[wjhuggins]

Would it be possible to apply the kind of reasoning you used to a discretization of space also?

One could imagine starting with a convolutional neural network that is also a residual network (I may be butchering the proper terminology here) and taking the limit of an infinitely fine discretization in space as well as time to arrive at a PDE instead of an ODE.

Would the adjoint method approach that you used for backpropagation work in this case?