Textbook in PDF format This book is an introduction to the use of machine learning and data-driven approaches in fluid simulation and animation, as an alternative to traditional modeling techniques based on partial differential equations and numerical methods – and at a lower computational cost. This work starts with a brief review of computability theory, aimed to convince the reader – more specifically, researchers of more traditional areas of mathematical modeling – about the power of neural computing in fluid animations. In these initial chapters, fluid modeling through Navier-Stokes equations and numerical methods are also discussed