Are there any algorithms which were developed using partial differential equations for tackling some of the machine learning problems? Most works I see online are in the field of computer vision and a few bizarre ones in topic modelling. But just curious if someone has used or seen it being used for some decision making process or classification problems?
Neil is correct. There are partial derivatives evwrywhere in gradient computation for machine learning models training.
For instance you can look at the gradient descent method used in the backpropagation method for a neural network. The course from AndrewNg on coursera describes it very well.