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

Our new Theoretically Dynamic Regression (TDR) modeling methodology was recently applied in three types of real data modeling cases using physically based dynamic model structures with low-order linear regression static functions. Two of the modeling cases achieved the validation set modeling goal of rfit,val ≥ 0.9. However, the third case, consisting of eleven (11) type one (1) sensor glucose data sets, and thus, eleven individual models, all fail considerably short of this modeling goal and the average rfit,val, r¯fit,val = 0.68. For this case, the dynamic forms are highly complex 60 min forecast, second-order-plus-dead-time-plus-lead (SOPDTPL) structures, and the static form is a twelve (12) input first-order linear regression structure. Using these dynamic structure results, the objective is to significantly increase rfit for each of the eleven (11) modeling cases using the recently developed Wiener-Physically-Informed-Neural-Network (W-PINN) approach as the static modeling structure. Two W-PINN stage-two static structures are evaluated–one developed using the JMP® Pro Version 16, Artificial Neural Network (ANN) toolbox and the other developed using a novel ANN methodology coded in Python version, 3.12.3. The JMP r¯fit,val = 0.74 with a maximum of 0.84. The Python r¯fit,val = 0.82 with a maximum of 0.93. Incorporating bias correction, using current and past SGC residuals, the Python estimator improved the average r¯fit,val from 0.82 to 0.87 with the maximum still 0.93.