Title: Towards Realtime Distributed Virtual Flow Meter via Compressed Continual Learning. Abstract: A robust-accurate estimation of fluid flow is the main building block of a distributed virtual flow meter. Unfortunately, a big leap in algorithm development would be required for this objective to come to fruition, mainly due to the inability of current machine learning algorithms to make predictions outside the training data distribution. To improve predictions outside the training distribution, we explore the Continual Learning (CL) paradigm for accurately estimating the characteristics of fluid flow in pipelines. A significant challenge facing CL is the concept of catastrophic forgetting. In this paper, we provide a novel approach of how to address the forgetting problem via compressing the distributed sensor data to increase the capacity of CL memory bank using a compressive learning algorithm. Through extensive experiments, we show that our approach provides around 8% accuracy improvement compared to other CL algorithms in the real-field distributed sensor dataset. Noticeable accuracy improvement is also achieved when using our proposed approach with the CL-benchmark datasets, achieving state-of-the-art accuracies of 94.95% and 77.27% for the MNIST and CIFAR-10 datasets, respectively.