Borehole Heat Exchanger (BHE) can be installed in different infrastructures to store or extract energy, such as pavement cooling in summer and de-icing in winter. Although there are approaches to estimating the performance of a BHE based on analytical, semi-analytical or numerical simulation methods, predicting the performance of a BHE in the perspective of Machine Learning (ML) is still necessary. In this investigation, four ML algorithms including Linear Regression (LR), Polynomial Regression (PR), Artificial Neural Network (ANN) and Random Forest (RF) were used to explore the underlying relationship between the Heat Extraction Rate (HER) and the influencing factors. In total, the annual HERs of 400 Thermal Performance Tests (TPTs) covering 12 major factors were computed in a validated numerical simulation framework. After providing necessary database, the 4 ML approaches were trained and evaluated. The results showed that the trained PR approach had the best performance. Specifically, the trained PR approach had a Root-Mean-Square Error (RMSE) lower than 1.74 W · m⁻¹, with the Coefficient of Determination (R²) higher than 0.99. Additionally, the trained approach was compared to an in-situ TPT in Shijiazhuang (China) and two numerical simulated scenarios in Alsace (France). The results showed that the trained PR approach predicted well the in-situ TPT by having 3 W · m⁻¹ of RMSE, and it predicted correctly the numerical simulated HER of a BHE with 0.09 and 0.72 W · m⁻¹ of RMSEs for two scenarios with 5 and 1 °C of inlet fluid temperatures. The proposed prediction model can be applied to estimate the performance of a BHE, providing another option to fast evaluate the BHE performance.

In this paper, we develop an average-derivative based second-order staggered-grid finite-difference (ADSSFD) scheme for performing 3D frequency-domain elastic wave modeling. The ADSSFD scheme applies the idea of average derivative to discretize the first-order derivative of the stress tensors and combines the anti-lumped mass strategy to obtain a set of optimal finite-difference (FD) coefficients. We combine the Levenberg-Marquardt method with simulated annealing to minimize the misfit between the normalized phase velocity and one, ensuring the solution avoids local minima. Dispersion analysis indicates that when the upper limit of the phase velocity error is set to 1%, the ADSSFD scheme can reduce the minimum number of grid points per shear wavelength to 3.6. Numerical experiments indicate that under the same numerical setting, the ADSSFD scheme exhibits higher accuracy than the classic fourth-order staggered-grid FD (FSFD) scheme and the compact second-order staggered-grid FD scheme. In addition, we find the feasibility of using the ADSSFD scheme to perform simulations in the 3D overthrust model. We use a parallel iteration solver to solve the large sparse linear system obtained after the discretization. Because the condition number of the matrix in the ADSSFD scheme is smaller than that of the FSFD scheme, the ADSSFD scheme is cheaper to run.