From Clutter to Clarity: Emergent Neural Operators via Questionnaire Metrics

Real-world datasets in chemical engineering and bioengineering processes--such as those from catalytic reactors, multiphase flows, polymerization reactors, bioreactors, and clinical trials--can often be unlabelled or disorganized, rendering the training of existing supervised learning models ineffective at learning the underlying dynamics. To salvage these datasets for decision-making, we first seek to obtain clarity from the cluttered data. Here, we present a framework for developing "structural" generative models, discovering emergent equations, and constructing efficient emulators from scrambled datasets by integrating unsupervised organizational learning techniques (Questionnaires) with advanced deep learning architectures (Deep Hidden Physics Models and Deep Operator Networks). Our approach is demonstrated on two illustrative systems: (a) a 1D advection-diffusion partial differential equation representing a winding underground pipe, relevant for chemical transport processes, and (b) an ensemble of Stuart-Landau oscillators, an agent-based system of coupled ordinary differential equations, analogous to complex, coupled reaction networks in reactors. In both cases, we successfully reconstruct meaningful spatial, temporal, and parameter embeddings from scrambled data, enabling good predictions of system dynamics. We highlight the framework's potential for broader applications, enabling data-driven system identification in fields with inherently disorganized or hidden parameter spaces.