Boundary Restrictions Research Articles

Exact quantum dynamics for two-level systems with time-dependent driving

Abstract It is well known that the time-dependent Schrrödinger equation can only be solved exactly in very rare cases, even for two-level quantum systems. Thus, finding the exact quantum dynamics under a time-dependent Hamiltonian is not only fundamentally important in quantum physics but also facilitates active quantum manipulations for quantum information processing. In this work, we present a method for generating nearly infinite analytically assisted solutions to the Schrrödinger equation for a qubit under time-dependent driving. These analytically assisted solutions feature free parameters with only boundary restrictions, making them applicable in a variety of precise quantum manipulations. Due to the general form of the time-dependent Hamiltonian in our approach, it can be readily implemented in various experimental setups involving qubits. Consequently, our scheme offers new solutions to the Schrrödinger equation, providing an alternative analytical framework for precise control over qubits.

UNICOMPARTMENTAL KNEE ARTHROPLASTY: WHAT IS THE OPTIMAL ALIGNMENT CORRECTION TO ACHIEVE SUCCESS? THE ROLE OF KINEMATIC ALIGNMENT. STATE OFF THE ART REVIEW

Unicompartmental knee arthroplasty (UKA) is in many ways the ultimate kinematic operation as the express aim is to resurface the diseased side of the joint and restore pre-arthritic alignment and balance while maintaining integrity of both cruciate ligaments. An increasing body of knowledge relates the outcomes of UKA to pre-arthritic anatomy rather than an arbitrarily defined neutral. The Coronal Plane Alignment of the Knee (CPAK) classification provides a validated technique for calculating pre-arthritic limb alignment (the Arithmetic Hip-Knee-Ankle Ankle (aHKA)) and Joint Line Obliquity (JLO) and will enable a greater understanding of the interactions between pre-arthritic anatomy, choice of prosthetic position and outcomes. When pre-arthritic alignment is not taken into consideration a post-operative limb alignment of mild to moderate varus for medial UKA and moderate valgus for lateral UKA appears produces the best outcomes. When pre-arthritic anatomy is taken into account superior results have been reported with restoration of pre-arthritic limb alignment and joint line obliquity. Restriction boundaries have yet to be clearly defined for tibial component coronal and Hip-Knee-Ankle (HKA) angles when applying this new paradigm, but existing evidence would suggest a 60 varus limit for the tibial coronal angle may be a reasonable starting point. Lateral UKA has inherent differences in terms of tibial component positioning and ligament balance targets. Mobile bearing UKA demands a three-dimensional understanding of the effect of implant position on bearing stability. Modification of technique is necessary to produce anatomic tibia component angles with equipment designed for mechanical alignment. Robotic technology allows accurate understanding of pre-arthritic anatomy, precise reproduction of patient specific virtual planning, equally precise manipulation of soft tissue balance and future research using these platforms likely to further clarify in terms of ideal patient specific component and limb alignment targets.

Optimized Backstepping-Based Containment Control for Multiagent Systems With Deferred Constraints Using a Universal Nonlinear Transformation.

This article investigates an optimized containment control problem for multiagent systems (MASs), where all followers are subject to deferred full-state constraints. A universal nonlinear transformation is proposed for simultaneously handling the cases with and without constraints. Particularly, for the constrained case, initial values of states are flexibly managed to the midpoint between upper and lower boundaries by utilizing a state-shifting function, thus eliminating the initial restriction conditions. By deferred constraints, the state is forced to fall back into the restrictive boundaries within a preassigned time. A neural network (NN)-based reinforcement learning (RL) algorithm is executed under the identifier-critic-actor architecture, where the Hamilton-Jacobi-Bellman (HJB) equation is built in every subsystem to optimize control performance. For actor and critic NNs, updating laws are simplified, since the gradient descent method is performed based on a simple positive function rather than square of Bellman residual error. In view of the Lyapunov stability theorem and graph theory, it is proved that all signals are bounded and the outputs of followers can eventually enter into the convex hull constituted by leaders. Finally, simulations confirm the validity of the proposed approach.

Municipal Politics and the PKK in the early 1970s: A citizenship perspective

This paper examines the Kurdistan Workers Party’s (PKK) municipal politics in the late 1970s through the lens of citizenship politics. The article introduces two concepts—activist citizenship and fugitive citizenship to analyse the PKK’s mobilisation in this period, before the 1980 military coup in Turkey. Activist citizenship challenges the restrictive boundaries of state-sanctioned citizenship, while fugitive citizenship creates alternative political spaces for marginalized groups. Both concepts highlight how individuals and groups, such as the PKK, can assert their political agency in contexts where they are denied formal citizenship. The research questions linear understandings of the PKK’s emergence as a political movement inevitably destined to become an insurgent movement.

