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- research-articleSeptember 2024
A multi-strategy surrogate-assisted social learning particle swarm optimization for expensive optimization and applications
AbstractEvolutionary algorithms (EAs) require extensive fitness evaluations, which constitutes a barrier to solving computationally complex problems. In contrast, surrogate-assisted evolutionary algorithms (SAEAs) have the potential to solve complex ...
Highlights- SASLPSO is proposed to solve expensive optimization problems.
- A novel RGBPS strategy is proposed to screen promising particles.
- An adaptive local surrogate (ALS) is proposed to local fitting.
- The proposed SASLPSO effectively ...
- research-articleJuly 2024
A hybrid kernel-based meshless method for numerical approximation of multidimensional Fisher’s equation
Mathematics and Computers in Simulation (MCSC), Volume 223, Issue CPages 130–157https://doi.org/10.1016/j.matcom.2024.04.003AbstractWe propose and analyze a meshless method of lines by considering some hybrid radial kernels. These hybrid kernels are constructed by linearly combining infinite smooth radial functions to piecewise smooth radial functions; which are then used for ...
- research-articleJuly 2024
A machine learning-based approach for estimation of deflection and contact area characteristics of tubeless and tube-type agricultural tyres
Engineering Applications of Artificial Intelligence (EAAI), Volume 133, Issue PDhttps://doi.org/10.1016/j.engappai.2024.108357AbstractSupport Vector Regression (SVR) models with different kernel functions (radial basis and polynomial) were developed for predicting deflection and contact area of tubeless and tube-type tractor tyres. Data were collected from experimental trials ...
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Highlights- Developed a displacement transducer for measuring tyre deflection.
- Tubeless tyre deformed more thus gave higher contact area as compared to tube-type.
- RBF kernel function based SVR models was better than poly SVR.
- RBF SVR ...
- research-articleJune 2024
Collocation methods for integral fractional Laplacian and fractional PDEs based on radial basis functions
Applied Mathematics and Computation (APMC), Volume 469, Issue Chttps://doi.org/10.1016/j.amc.2024.128548AbstractWe consider collocation methods for fractional elliptic equations with the integral fractional Laplacian on general bounded domains using radial basis functions (RBFs). Leveraging the Hankel transform, we develop highly efficient numerical ...
Highlights- Develop efficient methods for fractional Laplacian of radial basis functions with smooth Fourier transformations, e.g. Matern kernel.
- Devise a collocation formulation for fractional elliptic problems on complex domains.
- The ...
- research-articleJuly 2024
Anomaly detection using large-scale multimode industrial data: An integration method of nonstationary kernel and autoencoder
Engineering Applications of Artificial Intelligence (EAAI), Volume 131, Issue Chttps://doi.org/10.1016/j.engappai.2023.107839AbstractKernel methods and neural networks (NNs) are two mainstream nonlinear data modeling methods and have been widely applied to industrial process monitoring. However, they both present imperfect properties, so the relevant applications are limited. ...
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- research-articleJune 2024
A radial basis function partition of unity method for steady flow simulations
Journal of Computational Physics (JOCP), Volume 503, Issue Chttps://doi.org/10.1016/j.jcp.2024.112842AbstractA methodology is presented for the numerical solution of nonlinear elliptic systems in unbounded domains, consisting of three elements. First, the problem is posed on a finite domain by means of a proper nonlinear change of variables. The ...
Highlights- Infinite domain compression removes the need for artificial computational domain and the hard-to-quantify associated error.
- Nonlinear elliptic PDEs, particularly systems thereof, are very rare in the RBF literature.
- RBF-PU allows ...
- research-articleApril 2024
MultiPINN: multi-head enriched physics-informed neural networks for differential equations solving
Neural Computing and Applications (NCAA), Volume 36, Issue 19Pages 11371–11395https://doi.org/10.1007/s00521-024-09766-zAbstractRecently, the physics-informed neural network (PINN) has attracted much attention in solving partial differential equations (PDEs). The success is due to the strong generalization ability of the neural network (NN), which is supported by the ...
- research-articleMarch 2024
Numerical simulations of two-dimensional incompressible Navier-Stokes equations by the backward substitution projection method
Applied Mathematics and Computation (APMC), Volume 466, Issue Chttps://doi.org/10.1016/j.amc.2023.128472AbstractThe backward substitution method is a newly developed meshless method that has been used for the simulation of many problems in science and engineering with high accuracy and efficiency. In this paper, we explore the feasibility of employing the ...
Highlights- The backward substitution method is first raised for the simulation of incompressible flows.
- Investigated effects of the time step and the number of collocation points on the accuracy.
- Verification benchmark comprising several ...
- research-articleFebruary 2024
Stabilized interpolation using radial basis functions augmented with selected radial polynomials
Journal of Computational and Applied Mathematics (JCAM), Volume 437, Issue Chttps://doi.org/10.1016/j.cam.2023.115482AbstractInfinitely smooth radial basis functions (RBFs) have a shape parameter that controls their shapes. When using these RBFs (e.g., the Gaussian RBF) for interpolation problems, we have ill-conditioning when the shape parameter is very small, while ...
