2.6.1. Scaling of the Input and Output Data

The input data for the ML models are geometry parameters and, for the bar width, the bar spacing and the bar height measured in mm. The plane angle in measured in ∘. Except from the plane angle, the magnitude of the input data is approximately 1 × 10⁻¹, the magnitude of the plane angle is in the order of 1 × 10¹. The input data is scaled using mean and standard deviation of the data with:

In Equation (7), the quantity x★ represents the scaled input data, x¯ is the mean and y represents the standard deviation of the input data.

The Biot parameters, which is the output data of the ML models, have very different dimensions and scales, for example, the viscous and thermal characteristic lengths are geometric lengths, the static thermal permeability has the dimension of a surface, the porosity and tortuosity are dimensionless and the flow resistivity has the dimension Pa s/m2. Furthermore, the magnitude of these parameters is rather different and comprises a large range of values; for example, the magnitude to the flow resistivity is 1 × 10³–1 × 10⁵, the magnitude of the static thermal permeability is approx. 1 × 10⁻⁸. It could be found that the training process becomes rather unsuccessful when the input and output data is used directly. This is expected to be a result of the large range of values within the data. Therefore, variable scaling is introduced and applied to the Biot parameters in order to result in training data comprising a smaller value range. The resulting scaled Biot parameters are shown in Table 3:

Scaling of the Biot parameters to balance out the different magnitudes.

¹ flow resistivity, ² porosity, ³ tortuosity, ⁴ thermal characteristic length, ⁵ viscous characteristic length, ⁶ static thermal permeability.

The flow resistivity remains unscaled. This scaling is assumed to only improved the training performance of the ML models but does not affect the general procedure.