic parameters of both the PS and SBs on the seismic response. The results demonstrate significant energy dissipation within the stack due to sliding, which, if not considered, results in conservative displacement estimates. The study also evaluates how friction coefficients, mass ratios, and excitation levels affect the stack's energy dissipation capacity. A novel method to compute the modified primary structural period (Tnew) for design purposes is proposed, and an artificial neural network (ANN) model is developed, achieving a high prediction accuracy (R2 = 99 %). Sensitivity analysis is performed to assess the influence of input parameters on the output. This research highlights the need to include sliding loads in seismic design.

Analysis of Brownian motion and thermophoresis effects with chemical reaction on Williamson nanofluid flow over permeable stretching sheet

This study warrants a broad analysis on the simultaneous effects of Brownian and thermophoresis on the chemically reacting Williamson nanofluid flow via a permeable expanding sheet. The analysis includes the properties of slip velocity and thermal radiation, providing a more representative picture of the physical phenomena. The differential equations governed by demonstrating the fluid flow phenomena are renewed to a set of nonlinear differential equations utilizing similarity rules. These transformed equations are subsequently handled numerically adopting the fourth-order Runge-Kutta method. The results reveal the significant control of Brownian motion together with thermophoresis and additionally, the inclusion of velocity slip and thermal radiation remarkably affect the velocity, temperature, and concentration distributions. Parametric studies show the validation of the present system to variations in the Williamson fluid parameter, slip parameter, radiative heat parameter, Brownian motion parameter, and thermophoresis parameter.

A fourth order Runge-Kutta type of exponential time differencing and triangular spectral element method for two dimensional nonlinear Maxwell's equations

In this paper, we study a numerical scheme to solve the nonlinear Maxwell's equations. The discrete scheme is based on the triangular spectral element method (TSEM) in space and the exponential time differencing fourth-order Runge-Kutta (ETDRK4) method in time. TSEM has the advantages of spectral accuracy and geometric flexibility. The ETD method involves exact integration of the linear part of the governing equation followed by an approximation of an integral involving the nonlinear terms. The RK4 scheme is introduced for the time integration of the nonlinear terms. The stability region of the ETDRK4 method is depicted. Moreover, the contour integral in the complex plan is utilized and improved to compute the matrix function required by the implementation of ETDRK4. The numerical results demonstrate that our proposed method is of exponential convergence with the order of basis function in space and fourth order accuracy in time.

Vibrational and stability analysis of planar double pendulum dynamics near resonance

AbstractThe focus of this paper is to examine the motion of a novel double pendulum (DP) system with two degrees of freedom (DOF). This system operates under specific constraints to follow a Lissajous curve, with its pivot point moving along this path in a plane. The nonlinear differential equations governing this system are derived using Lagrange's equations. Their analytical solutions (AS) are subsequently calculated using the multiple-scales method (MSM), which provides higher-order approximations. These solutions are considered new, as the traditional MSM has been applied to this novel system for the first time. Additionally, the accuracy of these solutions is validated through numerical results obtained using the fourth-order Runge–Kutta method. The solvability conditions and characteristic exponents are determined based on resonance cases. The Routh–Hurwitz criteria (RHC) are employed to assess the stability of the fixed points corresponding to the steady-state solutions. They are also used to demonstrate the frequency response curves. The nonlinear stability analysis is performed by examining the stability and instability ranges. Resonance curves and time history plots are presented to analyze the behavior of the system for specific parameter values. The investigation delves into a comprehensive analysis of bifurcation diagrams (BDs) and Lyapunov exponent spectra (LEs), aiming to uncover the various types of motion present within the system. Systematic examination of these charts reveals critical insights into transitions between stable, quasi-stable, and chaotic dynamical behaviors. This work has practical applications in various fields, such as robotics, pump compressors, rotor dynamics, and transportation devices. It can be used to study the vibrational motion of these systems.

