Data-Driven Approach to Inverse Bifurcation Problems of Thin-Walled Systems Based on Neural Networks

• Datum: 2026
• Hauptverfasser: Гук, Наталія, Сіліч-Балгабаєва, Валентина, Степанова, Наталія
• Format: Artikel
• Sprache: Ukrainisch
• Veröffentlicht: Кам'янець-Подільський національний університет імені Івана Огієнка 2026
• Online Zugang: https://mcm-math.kpnu.edu.ua/article/view/360650
• Назва журналу: Mathematical and computer modelling. Series: Physical and mathematical sciences

The paper addresses the problem of predicting the bifurcation behaviour of thin-walled systems subjected predominantly to compressive loads in the presence of local impulsive disturbances. Under conditions of nonlinear deformation, such systems may exhibit multiple equilibrium states, and their dynamics are characterised by high sensitivity to loading parameters and initial conditions, which complicates the application of classical analytical and numerical methods. A data-driven approach to solving the inverse bifurcation problem is proposed, based on the use of neural network models for the identification and prediction of critical states from time series of measured displacements. A dynamic neural network based on a multilayer perceptron is developed, incorporating the time history of the deformation process through the introduction of regressors and delay elements, which allows the inertial properties of the system to be taken into account. The inverse problem is formulated as the task of predicting the onset of a bifurcation transition by minimising an error functional between observed and reference data. The output of the neural network is interpreted as a continuous estimate of the system’s proximity to a critical state, followed by binary classification. Computational experiments have been conducted to confirm the accuracy and efficiency of the proposed approach. It is shown that the neural network model provides reliable prediction of bifurcation in a time shorter than the time of its occurrence, and also demonstrates robustness to variations in parameters and external disturbances. The obtained results indicate the potential of data-driven methods for analysis, identification, and early diagnosis of stability loss in thin-walled structures.