Two-Stage Wiener-Physically-Informed-Neural-Network (W-PINN) AI Methodology for Highly Dynamic and Highly Complex Static Processes

The objective of this work is the development of a highly effective Wiener-Physically-Informed-Neural-Network (W-PINN) modeling methodology for systems and processes with highly nonlinear dynamic and highly nonlinear static behavior. This approach has two basic stages. The first stage estimates all the unknown linear dynamic modeling coefficients. With these estimates fixed, the second stage estimates all the unknown static coefficients in an artificial neural network (ANN) framework. When the ANN is a nonlinear function, as in this work, the fitted model is a nonlinear dynamic and nonlinear static structure. In a previous one stage, 60-minute forecast modeling case, the dynamic outputs (vij, where i = the subject number and j = the sample number) were estimated in Excel® for eleven (11) type 1, freely-living, diabetes data sets (cases) of approximately two weeks of data, yielding an average input-only sensor glucose concentration (SGC) validation fit () of 0.68. With these vij’s fixed, this new approach obtains final, two-stage (TS) W-PINN, 60-minute forecast fitted models, for each of the 11 cases, in two ways. One two-stage approach uses the JMP® ANN toolbox for second stage modeling and achieves an average input-only SGC of 0.74 and maximum of 0.84. The second two-stage approach uses a novel ANN methodology coded in Python® and achieves an average input-only SGC of 0.82 and maximum of 0.93. Incorporating bias correction, using current and past SGC residuals, the Python® estimator improved the average from 0.82 to 0.87 with the maximum still 0.93.