Parameter identification for wildfire forecasting models often relies on case-by-case tuning or posterior diagnosis/analysis, which can be computationally expensive due to the complexity of the forward prediction model. In this paper, we introduce an efficient parameter flexible fire prediction algorithm based on machine learning and reduced order modelling techniques. Using a training dataset generated by physics-based fire simulations, the method forecasts burned area at different time steps with a low computational cost. We then address the bottleneck of efficient parameter estimation by developing a novel inverse approach relying on data assimilation techniques (latent assimilation) in the reduced order space. The forward and the inverse modellings are tested on two recent large wildfire events in California. Satellite observations are used to validate the forward prediction approach and identify the model parameters. By combining these forward and inverse approaches, the system manages to integrate real-time observations for parameter adjustment, leading to more accurate future predictions.