A data-driven approach for discovering the most probable transition pathway for a stochastic carbon cycle system

Many natural systems exhibit tipping points where changing environmental conditions spark a sudden shift to a new and sometimes quite different state. Global climate change is often associated with the stability of marine carbon stocks. We consider a stochastic carbonate system of the upper ocean to capture such transition phenomena. Based on the Onsager-Machlup action functional theory, we calculate the most probable transition pathway between the metastable and oscillatory states via a neural shooting method. Furthermore, we explore the effects of external random carbon input rates on the most probable transition pathway, which provides a basis to recognize naturally occurring tipping points. Particularly, we investigate the transition pathway's dependence on the transition time and further compute the optimal transition time using a physics-informed neural network, toward the maximum carbonate concentration state in the oscillatory regimes. This work may offer some insights into the effects of noise-affected carbon input rates on transition phenomena in stochastic models.