Thermoelastic analysis of FG-CNTRC cylindrical shells with various boundary conditions and temperature-dependent characteristics using quasi-3D higher-order shear deformation theory

Abstract. This study focuses on performing static analysis of FG-CNTRC cylinder shells with various boundary restrictions, including thermomechanical responses. The governing equations are developed by taking into account the temperature-dependent material features, the quasi-3D high-order shear deformation hypothesis, and the normal transverse stress effect. The temperature gradient inside the thickness is expected to fluctuate, and the distribution pattern is derived by using the heat transfer equation and considering the temperature boundary limitations. A singular trigonometric series and the Laplace transform are used in an analytics solution to address basic equations. This study primarily examines the stress levels at the border region. The findings indicate that it is crucial to take into account the abrupt rise in stress at the boundary area, particularly when the shell’s relative length is small. The reciprocal impact of pressure and temperature load is also emphasized. Significant findings indicate that thermal load may either augment or diminish stress levels, contingent upon the orientation of the pressure and thermal load effect. The results of the study of this issue serve as the foundation for the calculation and design of relevant structures in practical applications. Furthermore, this serves as a foundation for the creation of more intricate issues in the forthcoming.

Study on the grain development and dislocation evolution from dynamic to post-dynamic stage in IN718Plus superalloy; the role of second-phase

The introduction of hexagonal η-Ni3(Al,Ti)0.5Nb0.5 phase can refine and homogenize the microstructure of IN718Plus superalloy during hot working, but produces more complicated recrystallization behavior associated with second-phase modified structural mechanisms. Derived from this perspective, the role of η phase on recrystallization mechanisms and grain development from dynamic deformation to post-dynamic dwell was systematically investigated. The results indicated that η phase delayed the throughout recrystallization procedure and grain development. During dynamic deformation, boundary η inhibited discontinuous dynamic recrystallization via preventing the bulging of original grain boundaries, while intragranular lamellar η promoted heterogeneous strain concentration, stimulated random dislocations for continuous dynamic recrystallization and dislocation walls for banded dislocation substructures, which limited recrystallization occurrence in dynamic stage. During post-dynamic dwell, boundary η dissolution increased the nucleation sites for discontinuous static recrystallization, and η phase restricted grain boundary migration to provide abundant nucleation sites for continuous static recrystallization (CSRX). The banded dislocation substructures slowly evolved into subgrains to further form banded CSRX grains, which reduced grain size during early post-dynamic stage. After fully recrystallization, the residual η protected the small grains and impeded grain growth, meanwhile controlled the grain distribution. As a result, η phase induced sluggish dislocation evolution and recrystallization nucleation, consequently suppressed grain development and obtained the more homogeneous and fine grain configuration.

Solvability of functional third-order problems of Ambrosetti–Prodi-type

This work presents an Ambrosetti–Prodi alternative for functional problems composed of a fully third-order differential equation with two types of functional boundary conditions. The discussion of existence and non-existence of solution is obtained in a more general case, and the multiplicity of solution is done with restrictive boundary conditions-The main arguments are based on the lower and upper solutions method, together with the Leray–Schauder topological degree theory. We stress that the multiplicity situation requires different speed growths on the variables.An example illustrates the results’ applicability and shows a technique to estimate the bifurcation values of the parameter.

Conspiracy Thinking About the 15-Minute City: Something from Nothing?

This paper interrogates the seemingly absurd conspiracies associated with the “15-minute City,” an idea taking hold of urban communities across the globe to bring more amenities, including parks, recreation facilities, and libraries, within a 15-minute walk of where people live. Introduced as a mundane planning initiative to improve livability, eliminate or shorten car trips, and improve health outcomes, the 15-minute City has encountered surprising, yet resolute attack by conspiracy theorists who view it as a concealed leftist tactic to imprison local inhabitants within restrictive neighbourhood boundaries. In exploring the origins of the 15-minute City idea and the emergence of conspiracy theories that surround it, this paper unpacks the complex interplay of social, political, and psychological factors that drive current conspiratorial thinking about ostensibly benign policies and practices. In so doing, it considers the responsibility of leisure scholars in an age of misinformation, alternative facts, and post truth.

