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ANN-based analysis of thin film Maxwell fluid dynamics with electro-osmotic and nonlinear thermal effects

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Alexandria Engineering Journal 2025年 127卷 392-410页

作者： Din, Irfan Saif Ud Siddique, Imran Zahid, Zohaib Nadeem, Muhammad Islam, S. Department of Mathematics University of Management and Technology Lahore54770 Pakistan Department of Mathematics University of Sargodha Sargodha40100 Pakistan Mathematics in Applied Sciences and Engineering Research Group Scientific Research Center Al-Ayen University Nasiriyah64001 Iraq Federal University of Technology Paran UTFPR Mechanical Engineering Department DAMEC Postgraduate Program in Mechanical and Materials Engineering PPGEM Research Center for Rheology and Non-Newtonian Fluids CERNN R. Deputado Heitor Alencar Furtado 5000 - Bloco N - Ecoville PR Curitiba81280-340 Brazil Department of Mechanical Engineering Prince Mohammad Bin Fahd University P.O Box 1664 Al Khobar31952 Saudi Arabia

An intelligent Levenberg-Marquardt Technique (LMT) with artificial neural network (ANN) backpropagation (BP) has been used to analyze the thermal heat and mass transfer of unsteady magnetohydrodynamics (MHD) thin film Maxwell fluid flow in a porous inclined sheet with an emphasis on the influence of electro-osmosis. The activation energy, chemical reaction, mixed convection, melting heat, joule heating, nonlinear thermal radiation, variable thermal conductivity and thermal source/sink effect are taken into account for transport expressions. Appropriate similarity transformations were used to translate partial differential equations (PDEs) into ordinary differential equations (ODEs). After that, the built-in MATLAB BVP4C method was used for a data set assessed using the LMT-ANN strategy to solve these ODEs. The physical significance of the designed parameters is thoroughly discussed in both tabular and graphical form. The observed R-squared value is 1, and the mean square error up to 10−15 demonstrates the LMT-ANN's precise and accurate computing capability. The model's validity is also confirmed by the strong agreement between the obtained predicted findings and numerical results, which shows a high degree of accuracy within the range of 10−8 to 10−11. It was revealed that radiative heat considerably increases surface heat energy through accumulation, improving heat transfer qualities, whereas fluid temperature is raised by Joule dissipation, variable thermal conductivity, and heat source. Electro-osmosis and magnetic fields reduce fluid velocity by generating opposing forces that resist the flow. This problem works best in microscale fluid transport systems and drilling operations, where magnetic and electro-osmotic control are crucial. These systems include micro-electromechanical systems, lab-on-a-chip devices, porous geological formations, and thin film coating technologies. © 2025 The Authors

关键词： Activation energy

Cosserat elasticity as the weak-field limit of Einstein-Cartan relativity

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Physical Review D 2024年第10期109卷 104052-104052页

作者： Matthew Maitra Jeroen Tromp Institut für Geophysik ETH Zürich Sonneggstrasse 5 Zürich 8092 Switzerland Department of Geosciences Program in Applied and Computational Mathematics Princeton University Princeton 08540 NJ United States

The weak-field limit of Einstein-Cartan (EC) relativity is studied. The equations of EC theory are rewritten such that they formally resemble those of Einstein general relativity (EGR); this allows ideas from post-Newtonian theory to be imported without essential change. The equations of motion are then written both at first post-Newtonian (1PN) order and at 1.5PN order. EC theory’s 1PN equations of motion are found to be those of a micropolar/Cosserat elastic medium, along with a decoupled evolution equation for nonclassical, spin-related fields. It seems that a necessary condition for these results to hold is that one chooses the nonclassical fields to scale with the speed of light in a certain empirically reasonable way. Finally, the 1.5PN equations give greater insight into the coupling between energy-momentum and spin within slowly moving, weakly gravitating matter. Specifically, the weakly relativistic modifications to Cosserat theory involve a gravitational torque and an augmentation of the gravitational force due to a dynamic mass moment density with an accompanying dynamic mass moment density flux, and new forms of linear momentum density captured by a dynamic mass density flux and a dynamic momentum density.

