Stochastic configuration networks for multi-dimensional integral evaluation

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Complex multi-dimensional integrals are widely used in various engineering problems. This paper proposes a novel numerical integration method based on stochastic configuration networks (SCNs), which is constructed by learning the integrand function. A corresponding primitive function based on a simple functional expression of the trained SCN can be analytically derived, and a general functional relation between the integrand and the primitive function is established based on SCN parameters. By repeatedly applying the derived functional relations, we can successfully evaluate many complex multi-dimensional integrals. The SCN-based numerical integral method provides a powerful tool for solving complex multi-dimensional integrals. Effectiveness of the proposed method in terms of both computational accuracy and stability is demonstrated through numerical experiments.