Convolutional Neural Networks for Problems in Transport Phenomena: A Theoretical Minimum
Convolutional neural network (CNN), a deep learning algorithm, has gained popularity in technological applications that rely on interpreting images (typically, an image is a 2D field of pixels). Transport phenomena is the science of studying different fields representing mass, momentum, or heat transfer. Some of the common fields are species concentration, fluid velocity, pressure, and temperature. Each of these fields can be expressed as an image(s). Consequently, CNNs can be leveraged to solve specific scientific problems in transport phenomena. Herein, we show that such problems can be grouped into three basic categories: (a) mapping a field to a descriptor (b) mapping a field to another field, and (c) mapping a descriptor to a field. After reviewing the representative transport phenomena literature for each of these categories, we illustrate the necessary steps for constructing appropriate CNN solutions using sessile liquid drops as an exemplar problem. If sufficient training data is available, CNNs can considerably speed up the solution of the corresponding problems. Finally, the present discussion is meant to be minimalistic such that readers can easily identify the transport phenomena problems where CNNs can be useful as well as construct and/or assess such solutions.