Xin Li

Ting Yu Tsai, Liangqiao Gui, Yineng Chen et al.

Deep learning models have achieved significant success in segmenting cardiovascular structures, but there is a growing need to improve their generalization and robustness. Current methods often face challenges such as overfitting and limited accuracy, largely due to their reliance on large annotated datasets and limited optimization techniques. This paper introduces the UU-Mamba model, an extension of the U-Mamba architecture, designed to address these challenges in both cardiac and vascular segmentation. By incorporating Sharpness-Aware Minimization (SAM), the model enhances generalization by seeking flatter minima in the loss landscape. Additionally, we propose an uncertainty-aware loss function that integrates region-based, distribution-based, and pixel-based components, improving segmentation accuracy by capturing both local and global features. We expand our evaluations on the ImageCAS (coronary artery) and Aorta (aortic branches and zones) datasets, which present more complex segmentation challenges than the ACDC dataset (left and right ventricles) used in prior work, showcasing the model's adaptability and resilience. Our results confirm UU-Mamba's superior performance compared to leading models such as TransUNet, Swin-Unet, nnUNet, and nnFormer. We also provide a more in-depth assessment of the model's robustness and segmentation accuracy through extensive experiments.

Xin Li, Chengli Zhao, Xue Zhang et al.

Differential equations are widely used to describe complex dynamical systems with evolving parameters in nature and engineering. Effectively learning a family of maps from the parameter function to the system dynamics is of great significance. In this study, we propose a novel learning framework of symbolic continuous-depth neural networks, termed Symbolic Neural Ordinary Differential Equations (SNODEs), to effectively and accurately learn the underlying dynamics of complex systems. Specifically, our learning framework comprises three stages: initially, pre-training a predefined symbolic neural network via a gradient flow matching strategy; subsequently, fine-tuning this network using Neural ODEs; and finally, constructing a general neural network to capture residuals. In this process, we apply the SNODEs framework to partial differential equation systems through Fourier analysis, achieving resolution-invariant modeling. Moreover, this framework integrates the strengths of symbolism and connectionism, boasting a universal approximation theorem while significantly enhancing interpretability and extrapolation capabilities relative to state-of-the-art baseline methods. We demonstrate this through experiments on several representative complex systems. Therefore, our framework can be further applied to a wide range of scientific problems, such as system bifurcation and control, reconstruction and forecasting, as well as the discovery of new equations.