Force Element Analysis in Vortex-Induced Vibrations of Side-by-Side Dual Cylinders: A Numerical Study

A numerical investigation was conducted in this study utilizing Force Element Analysis to explore the vortex-induced vibration (VIV) mechanism of side-by-side dual cylinders under the conditions of Reynolds number Re = 100, mass ratio m* = 10, and spacing ratios L/D ranging from 3 to 6. The hydrodynamic forces by force element formulas were incorporated into the vibration response calculations of elastically supported rigid cylinders using a User-Defined Function (UDF) and the fourth-order Runge–Kutta method. A comprehensive analysis was performed to elucidate the combined effects of the spacing ratio L/D and reduced velocity Ur on the vibration responses, quantifying the hydrodynamic forces involved in the mutual interaction during VIV for side-by-side dual cylinders. The influence mechanisms of inter-cylinder interaction and their effects on the resultant hydrodynamic phenomena were discussed. It was revealed that for side-by-side arranged dual cylinders outside the “lock-in region”, the lift and drag forces are predominantly supplied by the volume vorticity forces in conjunction with surface vortices (including frictional) forces. However, within the “lock-in region”, the surface acceleration lift forces provide greater force contributions, and the volume vorticity lift force contributes significantly to negative values. Notably, alterations to the spacing ratio do not change the proportion of force element components. The amplitudes of the cylinders’ mutual interaction forces are identical in magnitude but opposite in phase. Additionally, the “slapping” phenomenon near the “lock-in region” leads to “bounded” trajectories of cylinders.

The Impact of the Nonlinear Integral Positive Position Feedback (NIPPF) Controller on the Forced and Self-Excited Nonlinear Beam Flutter Phenomenon

This article presents a novel approach to impact regulation of nonlinear vibrational responses in a beam flutter system subjected to harmonic excitation. This study introduces the use of a Nonlinear Integral Positive Position Feedback (NIPPF) controller for this purpose. This technique models the system as a three-degree-of-freedom nonlinear system representing the beam flutter, coupled with a first-order and a second-order filter representing the NIPPF controller. By applying perturbation analysis to the linearized system model, the authors obtain analytical solutions for the autonomous system with the controller. This study aims to reduce vibration amplitudes in a nonlinear dynamic system, specifically when 1:1 internal resonance occurs. The Routh–Hurwitz criterion is utilized to evaluate the system’s stability. Furthermore, the frequency–response curves (FRCs) exhibit symmetry across a range of parameter values. The findings highlight that the effectiveness of vibration suppression is directly related to the product of the NIPPF control signal after comparing with different controllers. Numerical simulations, conducted using the fourth-order Runge–Kutta method, validate the analytical solutions and demonstrate the system’s amplitude response. The strong correlation between the analytical and numerical results highlights the accuracy and dependability of the proposed method.

Nonlinear effect on stable state and snap-through bistability of square composite laminate

Bistable structures with the elastic instability caused by buckling are confirmed to perform significantly in micro-electromechanical systems, metamaterials, energy harvester, vibration isolation and morphing structures. The target of this paper is to explore the dynamic responses of cross-ply bistable composite laminate, focusing on the nonlinear effect of the single- and double-well vibration. Both theoretical and finite element (FE) methods are employed to simulate the nonlinear vibration and dynamic snap-through of bistable composite laminate under the foundation excitation at the center. In the theoretical model, the governing equations are established via Lagrange's equation based on the first-order shear deformation theory, von Karman nonlinear strain-displacement relation and Rayleigh-Ritz method. The fourth-order Runge-Kutta method is adopted to solve the governing equations, and the numerical results are validated by FE model. Subsequently, the details of the dynamic responses are analyzed to identify the nonlinear effects in the form of bifurcation diagram, phase portrait, time history, Poincare maps and amplitude spectrum. The dynamic responses are examined for a series of excitation parameters in both time and frequency domain. Through fixed frequency and frequency sweep tests, the nonlinear phenomenon of the single- and double-well vibrations are analyzed including superharmonic resonance, stiffness softening, hysteresis phenomenon, various periodic and chaotic vibration. The diverse responses to external inputs contribute significantly to efficiently predicting mechanical behaviors in real-world conditions, thereby offering indispensable theoretical support for structural design applications.

