Solving fluid flow problems using semi-supervised symbolic regression on sparse data

The twenty first century is the century of data. Machine learning data and driven methods start to lead the way in many fields. In this contribution, we will show how symbolic regression machine learning methods, based on genetic programming, can be used to solve fluid flow problems. In particular, we will focus on the fluid drag experienced by ellipsoidal and spherocylinder particles of arbitrary aspect ratio. The machine learning algorithm is trained semisupervised by using a very limited amount of data for a specific single aspect ratio of 2.5 for ellipsoidal and 4 for spherocylindrical particles. The effect of the aspect ratio is informed to the algorithm through what we call previous knowledge, for example, known analytical solutions in certain limits, or through interbreeding of different flow solutions from the literature. Our results show good agreement with literature results, while they are obtained computationally faster and with less computing resources. Also, the machine learning algorithm discovered that for the case of prolate spheroids, the difference between the drag coefficients perpendicular and parallel to the flow in the high Reynolds number regime only depend on the aspect ratio of the geometry, even when the individual drag coefficients still decrease with increasing Re.