Quantitative Prediction of Coal–Gangue Content Using Terahertz Time-Domain Spectroscopy and Physics-Informed Machine Learning

Quantitative determination of gangue content is important for efficient coal use and intelligent coal–gangue separation. We combine transmission terahertz time-domain spectroscopy (THz-TDS), multidomain feature fusion, and machine learning to predict gangue mass fraction in coal–gangue mixtures. Time- and frequency-domain signals, refractive index, absorption and extinction coefficients, and complex permittivity were extracted from samples with different gangue contents. Five-fold cross-validation was used to compare random forest, support vector regression, Gaussian process regression, an artificial neural network, and an Effective Medium Theory-constrained Physics-Informed Neural Network (EMT-PINN). EMT-PINN achieved the best performance, with a coefficient of determination (R2) of 0.81 ± 0.15, a mean absolute error (MAE) 3.17 ± 0.59%, and a root mean square error (RMSE) of 5.79 ± 0.21%, compared with R2 values of 0.72 ± 0.08, 0.61 ± 0.21, 0.74 ± 0.11, and 0.64 ± 0.18 for RF, SVR, GPR, and ANN, respectively. These results demonstrate the potential of physics-informed THz spectroscopy for rapid and physically interpretable quantitative characterization of coal–gangue mixtures.