Functional Uncertainty Constrained by Law and Experiment

Many physical processes are modeled by unspecified functions. Here, we introduce the F_UNCLE project which uses the Python ecosystem of scientific software to develop and explore techniques for estimating such unknown functions and our uncertainty about them. The work provides ideas for quantifying uncertainty about functions given the constraints of both laws governing the function’s behavior and experimental data. We present an analysis of pressure as a function of volume for the gases produced by detonating an imaginary explosive, estimating a best pressure function and using estimates of Fisher information to quantify how well a collection of experiments constrains uncertainty about the function. A need to model particular physical processes has driven our work on the project, and we conclude with a plot from such a process.