Beyond conventional models: integer and fractional order analysis of nonlinear Michaelis-Menten kinetics in immobilised enzyme reactors

PurposeThis study explores the immobilisation of enzymes within porous catalysts of various geometries, including spheres, cylinders and flat pellets. The objective is to understand the irreversible Michaelis-Menten kinetic process within immobilised enzymes through advanced mathematical modelling.Design/methodology/approachMathematical models were developed based on reaction-diffusion equations incorporating nonlinear variables associated with Michaelis-Menten kinetics. This research introduces fractional derivatives to investigate enzyme reaction kinetics, addressing a significant gap in the existing literature. A novel approximation method, based on the independent polynomials of the complete bipartite graph, is employed to explore solutions for substrate concentration and effectiveness factor across a spectrum of parameter values. The analytical solutions generated through the bipartite polynomial approximation method (BPAM) are rigorously tested against established methods, including the Bernoulli wavelet method (BWM), Taylor series method (TSM), Adomian decomposition method (ADM) and fourth-order Runge-Kutta method (RKM).FindingsThe study identifies two main findings. Firstly, the behaviour of dimensionless substrate concentration with distance is analysed for planar, cylindrical and spherical catalysts using both integer and fractional order Michaelis-Menten modelling. Secondly, the research investigates the variability of the dimensionless effectiveness factor with the Thiele modulus.Research limitations/implicationsThe study primarily focuses on mathematical modelling and theoretical analysis, with limited experimental validation. Future research should involve more extensive experimental verification to corroborate the findings. Additionally, the study assumes ideal conditions and uniform catalyst properties, which may not fully reflect real-world complexities. Incorporating factors such as mass transfer limitations, non-uniform catalyst structures and enzyme deactivation kinetics could enhance the model’s accuracy and broaden its applicability. Furthermore, extending the analysis to include multi-enzyme systems and complex reaction networks would provide a more comprehensive understanding of biocatalytic processes.Practical implicationsThe validated bipartite polynomial approximation method presents a practical tool for optimizing enzyme reactor design and operation in industrial settings. By accurately predicting substrate concentration and effectiveness factor, this approach enables efficient utilization of immobilised enzymes within porous catalysts. Implementation of these findings can lead to enhanced process efficiency, reduced operating costs and improved product yields in various biocatalytic applications such as pharmaceuticals, food processing and biofuel production. Additionally, this research fosters innovation in enzyme immobilisation techniques, offering practical insights for engineers and researchers striving to develop sustainable and economically viable bioprocesses.Social implicationsThe advancement of enzyme immobilisation techniques holds promise for addressing societal challenges such as sustainable production, environmental protection and healthcare. By enabling more efficient biocatalytic processes, this research contributes to reducing industrial waste, minimizing energy consumption and enhancing access to pharmaceuticals and bio-based products. Moreover, the development of eco-friendly manufacturing practices through biocatalysis aligns with global efforts towards sustainability and mitigating climate change. The widespread adoption of these technologies can foster a more environmentally conscious society while stimulating economic growth and innovation in biotechnology and related industries.Originality/valueThis study offers a pioneering approximation method using the independent polynomials of the complete bipartite graph to investigate enzyme reaction kinetics. The comprehensive validation of this method through comparison with established solution techniques ensures its reliability and accuracy. The findings hold promise for advancing the field of biocatalysts and provide valuable insights for designing efficient enzyme reactors.

Entropy optimization on Casson nanofluid flow with radiation and Arrhenius activation energy over different geometries: A numerical and statistical approach

This study employs numerical and statistical approaches to investigate the entropy optimization of steady Casson nanofluid flow over three different geometries subject to boundary conditions induced by convective flow. Multiple linear regression is employed to statistically examine. The present model incorporates several novel elements, such as Arrhenius activation energy, Brownian motion, the Cattaneo-Christov dual flux, thermophoresis, thermal radiation, and so on. Moreover, a comparison is presented between Newtonian and non-Newtonian fluids. By applying the proper similarity transformations, ordinary differential equations (ODEs) are obtained by converting foundational partial differential equations (PDEs). The Runge-Kutta fourth-order method is utilised to solve the obtained ODEs along with the shooting technique. The outcomes are visually depicted via tables and graphs. The velocity drops with increasing Grashof number, and the magnetic field becomes progressively more forceful as the suction parameter increases. The temperature gets reduced with the increase of the suction parameter, solute Grashof number increases with the magnetic field, thermophoresis, and radiation parameters. The entropy is observed to rise with the increase of the effective parameters (magnetic field, Brinkmann number and radiation). The MAD (mean absolute deviation), MSE (mean squared error), and RMSE (root mean square error) values are approaching zero, indicating that the derived outcomes are highly accurate. A lower MAPE (mean absolute percentage error) suggests that the model has a higher level of precision. Therefore, the outcomes of the present model are more precise and reliable. This study has various potential applications such as power plant heat exchangers, material processing industries, and solar thermal energy systems.