2026-10-12T18:49:14Z https://www.scidb.cn/oai

10.57760/sciencedb.46026 2026-08-21T17:15:33Z

2026-08-21 The model and data for HXI-PINN doi:10.57760/sciencedb.46026 en Solar flare hard X-ray (HXR) imaging is a key diagnostic of flare energy release and electron acceleration. The Hard X-ray Imager (HXI) on board ASO-S employs 91 bi-grid sub-collimators, compressing the two-dimensional source distribution into a 91-dimensional counts vector through Fourier-modulation imaging---an inherently underdetermined inverse problem of recovering a high dimensional distribution from low-dimensional measurements. The conventional CLEAN algorithm relies on a point-source prior, fragments extended complex morphologies, and depends on manual parameter tuning, while existing deep-learning methods (HXI-DLA, FCD) learn a data-driven counts-to-image mapping without guaranteeing consistency with the forward physical equation. Addressing this fundamental challenge, this paper derives a counts mean--shape decoupling theory (DC--AC decomposition) from the principle of modulation imaging: analysis proves that the counts mean is proportional to the total source energy and the normalized counts shape is determined by the source spatial position and scale, and the two are separable in the measurement domain, providing independently enforceable physical constraints. Based on this theory, a physics-constrained inversion network, HXI-PINN, is constructed by explicitly embedding the forward equation into the network architecture and optimization: the output layer enforces strict zero-error energy closure through ReLU non-negativity and counts-mean rescaling, while the loss function is dominated by counts-domain constraints (total weight 0.93) to approximate the full-channel forward response. Three-level experiments demonstrate that HXI-PINN achieves NRMSE below 0.01 and SSIM above 0.98 on Gaussian sources, significantly and stably outperforming HXI-DLA, which degrades sharply with increasing morphological complexity; double-source dynamic-range tests (peak ratios 1:1--1:30) consistently achieve double-peak detection with counts-shape correlation above 0.9993 and zero energy-closure error, resolving two independent sources at the $\sim$3\arcsec\ instrumental resolution limit; on temporally independent soft X-ray complex morphologies, the network successfully reconstructs complex loop and extended flare source structures, verifying cross-morphology generalization; on the HXI observation event (2024 March 23), re-projected counts consistency slightly exceeds the CLEAN baseline, and the reconstructed bright region is overall consistent with SDO/AIA multi-band observations. This paper systematically introduces physics-informed neural network (PINN) principles into HXI bi-grid modulation imaging, replacing pure data fitting with executable hard constraints that endow the reconstruction with mathematical-level physical consistency guarantees, and 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. The framework is in principle transferable to other modulation-imaging instruments such as Solar Orbiter/STIX and Yohkoh/HXT; its deterministic, millisecond-level inference and energy-conservation properties are suitable for real-time flare monitoring and batch processing. Hard X-ray imaging; Solar flares; Deep learning; Image inversion; Modulation imaging; Physics-informed neural networks zousizhong PUBLIC https://api.github.com/licenses/apache-2.0 dataset Science Data Bank