Deep learning has produced excellent results in several applied domains including computer vision, natural language processing, speech recognition, etc. Physics-informed neural networks (PINN) are a new family of deep learning models that combine prior knowledge of physics in the form of high-level abstraction of natural phenomena with data-driven neural networks. PINN has emerged as a flourishing area of scientific computing to deal with the challenges of shortage of training data, enhancing physical plausibility, and specifically aiming to solve complex differential equations. However, building PINNs for modeling and forecasting the dynamics of extreme climatic events of geophysical systems remains an open scientific problem. This study proposes Van der Pol-informed Neural Networks (VPINN), a physics-informed differential learning approach, for modeling extreme nonlinear dynamical systems such as climatic events, exploiting the physical differentials as the physics-derived loss function. Our proposal is compared to state-of-the-art time series forecasting models, showing superior performance.