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Obtaining the solutions of partial differential equations based on variousmachine learning methods has drawn more and more attention in the fields ofscientific computation and engineering applications. In this work, we firstpropose a coupled Extreme Learning Machine (called CELM) method incorporatedwith the physical laws to solve a class of fourth-order biharmonic equations byreformulating it into two well-posed Poisson problems. In addition, someactivation functions including tangent, gauss, sine, and trigonometric(sin+cos) functions are introduced to assess our CELM method. Notably, the sineand trigonometric functions demonstrate a remarkable ability to effectivelyminimize the approximation error of the CELM model. In the end, severalnumerical experiments are performed to study the initializing approaches forboth the weights and biases of the hidden units in our CELM model and explorethe required number of hidden units. Numerical results show the proposed CELMalgorithm is high-precision and efficient to address the biharmonic equation inboth regular and irregular domains.

Extreme Learning Machine-Assisted Solution of Biharmonic Equations via Its Coupled Schemes