Influence of the Neural Network Morphology Symmetry on the Complex Dynamic Objects’ Diagnostics

In this article, to study the influence of neural networks’ morphology symmetry, a mathematical model is developed that considers dynamic symmetry for diagnosing complex dynamic objects. The developed mathematical model includes the symmetric architecture concept with adaptive parameters, according to which the neural network is represented by a function that relates the input data to the diagnostic outputs. A dynamic symmetry function is introduced to the neural networks’ weight change depending on the systems’ state. To achieve symmetric training, the loss function is minimised with regularisation considering deviations from the symmetric state. The theorem “On the symmetric neural network optimisation stability” is formulated and proven, demonstrating the symmetric neural network optimisation stability, which is confirmed by the weights’ stability and the loss functions’ global optimisation, which includes symmetric regularisation, which stabilises the weights and reduces their sensitivity to minor disturbances. It is shown that in the training process, gradient descent with symmetric regularisation contributes to stable convergence and a decrease in weight asymmetry. In this case, an energy function that tends to zero with the optimal weights’ achievement is introduced. The analysis showed that symmetric regularisation minimises the weights’ deviation and prevents their overtraining. It was experimentally established that the optimal regularisation coefficient λ = 1.0 ensures a balance between the models’ symmetry and flexibility, minimising the diagnostic error. The results show that symmetric regularisation contributes to practical training and increases the diagnostic models’ accuracy.