关键词： Alternative gravity theories Solar system & its planets

A Method for Computing Inverse Parametric PDE Problems with Random-Weight Neural Networks

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arXiv 2022年

作者： Dong, Suchuan Wang, Yiran Center for Computational and Applied Mathematics Department of Mathematics Purdue University United States

We present a method for computing the inverse parameters and the solution field to inverse parametric partial differential equations (PDE) based on randomized neural networks. This extends the local extreme learning machine technique originally developed for forward PDEs to inverse problems. We develop three algorithms for training the neural network to solve the inverse PDE problem. The first algorithm (termed NLLSQ) determines the inverse parameters and the trainable network parameters all together by the nonlinear least squares method with perturbations (NLLSQ-perturb). The second algorithm (termed VarPro-F1) eliminates the inverse parameters from the overall problem by variable projection to attain a reduced problem about the trainable network parameters only. It solves the reduced problem first by the NLLSQ-perturb algorithm for the trainable network parameters, and then computes the inverse parameters by the linear least squares method. The third algorithm (termed VarPro-F2) eliminates the trainable network parameters from the overall problem by variable projection to attain a reduced problem about the inverse parameters only. It solves the reduced problem for the inverse parameters first, and then computes the trainable network parameters afterwards. VarPro-F1 and VarPro-F2 are reciprocal to each other in some sense. The presented method produces accurate results for inverse PDE problems, as shown by the numerical examples herein. For noise-free data, the errors of the inverse parameters and the solution field decrease exponentially as the number of collocation points or the number of trainable network parameters increases, and can reach a level close to the machine accuracy. For noisy data, the accuracy degrades compared with the case of noise-free data, but the method remains quite accurate. The presented method has been compared with the physics-informed neural network method. Copyright © 2022, The Authors. All rights reserved.

关键词： Inverse problems

An Efficient Three-Factor Authenticated Key Agreement Technique Using FCM Under HC-IoT Architectures

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Computers, Materials & Continua 2022年第7期72卷 1373-1389页

作者： Chandrashekhar Meshram Agbotiname Lucky Imoize Sajjad Shaukat Jamal Parkash Tambare Adel R.Alharbi Iqtadar Hussain Department of Post Graduate Studies and Research in Mathematics Jayawanti Haksar Government Post-Graduation CollegeCollege of Chhindwara UniversityBetul460001M.P.India Department of Electrical and Electronics Engineering Faculty of EngineeringUniversity of LagosAkokaLagos100213Nigeria Department of Electrical Engineering and Information Technology Institute of Digital CommunicationRuhr University44801BochumGermany Department of Mathematics College of ScienceKing Khalid UniversityAbhaSaudi Arabia Water Resources&Applied Mathematics Research Lab Nagpur440027India College of Computing and Information Technology University of TabukTabuk71491Saudi Arabia Mathematics Program Department of MathematicsStatistics and PhysicsCollege of Arts and SciencesQatar University2713DohaQatar

The Human-Centered Internet of Things(HC-IoT)is fast becoming a hotbed of security and privacy *** users can establish a common session key through a trusted server over an open communication channel using a three-party authenticated key *** of the early authenticated key agreement systems relied on pairing,hashing,or modular exponentiation processes that are computationally intensive and *** order to address this problem,this paper offers a new three-party authenticated key agreement technique based on fractional chaotic *** new scheme uses fractional chaotic maps and supports the dynamic sensing of HC-IoT devices in the network architecture without a password *** projected security scheme utilized a hash function,which works well for the resource-limited HC-IoT *** results show that our new technique is resistant to password guessing attacks since it does not use a ***,our approach provides users with comprehensive privacy protection,ensuring that a user forgery attack causes no ***,our new technique offers better security features than the techniques currently available in the literature.

关键词： Three-party authenticated key agreement anonymity fractional chaotic maps Chebyshev polynomial password table human-centered internet of things(HC-IoT)

Numerical Approximation of Partial Differential Equations by a Variable Projection Method with Artificial Neural Networks

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arXiv 2022年

作者： Dong, Suchuan Yang, Jielin Center for Computational and Applied Mathematics Department of Mathematics Purdue University United States

We present a method for solving linear and nonlinear partial differential equations (PDE) based on the variable projection framework and artificial neural networks. For linear PDEs, enforcing the boundary/initial value problem on the collocation points gives rise to a separable nonlinear least squares problem about the network coefficients. We reformulate this problem by the variable projection approach to eliminate the linear output-layer coefficients, leading to a reduced problem about the hidden-layer coefficients only. The reduced problem is solved first by the nonlinear least squares method to determine the hidden-layer coefficients, and then the output-layer coefficients are computed by the linear least squares method. For nonlinear PDEs, enforcing the boundary/initial value problem on the collocation points gives rise to a nonlinear least squares problem that is not separable, which precludes the variable projection strategy for such problems. To enable the variable projection approach for nonlinear PDEs, we first linearize the problem with a Newton iteration, using a particular linearization formulated in terms of the updated approximation field. The linearized system is solved by the variable projection framework together with artificial neural networks. Upon convergence of the Newton iteration, the neural-network coefficients provide the representation of the solution field to the original nonlinear problem. We present ample numerical examples with linear and nonlinear PDEs to demonstrate the performance of the method developed herein. For smooth field solutions, the errors of the current method decrease exponentially as the number of collocation points or the number of output-layer coefficients increases. We compare extensively the current method with the extreme learning machine (ELM) method from a previous work. Under identical conditions and network configurations, the current method exhibits an accuracy significantly superior to the ELM method. Copyri

