Guanyu Zhou

Hongyan Li, Song Jiang, Wenjun Sun et al.

We propose a model-data asymptotic-preserving neural network(MD-APNN) method to solve the nonlinear gray radiative transfer equations(GRTEs). The system is challenging to be simulated with both the traditional numerical schemes and the vanilla physics-informed neural networks(PINNs) due to the multiscale characteristics. Under the framework of PINNs, we employ a micro-macro decomposition technique to construct a new asymptotic-preserving(AP) loss function, which includes the residual of the governing equations in the micro-macro coupled form, the initial and boundary conditions with additional diffusion limit information, the conservation laws, and a few labeled data. A convergence analysis is performed for the proposed method, and a number of numerical examples are presented to illustrate the efficiency of MD-APNNs, and particularly, the importance of the AP property in the neural networks for the diffusion dominating problems. The numerical results indicate that MD-APNNs lead to a better performance than APNNs or pure data-driven networks in the simulation of the nonlinear non-stationary GRTEs.

Shenghao Zhu, Yifei Chen, Weihong Chen et al.

Accurate brain tumor segmentation is essential for preoperative evaluation and personalized treatment. Multi-modal MRI is widely used due to its ability to capture complementary tumor features across different sequences. However, in clinical practice, missing modalities are common, limiting the robustness and generalizability of existing deep learning methods that rely on complete inputs, especially under non-dominant modality combinations. To address this, we propose AdaMM, a multi-modal brain tumor segmentation framework tailored for missing-modality scenarios, centered on knowledge distillation and composed of three synergistic modules. The Graph-guided Adaptive Refinement Module explicitly models semantic associations between generalizable and modality-specific features, enhancing adaptability to modality absence. The Bi-Bottleneck Distillation Module transfers structural and textural knowledge from teacher to student models via global style matching and adversarial feature alignment. The Lesion-Presence-Guided Reliability Module predicts prior probabilities of lesion types through an auxiliary classification task, effectively suppressing false positives under incomplete inputs. Extensive experiments on the BraTS 2018 and 2024 datasets demonstrate that AdaMM consistently outperforms existing methods, exhibiting superior segmentation accuracy and robustness, particularly in single-modality and weak-modality configurations. In addition, we conduct a systematic evaluation of six categories of missing-modality strategies, confirming the superiority of knowledge distillation and offering practical guidance for method selection and future research. Our source code is available at https://github.com/Quanato607/AdaMM.

Hongyan Li, Song Jiang, Wenjun Sun et al.

We develop a Macroscopic Auxiliary Asymptotic-Preserving Neural Network (MA-APNN) method to solve the time-dependent linear radiative transfer equations (LRTEs), which have a multi-scale nature and high dimensionality. To achieve this, we utilize the Physics-Informed Neural Networks (PINNs) framework and design a new adaptive exponentially weighted Asymptotic-Preserving (AP) loss function, which incorporates the macroscopic auxiliary equation that is derived from the original transfer equation directly and explicitly contains the information of the diffusion limit equation. Thus, as the scale parameter tends to zero, the loss function gradually transitions from the transport state to the diffusion limit state. In addition, the initial data, boundary conditions, and conservation laws serve as the regularization terms for the loss. We present several numerical examples to demonstrate the effectiveness of MA-APNNs.