), where f is an unknown functional on the emergent space. We begin with learning the tracer concentration on the emergent space-time grid for a single experiment (one Péclet number) with a DHPM consisting of two DNNs; each with 4 fully connected hidden layers of 40 neurons each. The hidden layers are followed by Tanh activation functions, and weights are initialized with uniform Xavier normalization. The first DNN, N sol , takes as inputs ζ and τ and outputs the predicted tracer concentration, Ĉpred . We recognize that the output of the DNN, Ĉpred , is differentiable with respect to the inputs, ζ and τ . Hence, we use reverse-mode automatic differentiation (AD) to estimate