Physically constrained data-driven inversion of 2D fast-ion velocity distributions from single view CTS spectra

Abstract Reconstructing fast-ion velocity distributions from collective Thomson scattering (CTS) spectra is an ill-posed inverse problem due to the spectral nonlinearity, strong parameter coupling and measurement noise. To mitigate the ill-posed problems in single-view inversions, a hybrid spectrum–parameter conditioned encoder (HSPCE) is proposed to reconstruct two-dimensional (2D) fast-ion velocity distributions based on the electromagnetic forward model. For feasibility validation, one-dimensional (1D) inversion is firstly carried out using an electrostatic CTS model under HL-3 operating parameters. Compared with the least squares with nuisance parameters (LSN), the machine-learning approach demonstrates markedly improved robustness and accuracy, maintaining an R 2 of 0.985 with 10% Gaussian noise. Extending to 2D, the velocity distribution is represented as an image and reduced in dimensionality through principal component analysis (PCA), with additional soft constraints applied in both coefficient and pixel spaces to preserve physical consistency. Benchmarking against the 1D baseline model, HSPCE shows that the higher structural similarity (SSIM) and lower normalized root mean square error (NRMSE) with different Gaussian noise, with 0.930 and 0.043 at noise level of 0.1 respectively. Further analysis indicates that the fraction of fast ions plays an important role in enabling the network to extract reliable fast-ion information, with higher fractions yielding clearer reconstructions and reduced uncertainty. Overall, the proposed framework suggests that neural networks offer a promising and robust approach for improving the interpretability and reliability of fast-ion diagnostics based on CTS in magnetically confined plasmas.