Numerous social movements (SMs) around the world help support the UN's Sustainable Development Goals (SDGs). Understanding how key events shape SMs is key to the achievement of the SDGs. We have developed SMART (Social Media Analysis & Reasoning Tool) to track social movements related to the SDGs. SMART was designed by a multidisciplinary team of AI researchers, journalists, communications scholars and legal experts. This paper describes SMART's transformer-based multivariate time series Discourse Evolution Engine for Predictions about Social Movements (DEEP) to predict the volume of future articles/posts and the emotions expressed. DEEP outputs probabilistic forecasts with uncertainty estimates, providing critical support for editorial planning and strategic decision-making. We evaluate DEEP with a case study of the #MeToo movement by creating a novel longitudinal dataset (433K Reddit posts and 121K news articles) from September 2024 to June 2025, which is publicly available for research purposes.