Reconstruction of ASO-S/HXI Solar Flare Hard X-ray Source Images with Physics-Constrained Deep Network
Solar flare hard X-ray imaging is a key diagnostic of flare energy release and electron acceleration. The ASO-S Hard X-ray Imager (HXI) employs 91 bi-grid sub-collimators, compressing the two-dimensional source distribution into a 91-dimensional counts vector---an inherently underdetermined inverse problem. The conventional CLEAN algorithm relies on a point-source prior and manual parameter tuning, while existing deep-learning methods (HXI-DLA) learn data-driven mappings without guaranteeing consistency with the forward physical equation. This paper introduces a physics-constrained deep learning framework whose core innovation is a counts mean--shape decoupling theory (DC--AC decomposition) derived from modulation imaging principles: the counts mean is proportional to total source energy and the normalized counts shape is determined by source position and scale, yielding two independently enforceable physical constraints. Based on this theory, HXI-PINN embeds the forward equation into both the network architecture---via ReLU non-negativity and counts-mean rescaling enforcing zero-error energy closure---and the optimization objective, where counts-domain constraints dominate the loss. Unlike data-driven approaches, HXI-PINN replaces heuristic regularization with executable hard constraints, ensuring every reconstruction satisfies the governing physics. Experiments on simulated Gaussian sources, soft X-ray morphologies, and a real HXI flare event confirm that the framework generalizes across source configurations, with advantages over CLEAN on ring-shaped sources and over HXI-DLA on complex morphologies. This work demonstrates that ``physical constraints + deep prior'' is an effective paradigm for underdetermined inversion---constraints anchor the solution in the feasible subspace satisfying the forward equation, while the deep prior selects the optimal solution within it.