- research-articleMarch 2024
A new type of non-polynomial based TENO scheme for hyperbolic conservation laws
Journal of Computational Physics (JOCP), Volume 497, Issue Chttps://doi.org/10.1016/j.jcp.2023.112618AbstractFor classical WENO/TENO reconstructions, the high-order polynomial interpolation is one of the main building-blocks for constructing the numerical fluxes. However, due to the inherent characteristics of polynomials, the polynomial interpolation ...
- research-articleJanuary 2024
An efficient radial basis function generated finite difference meshfree scheme to price multi-dimensional PDEs in financial options
Journal of Computational and Applied Mathematics (JCAM), Volume 436, Issue Chttps://doi.org/10.1016/j.cam.2023.115382AbstractIn this paper, the purpose is to focus on proposing a new solver for pricing financial option at the presence of several assets. Toward this goal, first we introduce the weighting coefficients of the radial basis function-finite ...
- research-articleApril 2024
Adaptive surrogate assisted multi-objective optimization approach for highly nonlinear and complex engineering design problems
AbstractDespite enormous advances in computer power, computationally costly models impede the use of traditional optimization approaches that must be invoked repeatedly during the optimization process in practical engineering applications. Surrogate ...
Highlights- Adaptive Surrogate Assisted Multi-Objective Optimization Approach is introduced.
- Surrogate approximations were utilized to determine Pareto front of multi-objective problems.
- Sample guiding function is applied to guide search and ...
- research-articleDecember 2023
RBF-FD based some implicit-explicit methods for pricing option under regime-switching jump-diffusion model with variable coefficients
Numerical Algorithms (SPNA), Volume 97, Issue 2Pages 645–685https://doi.org/10.1007/s11075-023-01719-2AbstractIn this manuscript, we introduced the radial basis function based three implicit-explicit (IMEX) finite difference techniques for pricing European and American options in an extended Markovian regime-switching jump-diffusion (RSJD) economy. A ...
- research-articleDecember 2023
A surrogate-assisted evolutionary algorithm with clustering-based sampling for high-dimensional expensive blackbox optimization
Journal of Global Optimization (KLU-JOGO), Volume 89, Issue 1Pages 93–115https://doi.org/10.1007/s10898-023-01343-3AbstractMany practical problems involve the optimization of computationally expensive blackbox functions. The computational cost resulting from expensive function evaluations considerably limits the number of true objective function evaluations allowed in ...
- research-articleFebruary 2024
A rapid method to predict biaxial fatigue life of automotive wheels using proper orthogonal decomposition and radial basis function algorithm
Advances in Engineering Software (ADES), Volume 186, Issue Chttps://doi.org/10.1016/j.advengsoft.2023.103543Highlights- A rapid method based on proper orthogonal decomposition and radial basis function is presented for wheel fatigue evaluation.
- The computational efficiency in predicting wheel fatigue life under biaxial load spectrum is significantly ...
This paper presents a rapid method for predicting the biaxial fatigue life of automotive wheels using a combination of proper orthogonal decomposition and radial basis function algorithm. Currently, numerical simulations of biaxial fatigue tests ...
- research-articleNovember 2023
A multi-strategy surrogate-assisted competitive swarm optimizer for expensive optimization problems
AbstractEvolutionary computation is a powerful tool for solving nonconvex optimization problems. Generally, evolutionary algorithms take numerous fitness evaluations to obtain the potential optimal solutions. This poses a critical challenge for applying ...
Highlights- SACSO is proposed to solve expensive optimization problems and applied to speed reducer design.
- Particle selection criteria contain global search, local search, and opposition-based search.
- A dynamic adaptation strategy is proposed ...
- research-articleOctober 2023
Surrogate modeling of time-domain electromagnetic wave propagation via dynamic mode decomposition and radial basis function
Journal of Computational Physics (JOCP), Volume 491, Issue Chttps://doi.org/10.1016/j.jcp.2023.112354AbstractThis work introduces an ‘equation-free’ non-intrusive model order reduction (NIMOR) method for surrogate modeling of time-domain electromagnetic wave propagation. The nested proper orthogonal decomposition (POD) method, as a prior ...
- research-articleOctober 2023
Meshfree methods for nonlinear equilibrium radiation diffusion equation with jump coefficient
Computers & Mathematics with Applications (CMAP), Volume 147, Issue CPages 239–258https://doi.org/10.1016/j.camwa.2023.07.027AbstractThe equilibrium radiation diffusion equation has been widely used in astrophysics, inertial confinement fusion and others. Since the simulation domain consists of many complicated domains and the material properties in each domain are ...
- research-articleSeptember 2023
A Gaussian–cubic backward substitution method for the four-order pure stream function formulation of two-dimensional incompressible viscous flows
Engineering with Computers (ENGC), Volume 40, Issue 3Pages 1813–1830https://doi.org/10.1007/s00366-023-01896-7AbstractIn this study, a novel meshless collocation method based on the Gaussian–cubic hybrid kernel function in conjunction with the ghost-points method and the general Newton–Raphson method is proposed for solving the four-order stream function ...
- research-articleSeptember 2023
Meshfree methods for the variable-order fractional advection–diffusion equation
Mathematics and Computers in Simulation (MCSC), Volume 211, Issue CPages 489–514https://doi.org/10.1016/j.matcom.2023.04.003AbstractThe fractional advection–diffusion equation can describe the anomalous diffusion associated with complicated diffusion medium and pollution source in application problems. The variable-order fractional advection–diffusion equation can ...