Acute Respiratory Distress Syndrome (ARDS), also known as noncardiogenic pulmonary edema, is a severe condition that affects around one in ten-thousand people every year with life-threatening consequences. Its pathophysiology is characterized by bronchoalveolar injury and alveolar collapse (i.e., atelectasis), whereby its patient diagnosis is based on the so-called ‘Berlin Definition‘. One common practice in Intensive Care Units (ICUs) is to use lung recruitment manoeuvres (RMs) in ARDS to open up unstable, collapsed alveoli using a temporary increase in transpulmonary pressure. Many RMs have been proposed, but there is also confusion regarding the optimal way to achieve and maintain alveolar recruitment in ARDS. Therefore, the best solution to prevent lung damages by ARDS is to identify the onset of ARDS which is still a matter of research. Determining ARDS disease onset, progression, diagnosis, and treatment required algorithmic support which in turn raises the demand for cutting-edge computing power. This paper thus describes several different data science approaches to better understand ARDS, such as using time series analysis and image recognition with deep learning methods and mechanistic modelling using a lung simulator. In addition, we outline how High-Performance Computing (HPC) helps in both cases. That also includes porting the mechanistic models from serial MatLab approaches and its modular supercomputer designs. Finally, without losing sight of discussing the datasets, their features, and their relevance, we also include broader selected lessons learned in the context of ARDS out of our Smart Medical Information Technology for Healthcare (SMITH) research project. The SMITH consortium brings together technologists and medical doctors of nine hospitals, whereby the ARDS research is performed by our Algorithmic Surveillance of ICU (ASIC) patients team. The paper thus also describes how it is essential that HPC experts team up with medical doctors that usua...