Artificial Neural Networks (ANNs) can be viewed as a mathematical model to simulate natural and biological systems on the basis of mimicking the information processing methods in the human brain. The capability of current ANNs only focuses on approximating arbitrary deterministic input-output mappings. However, these ANNs do not adequately represent the variability which is observed in the systems’ natural settings as well as capture the complexity of the whole system behaviour. This thesis addresses the development of a new class of neural networks called Stochastic Neural Networks (SNNs) in order to simulate internal stochastic properties of systems. Developing a suitable mathematical model for SNNs is based on canonical representation of stochastic processes or systems by means of Karhunen-Loève Theorem. Some successful real examples, such as analysis of full displacement field of wood in compression, confirm the validity of the proposed neural networks. Furthermore, analysis of internal workings of SNNs provides an in-depth view on the operation of SNNs that help to gain a better understanding of the simulation of stochastic processes by SNNs.

Artificial Neural Networks (ANNs) can be viewed as a mathematical model to simulate natural and biological systems on the basis of mimicking the information processing methods in the human brain. The capability of current ANNs only focuses on approximating arbitrary deterministic input-output mappings. However, these ANNs do not adequately represent the variability which is observed in the systems' natural settings as well as capture the complexity of the whole system behaviour. This thesis addresses the development of a new class of neural networks called Stochastic Neural Networks (SNNs) in order to simulate internal stochastic properties of systems. Developing a suitable mathematical model for SNNs is based on canonical representation of stochastic processes or systems by means of Karhunen-Loéve Theorem. Some successful real examples, such as analysis of full displacement field of wood in compression, confirm the validity of the proposed neural networks. Furthermore, analysis of internal workings of SNNs provides an in-depth view on the operation of SNNs that help to gain a better understanding of the simulation of stochastic processes by SNNs.