\begin{equation}
    \mathcal{L}^{\text{BC}}=\dfrac{1}{N_{\text{BCU}}}\sum_{i=1}^{N_{\text{BCU}}} |\tilde{\textbf{u}}(\textbf{X};t)-\bar{\textbf{u}}(\textbf{X};t)|^2 + \dfrac{1}{N_{\text{BCP}}}\sum_{i=1}^{N_{\text{BCP}}} |\tilde{\textbf{P}}(\textbf{X};t)\textbf{N}(\textbf{X})-\bar{\textbf{T}}(\textbf{X};t)|^2
\end{equation}
