Stochastic configuration networks for multi-dimensional integral evaluation

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 multidimensional 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.(c) 2022 Elsevier Inc. All rights reserved.