关键词： Linearization

A Method for Computing Inverse Parametric Pde Problems with Random-Weight Neural Networks

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SSRN

SSRN 2022年

作者： Dong, Suchuan Steven Wang, Yiran Center for Computational and Applied Mathematics Department of Mathematics Purdue University United States

关键词： Inverse problems

A class of Discontinuous Galerkin methods for nonlinear variational problems

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arXiv 2023年

作者： Grekas, Georgios Koumatos, Konstantinos Makridakis, Charalambos Vikelis, Andreas Institute of Applied & Computational Mathematics Foundation for Research & Technology-Hellas Greece Aerospace Engineering and Mechanics University of Minnesota Minneapolis United States Department of Mathematics University of Sussex United Kingdom Department of Mathematics and Applied Mathematics University of Crete Greece Faculty of Mathematics University of Vienna Austria

In the context of Discontinuous Galerkin methods, we study approximations of nonlinear variational problems. We propose elementwise nonconforming finite element methods to discretize the continuous minimisation problem. Using Γ-convergence arguments we show that for convex energies the discrete minimisers converge to a minimiser of the continuous problem as the mesh parameter tends to zero, under the additional contribution of appropriately defined penalty terms at the level of the discrete energies. In addition, we provide error analysis in the case where the solution of the continuous minimization problem is smooth enough. Under appropriate assumptions we show local existence, uniqueness and corresponding optimal order error estimates for the discrete Euler-Lagrange equations of our scheme. We finally substantiate the feasibility of our methods by numerical examples. Copyright © 2023, The Authors. All rights reserved.

关键词： Finite element method

Cheaper and more noise-resilient quantum state preparation using eigenvector continuation

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Physical Review A 2025年第3期111卷 032607-032607页

作者： Anjali A. Agrawal João C. Getelina Akhil Francis A. F. Kemper Department of Physics North Carolina State University Raleigh North Carolina 27695 USA Applied Mathematics and Computational Research Division Lawrence Berkeley National Laboratory Berkeley California 94720 USA

Subspace methods are powerful, noise-resilient methods that can effectively prepare ground states on quantum computers. The challenge is to get a subspace with a small condition number that spans the states of interest using minimal quantum resources. In this work, we will use eigenvector continuation to build a subspace from the low-lying states of a set of Hamiltonians. The basis vectors are prepared using truncated versions of standard state preparation methods such as imaginary-time evolution (ITE), adiabatic state preparation (ASP), and variational quantum eigensolver. By using these truncated methods combined with eigenvector continuation, we can directly improve upon them, obtaining more accurate ground-state energies at a reduced cost. We use several spin systems to demonstrate convergence even when methods like ITE and ASP fail, such as ASP in the presence of level crossings and ITE with vanishing energy gaps. We also showcase the noise resilience of this approach beyond the gains already made by having shallower quantum circuits. Our findings suggest that eigenvector continuation can be used to improve existing state preparation methods in the near term.

关键词： Quantum computers

Numerical Computation of Partial Differential Equations by Hidden-Layer Concatenated Extreme Learning Machine

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arXiv 2022年

作者： Ni, Naxian Dong, Suchuan Center for Computational and Applied Mathematics Department of Mathematics Purdue University United States

The extreme learning machine (ELM) method can yield highly accurate solutions to linear/nonlinear partial differential equations (PDEs), but requires the last hidden layer of the neural network to be wide to achieve a high accuracy. If the last hidden layer is narrow, the accuracy of the existing ELM method will be poor, irrespective of the rest of the network configuration. In this paper we present a modified ELM method, termed HLConcELM (hidden-layer concatenated ELM), to overcome the above drawback of the conventional ELM method. The HLConcELM method can produce highly accurate solutions to linear/nonlinear PDEs when the last hidden layer of the network is narrow and when it is wide. The new method is based on a type of modified feedforward neural networks (FNN), termed HLConcFNN (hidden-layer concatenated FNN), which incorporates a logical concatenation of the hidden layers in the network and exposes all the hidden nodes to the output-layer nodes. HLConcFNNs have the interesting property that, given a network architecture, when additional hidden layers are appended to the network or when extra nodes are added to the existing hidden layers the representation capacity of the HLConcFNN associated with the new architecture is guaranteed to be not smaller than that of the original network architecture. Here representation capacity refers to the set of all functions that can be exactly represented by the neural network of a given architecture. We present ample benchmark tests with linear/nonlinear PDEs to demonstrate the computational accuracy and performance of the HLConcELM method and the superiority of this method to the conventional ELM from previous works. Copyright © 2022, The Authors. All rights reserved.

关键词： Machine learning