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Neural networks in stochastic mechanics

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Summary

A state of art on the application of neural networks in Stochastic Mechanics is presented. The use of these Artificial Intelligence numerical devices is almost exclusively carried out in combination with Monte Carlo simulation for calculating the probability distributions of response variables, specific failure probabilities or statistical quantities. To that purpose the neural networks are trained with a few samples obtained by conventional Monte Carlo techniques and used henceforth to obtain the responses for the rest of samples. The advantage of this approach over standard Monte Carlo techniques lies in the fast computation of the output samples which is characteristic of neural networks in comparison to the lengthy calculation required by finite element solvers. The paper considers this combined method as applied to three categories of stochastic mechanics problems, namely those modelled with random variables, random fields and random processes. While the first class is suitable to the analysis of static problems under the effect of values of loads and resistances independent from time and space, the second is useful for describing the spatial variability of material properties and the third for dynamic loads producing random vibration. The applicability of some classical and special neural network types are discussed from the points of view of the type of input/output map**, the accuracy and the numerical efficiency.

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  1. Universidad Nacional de Colombia, Apartado 127, Manizales, Colombia

    Jorge E. Hurtado

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Hurtado, J.E. Neural networks in stochastic mechanics. ARCO 8, 303–342 (2001). https://doi.org/10.1007/BF02736646

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