Analysis of the Utility Tunnel Joint's Stress Characteristics Under Well Point Precipitation Conditions

The method by which groundwater influences subsurface buildings is relatively complex in the groundwater-rich regions of southern China. Notably, it substantially affects the pipe corridor junctions, which are crucial to impermeability. In order to analyze the forces on the utility tunnel joints during well-point precipitation, numerical modeling of the utility tunnel joints using the well-point precipitation method based on Finite element software was carried out, and a precipitation model tank was made to verify the model parameters and boundary restrictions. The results indicate that under well-point precipitation, the force variation of the bottom plate is more significant than that of the top plate at the same port and that in the joint section close to the precipitation point, the force variation of the bottom plate can reach 2-3 times that of the top plate. The spigot joint's bottom plate has a maximum tensile stress of 319.52 kPa, which raises the possibility of tensile damage. The well-point dewatering method has a higher likelihood of bottom plate cracks, which makes it a critical component to be watched during construction and operation.

An enhanced higher-order finite element formulation for wrinkling analysis of thick sandwich plates

Sandwich structures are susceptible to wrinkling when subject to in-plane compressive loads, which threatens structural safety. To accurately investigate the failure behavior, the following work is to be required. Firstly, the wrinkling behavior of sandwich plates is a typical three-dimensional (3D) issue. To consider a 3D effect, an enhanced higher-order finite element formulation including transverse normal strain has been proposed for the first time. Utilizing the proposed finite element formulation, a refined quadrilateral element model has been constructed. Secondly, the buckling and wrinkling behaviors of square sandwich plates have been investigated. The performance of the proposed model has been evaluated by comparing it with the quasi-3D solutions, the results obtained from the 3D finite element method (3D-FEM), and other models. The differences between the buckling and wrinkling failure behaviors have been carefully explained. Thirdly, the effects of boundary conditions on buckling and wrinkling deformation have been explored in detail. By utilizing the proposed model, the translation mechanism between the buckling and wrinkling deformations of sandwich plates under different boundary conditions has been revealed, which can help other investigators to well understand the buckling and wrinkling behaviors of sandwich plates. It can be shown that the wrinkling behaviors of thick sandwich plates occur earlier than the buckling behaviors when the thickness ratio of core to face panel is more than 35. Besides, it also can be shown that the buckling and wrinkling loads decrease gradually with the relaxation of the boundary restriction.

Stellar Occultations in the Era of Data Mining and Modern Regression Models: Using Gaussian Processes to Analyze Light Curves and Improve Predictions

Gaussian process (GP) regression is a nonparametric Bayesian approach that has been used successfully in various astronomical domains, especially in time-domain astronomy. The most common applications are the smoothing of data for interpolation and the detection of periodicities. The ability to create unbiased data-driven models without a predefined physical model can be a major advantage over conventional regression methods. Prior knowledge can be included by setting boundary conditions or constraining hyperparameter values, while unknown hyperparameters are optimized during the conditioning of the model. We have adapted and transformed previous approaches of GP regression and introduce three new applications for this regression method, especially in the context of stellar occultations: the modeling of occultation light curves, the correction of public JPL ephemerides of minor planets based on publicly available image data of the Zwicky Transient Facility, and the detection of natural satellites. We used data from observations of stellar occultations to validate the models and achieved promising results in all cases, and thus we confirmed the flexibility of GP regression models. Considering various existing use cases in addition to our novel applications, GP regression can be used to model diverse data sets addressing a wide range of problems. The accuracy of the model depends on the input data and on the set boundary conditions. Generally, high-quality data allow the usage of loose boundary conditions, while low-quality data require more restrictive boundary conditions to avoid overfitting.

Harmonic extension elements: Eigenproblems and error estimation

A non-intrusive extension to the standard p-version of the finite element method, so-called harmonic extension elements, is studied in the context of eigenproblems. The standard polynomial shape functions are replaced where appropriate with harmonic extensions of the boundary restrictions of the standard shape functions or solutions to a local Poisson problem. The reference elements are adapted to include extensions in order to ensure a conforming discretisation even if the meshes are not conforming. The hierarchic structure of the extension basis means that auxiliary space error estimators of the p-version of the finite element method are directly applicable. The additional computational workload in construction of the required extensions can be reduced using symmetries and multimesh techniques. The numerical experiments demonstrate the efficiency of the proposed extension resulting in exponential convergence in the quantities of interest if the mesh is properly graded.

