English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Zendy Plus

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Zendy Tools

Zendy Open

To address the sensitivity of parameters and limited precision forphysics-informed extreme learning machines (PIELM) with common activationfunctions, such as sigmoid, tangent, and Gaussian, in solving high-orderpartial differential equations (PDEs) relevant to scientific computation andengineering applications, this work develops a Fourier-induced PIELM (FPIELM)method. This approach aims to approximate solutions for a class of fourth-orderbiharmonic equations with two boundary conditions on both unitized andnon-unitized domains. By carefully calculating the differential and boundaryoperators of the biharmonic equation on discretized collections, the solutionfor this high-order equation is reformulated as a linear least squaresminimization problem. We further evaluate the FPIELM with varying hidden nodesand scaling factors for uniform distribution initialization, and then determinethe optimal range for these two hyperparameters. Numerical experiments andcomparative analyses demonstrate that the proposed FPIELM method is morestable, robust, precise, and efficient than other PIELM approaches in solvingbiharmonic equations across both regular and irregular domains.

Augmented physics informed extreme learning machine to solve the biharmonic equations via Fourier expansions