Cancer and bacterial infections are estimated to kill 18 million people worldwide each year by 2050. Fast and reliable diagnostics are essential for early and targeted treatments. Microfluidics is an emerging technology where tiny samples of liquids or biological fluids (blood or urine) are processed and analysed. Microfluidics is already used for fast and early diagnostics, for example, lateral flow tests that have become popular during the COVID pandemic. Inertial particle microfluidics (IPMF) is a type of microfluidics where the fluid sample moves at high speeds. IPMF is particularly useful for separating biological particles, for example, the isolation of cancer cells or bacteria from the blood. However, the underlying principles and physical rules of IPMF are not well understood, making technological progress slow and costly. In the SIRIUS project, we develop computational methods to analyse and better understand IPMF.