Buckling variability analysis in damaged composite laminates subjected to thermally varying environment

The present study investigates the effect of internal defects on the composite laminated (CL) plates comprised of two distinct graphite-epoxy materials (AS4/3501-6 and T300/5208). The centrally damaged laminates stacked in two distinct lamination sequences are exposed in thermally varying environments. The CL plates are considered to experience damage in two different combinations of damage parameters. The improved first-order shear deformation theory (IFSDT) based finite element (FE) model is employed to estimate the thermal buckling of CL plates comprised of multiple fiber orientation angles and constrained to C-S-C-S and S-C-S-C boundary restrictions. The implementation of a Radial basis function network (RBFN) surrogate model has demonstrated its potential as a feasible substitute for the computationally demanding Monte-Carlo simulations (MCS) in the context of stochastic exploration. The present investigation scrutinizes the probabilistic properties of diverse materials and their associated damage characteristics. Subsequently, the RBFN-based surrogate model is employed to evaluate the likelihood of failure.

IoT-based livestock tracking: Addressing challenges in Somali livestock farming

Livestock plays a vital role in Somalia's economy, contributing more than 60% of the country's gross domestic product. However, livestock production in Somalia faces many challenges, including conflict, insecurity, climate change and environmental degradation. These challenges can lead to livestock losses, which can significantly affect the livelihoods of livestock owners. This paper proposes an Internet of Things (IoT)-based livestock tracking system to help farmers locate their lost livestock. The system uses GPS and GSM/GPRS technology to track the location of livestock in real-time. The system also includes a boundary restriction feature that can be used to ensure that livestock remains within a designated area. The IoT-based livestock tracking system has the potential to address a number of challenges facing livestock production in Somalia. The system can help reduce livestock losses, improve livestock management practices, and increase productivity. The system is currently being field-tested in Somalia. The system successfully detects livestock crossing the border and transmits the livestock's location in real-time. Field test results show successful real-time tracking of livestock. The test data will be used to improve the system and assess its effectiveness in helping farmers locate their lost livestock.

Melting and heat generating influences on radiative flow of two-phase magneto-Williamson nanofluid via stretchable surface with slippage velocity and activation energy

Melting heat and solutal transference in a magnetohydrodynamic flowing of Williamson nanofluid have been described, with the mathematical model guided by Arrhenius activation energy, chemically reactive species, and convective boundary restrictions. By implementing suitable similarity conversions, the regulating equations of partial differential equations (PDEs) (formed by continuity, impetus, energy, and concentricity components) are condensed to an arrangement of ordinary differential equations (ODEs). These commonalities are in nonlinear form, which includes the fluid’s velocity, heat, and concentration changes. Finally, the standard Keller box approach is used to solve this ODEs system computationally (KBM). Under the influence of regulating parameters, the computational results are tallied and displayed in suitable diagrams. The friction force factor, local Nusselt, and Sherwood values are tabulated. Furthermore, the velocity, energy, and concentration contours are plotted versus fluid thickness. The attributes of Williamson nanofluid flowing, melting heat transfer, and mass transference are debated in depth toward the end of this study. Among the most important outcomes that have been reached is that the rate of heat and solutal transport heightened between 52.5 and 55.2% by detraction of the magnetic field, Weissenberg number, and Brownian motion. We also found that there is an inverse relationship between the mass transmission and heat generating factor.

A Restricted Functional Balancing Technique for Total Knee Arthroplasty With a Varus Deformity: Does a Medial Soft-Tissue Release Result in a Worse Outcome?

BackgroundA functional alignment technique for total knee arthroplasty (TKA) utilizes implant position modifications to balance the soft tissues. There is concern that, in some cases, extreme coronal and tibial component alignment could facilitate early implant failure. To be cautious, a restricted functional alignment may be used. The purpose of our study was to evaluate the results of TKA in patients who have varus deformities using a restricted functional alignment technique. We hypothesized that adding a medial soft-tissue release within restricted boundaries would not result in inferior outcomes. MethodsA retrospective review was performed on robotic arm-assisted TKA patients with varus deformities utilizing a functional balancing strategy with a three-degree varus coronal limb and tibial component alignment restriction. Outcome scores of those patients still requiring a medial-soft tissue release were compared to those without for inferior outcomes. ResultsA total of 202 of 259 (78.0%) knees were able to be balanced without any medial soft-tissue release with an average final hip-knee-ankle alignment of 1.9° varus. The remaining 57 knees required a medial soft-tissue release. They had an average final hip-knee-ankle of 2.8° varus and an average medial proximal tibial angle of 2.5° varus. Comparing the cohorts without and with a release, at final follow-up averaging two years, there was not a statistically significant difference in Knee Society-Knee Score (97.7 and 98.4, P = .525), Functional Score (86.7 and 88.7, P = .514), Forgotten Joint Score (59.8 and 66.6, P = .136), and Knee Injury Osteoarthritis Outcome Survey for Joint Replacement Junior Score (79.5 and 84.8, P = .066). ConclusionsUtilizing a restrictive functional balancing strategy for TKA minimizes the need for soft-tissue releases and provides for excellent overall outcomes. An additional medial soft-tissue release can still be utilized without an inferior average two-year outcome.

