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, and further 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 effect of the transition time on the transition pathway and further compute the optimal transition time using physics informed neural network, towards the maximum carbonate concentration state in the oscillatory regimes. This work offers some insights on the effects of random carbon input on climate transition in a simple model. Key words: Onsager-Machlup action functional, the most probable transition pathway, neural shooting method, stochastic carbon cycle system.