A physics-informed data-driven approach for forecasting bifurcations in dynamical systems

Nonlinear stability analysis plays a key role in the design and evaluation of dynamical systems. Model-based analysis methods require extensive calibration and computational resources. While data-driven methods might offer a solution to this challenge, they are limited to available data and fail to generalize. Incorporating physical information about the system into data-driven methods can extend the applicability of these methods and improve their accuracy. In this paper, we present a physics-informed forecasting approach to predict bifurcation diagrams in nonlinear systems prone to instabilities using measurements of system dynamics before instabilities occur. The proposed method is a hybrid approach that combines an asymptotic analysis provided by the method of multiple scales and a data-driven forecasting technique. In particular, the approach uses information about the nonlinearities exhibited in the system to obtain the normal form using the method of multiple scales. The coefficients of this generic pre-identified form are then approximated using data from time series in the pre-bifurcation regime. We demonstrate the applicability of the proposed method in identifying post-bifurcation dynamics of nonlinear systems prone to instabilities through the application of the approach to several classes of nonlinear systems.