Microstructure and compressive deformation behavior of W-Ni3Al-Co model alloys by two-step sintering

The regulation of microstructure can improve the mechanical properties of tungsten alloys. To regulate the microstructure, the W-Ni3Al-Co alloys with different Ni3Al/Co ratios were prepared using a two-step sintering method, and the microstructure and compressive deformation behavior were investigated. The results showed that the particle sizes of the W-rich phase in the network structure were refined with the increase of the Ni3Al/Co ratio, and a large fraction of twin boundaries were detected in the adhesive phase. The compressive deformation behavior of a W-7Ni3Al-3Co alloy with excellent compressive properties was investigated by the EBSD technique. The results demonstrated that twins in the FCC binder phase hindered the stress concentration in the binder phase and at the interface of the W/binder phases through twin-dislocation interactions. The W network structure underwent the uniform global deformation that restricted grain boundary sliding during deformation and prevented crack extension and consolidation. Twins in the binder phase and the W network structure were both important factors in improving the compressive properties of W-Ni3Al-Co alloys.

Editorial Letter

As the problems facing modern societies become increasingly complex, interdisciplinary research has emerged as a critical approach for developing comprehensive solutions. Issues such as climate change, infectious diseases, environmental degradation, and bioethics defy traditional disciplinary boundaries and require integrating insights from fields including surgery, biology, physics, chemistry, social sciences and more. At the same time, new technologies like artificial intelligence (AI) and biotechnology have applications across multiple domains of science and depend on cross-cutting perspectives from different areas of expertise. However, conducting interdisciplinary research poses significant challenges within the current structures of higher education and research centers. Disciplinary silos remain entrenched and cultural norms continue to overly value specialization. Funding interdisciplinary teams that span departmental divisions is also difficult in terms of coordinating budgets and timelines. Machine learning (ML) is a transformative technology that bridges disciplines and enables interdisciplinary collaboration. ML processes data, recognizes patterns, and makes predictions across various fields. By integrating insights from diverse disciplines, such as biology and social sciences, ML enhances decision-making. Collaboration among experts from different fields fuels innovation and uncovers hidden relationships within complex systems. Embracing interdisciplinary collaboration and leveraging the power of ML unlocks new frontiers of knowledge, drives scientific progress, and addresses complex challenges. Despite these obstacles, there are promising signs that more support is growing for interdisciplinary collaboration. Universities are taking steps to break down structural and cultural barriers, and funders are steering more grants towards projects integrating diverse fields. When done effectively, interdisciplinary research has yielded important advances such as computational neuroscience, biochemistry, neuropsychology and bioinformatics - improving our understanding of brain functioning, cellular mechanisms, psychological disorders and disease treatments. As the societal problems become more complex, an ability to bridge unique disciplines will be increasingly vital. Universities have a pivotal role to play in facilitating interdisciplinary work. By establishing interdisciplinary programs and labs, offering joint workshops and training, enhancing cross-faculty collaboration and hiring researchers with diverse perspectives, universities can help take knowledge out of narrow silos and promote cooperation across differing areas of expertise. This will allow us to gain novel insights and develop more comprehensive solutions to life's intricate challenges. With continued support, interdisciplinary research has enormous potential to advance science and better address the problems of today and tomorrow. By embracing interdisciplinary collaborations, researchers are able to tackle complex problems that cannot be addressed by a single discipline alone. This approach allows for the examination of issues from multiple view points, leading to a more comprehensive analysis. Moreover, interdisciplinary research has the potential to open up new areas of inquiry and foster the discovery of new and improved solutions. By integrating insights from different fields, researchers can combine diverse expertise, which in turn sparks creative ideas and promotes innovation. Adopting a multidimensional approach is essential for gaining a comprehensive understanding of intricate systems and interconnected issues that encompass various domains such as social, economic, environmental, biological, and technological aspects. Interdisciplinary research plays a pivotal role in addressing complex societal challenges that require a multidimensional perspective. Issues like climate change, pandemics, sustainability, and the impact of AI cannot be effectively tackled through narrow, discipline-specific thinking. Instead, researchers need to integrate knowledge from diverse fields to develop comprehensive and holistic solutions. Furthermore, interdisciplinary research encourages researchers to critically examine their own assumptions and overcome the limitations imposed by restricted disciplinary boundaries. By embracing insights from other domains, researchers expand their perspectives, leading to innovative breakthroughs and advancements. Beyond advancing knowledge, interdisciplinary research also has practical benefits. It fosters the development of new interdisciplinary fields that defy traditional academic categorizations, expanding the frontiers of knowledge. Furthermore, it cultivates valuable collaborative and communication skills among researchers, as they learn to bridge different languages, tools, and perspectives from diverse fields. Final Remarks Importantly, interdisciplinary research facilitates the application of knowledge across domains, translating research insights into practical solutions that can benefit multiple sectors. This translational aspect enhances the societal impact of research, making it more relevant and applicable to real-world problems. Lastly, interdisciplinary research often increases the competitiveness of research projects for funding. By demonstrating broader impacts and alignment with real-world problems, interdisciplinary research projects showcase their potential to address pressing issues and attract funding from various sources. Interdisciplinary research offers many advantages, including the ability to tackle complex problems, discover new solutions, enhance comprehensive understanding, address social challenges, challenge assumptions, develop new fields, and foster collaborative skills thereby facilitating the application of knowledge, and increasing competition for funding. Embracing interdisciplinary approaches is crucial for advancing scientific knowledge and addressing the multifaceted challenges of our time. In light of this, a group of researchers decided to establish the Scientific Hypotheses (SCIHYP) in 2023 as a means to tackle such problems. Financial support and sponsorship None. Conflicts of interest There are no conflicts of interest.

