To demonstrate our ability to use "shuffled and disorganized" data to build structural generative models, we present two illustrative examples. First, we consider a 1D partial differential equation (PDE) that models the evolving concentration field of a tracer in a turbulent flow pipe. We develop a DHPM for a tracer injection step test and then construct a DeepONet model for a series of step tests under different operating conditions. Second, we examine an ensemble of Stuart-Landau oscillators, an agent-based system of coupled ordinary differential equations (ODEs). Initially, no physical spatial dimension exists, but one emerges through the use of Questionnaires, allowing us to smoothly order the agent trajectories. We use scrambled trajectories at various parameter values to build a DeepONet model. The datasets for both examples are artificially shuffled in the time dimension to demonstrate our ability to reorganize and utilize three tensor axes. If the time axis were not scrambled, we could still apply the same techniques using the real-time coordinate instead of the emergent time embedding. Throughout this work, Greek letters denote the emergent embeddings, and Latin letters denote the original, "true" coordinates. While we have access to these true coordinates for validation, they would typically be unknown in practical applications.