Neural networks in stochastic mechanics

A state of art on the application of neural networks in Stochastic Mechanic s is presented. The use of these Artificial Intelligence numerical devices is almost exclusively carried out in combination with Monte Carlo simulatio n for calculating the probability distributions of response variables, spec ific failure probabilities or statistical quantities. To that purpose the n eural networks are trained with a few samples obtained by conventional Mont e Carlo techniques and used henceforth to obtain the responses for the rest of samples. The advantage of this approach over standard Monte Carlo techn iques lies in the fast computation of the output samples which is character istic of neural networks in comparison to the lengthy calculation required by finite element solvers. The paper considers this combined method as appl ied to three categories of stochastic mechanics problems, namely those mode lled with random variables, random fields and random processes. While the f irst class is suitable to the analysis of static problems under the effect of values of loads and resistances independent from time and space, the sec ond is useful for describing the spatial variability of material properties and the third for dynamic loads producing random vibration. The applicabil ity of some classical and special neural network types are discussed from t he points of view of the type of input/output mapping, the accuracy and the numerical efficiency.