Nuclear induction line shape: Non-Markovian diffusion with boundaries.

The dynamics of viscoelastic fluids are governed by a memory function, essential yet challenging to compute, especially when diffusion faces boundary restrictions. We propose a computational method that captures memory effects by analyzing the time-correlation function of the pressure tensor, a viscosity indicator, through the Stokes-Einstein equation's analytic continuation into the Laplace domain. We integrate this equation with molecular dynamics simulations to derive necessary parameters. Our approach computes nuclear magnetic resonance (NMR) line shapes using a generalized diffusion coefficient, accounting for temperature and confinement geometry. This method directly links the memory function with thermal transport parameters, facilitating accurate NMR signal computation for non-Markovian fluids in confined geometries.

Investigation of Magnetized Casson Nanofluid Flow along Wedge: Gaussian Process Regression

An unsteady two-dimensional magnetized Casson nanofluid flow model is constructed over a wedge under the effect of thermal radiation and chemical reaction. The multiple slip effects are also assumed near the surface of the wedge along with the convective boundary restrictions. This study investigates the application of soft computing techniques to address the challenges posed by the complexity of problem modeling and numerical methods. Traditional approaches incorporating various model factors may struggle to provide accurate solutions. To resolve this issue, Gaussian process regression (GPR) is employed to predict the solution of the proposed flow model. With the help of the numerical shooting method together with Runge–Kutta–Fehlberg fourth-fifth-order (RKF-45) reference data, the GPR model is trained. The numerical simulation illustrated that the Casson fluid parameter β and the unsteadiness parameter S strengthen the friction factor, and the heat transfer rate is enhanced as the radiation parameter Rd becomes larger. In addition, the Biot numbers Bi1 & Bi2 lead to strengthen nanoparticle temperature; an opposite behavior is noticed with the skin friction coefficient S˜fxRex0.5, heat transfer rate H˜tx Rex0.5, and nanoparticle transfer rate C˜txRex0.5. The GPR model with the exponential Kernel function provided better performance than other functions on both training and checking datasets to predict S˜fxRex0.5,H˜tx Rex0.5, and C˜txRex0.5. Statistical metrics including RMSE, MAE, MAPE, MSE, R2, and R are employed to check the accuracy and convergences of the predicted and numerical solutions obtained through GPR and RKF-45. It is observed that all three GPR models had an R2 value of higher than 0.9. The proposed study demonstrates the advantages of employing soft computing methods (GPR) to effectively analyse the behavior of complex flow models.