The DeepONet architecture consists of two concurrent DNNs, a branch network, and a trunk network. The branch network encodes the varying input realizations, {π j } Nex j=1 that are the emergent parameter coordinates of each experiment; the trunk network takes the spatial and temporal embeddings, { ζj , τj } N ẑ ×N τ j=1 , the locations where the unknown PDE is evaluated. The solution operator for an input realization, π1 , can be expressed as: