From disorganized data to emergent dynamic models: Questionnaires to partial differential equations.

ABSTRACT: Starting with sets of disorganized observations of spatially varying and temporally evolving systems, obtained at different (also disorganized) sets of parameters, we demonstrate the data-driven derivation of parameter dependent, evolutionary partial differential equation (PDE) models capable of generating the data. This tensor type of data is reminiscent of shuffled (multidimensional) puzzle tiles. The independent variables for the evolution equations (their "space" and "time") as well as their effective parameters are all emergent, i.e. determined in a data-driven way from our disorganized observations of behavior in them. We use a diffusion map based questionnaire approach to build a smooth parametrization of our emergent space/time/parameter space for the da

SUBMITTER: Sroczynski DW 

PROVIDER: S-EPMC11786195 | biostudies-literature | 2025 Feb

REPOSITORIES: biostudies-literature