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 r f i t , v a l ≥ 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 r f i t , v a l , r ¯ f i t , v a l = 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 r f i t 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 ¯ f i t , v a l = 0.74 with a maximum of 0.84. The Python r ¯ f i t , v a l = 0.82 with a maximum of 0.93. Incorporating bias correction, using current and past SGC residuals, the Python estimator improved the average r ¯ f i t , v a l from 0.82 to 0.87 with the maximum still 0.93.