Fig. 6.

The hierarchical framework for predicting ${\mathrm{\Gamma }}_{\text{pent}}$ based on knowledge transfer. (A) The predictive framework utilizes the well-established auxiliary solution, ${\mathrm{\Gamma }}_{2D}$, and the discovered connection to predict ${\mathrm{\Gamma }}_{\text{pent}}$. The switchable kernel in this framework, which concretizes the dependence of $\alpha$ on $\underset{¯}{x}$, can have multiple versions, i.e., $\overline{\alpha }$ and $\widehat{\alpha }$ (Eqs. 6 and 7). (B) These two versions feature different levels of error tolerance, less than 7% and 3% relative error for $\overline{\alpha }$ and $\widehat{\alpha }$, respectively. Note that the original form of $\alpha$ in Eq. 5 shows the best approximation capability but does not provide a solid connection between ${\mathrm{\Gamma }}_{2D}$ and ${\mathrm{\Gamma }}_{\text{pent}}$. The second kernel, $\widehat{\alpha }$, is established with a simple fully connected NN (“2/4/1”), which adds 1.3% relative error.