SVD-Preconditioned Gradient Descent Method for Solving Nonlinear Least Squares Problems

This paper introduces a novel optimization algorithm designed for nonlinear least-squares problems. The method is derived by preconditioning the gradient descent direction using the Singular Value Decomposition (SVD) of the Jacobian. This SVD-based preconditioner is then integrated with the first- and second-moment adaptive learning rate mechanism of the Adam optimizer. We establish the local linear convergence of the proposed method under standard regularity assumptions and prove global convergence for a modified version of the algorithm under suitable conditions. The effectiveness of the approach is demonstrated experimentally across a range of tasks, including function approximation, partial differential equation (PDE) solving, and image classification on the CIFAR-10 dataset. Results show that the proposed method consistently outperforms standard Adam, achieving faster convergence and lower error in both regression and classification settings.

Fisher-Informed Parameterwise Aggregation for Federated Learning with Heterogeneous Data

Federated learning aggregates model updates from distributed clients, but standard first order methods such as FedAvg apply the same scalar weight to all parameters from each client. Under non-IID data, these uniformly weighted updates can be strongly misaligned across clients, causing client drift and degrading the global model. Here we propose Fisher-Informed Parameterwise Aggregation (FIPA), a second-order aggregation method that replaces client-level scalar weights with parameter-specific Fisher Information Matrix (FIM) weights, enabling true parameter-level scaling that captures how each client's data uniquely influences different parameters. With low-rank approximation, FIPA remains communication- and computation-efficient. Across nonlinear function regression, PDE learning, and image classification, FIPA consistently improves over averaging-based aggregation, and can be effectively combined with state-of-the-art client-side optimization algorithms to further improve image classification accuracy. These results highlight the benefits of FIPA for federated learning under heterogeneous data distributions.

Unsupervised operator learning approach for dissipative equations via Onsager principle

Existing operator learning methods rely on supervised training with high-fidelity simulation data, introducing significant computational cost. In this work, we propose the deep Onsager operator learning (DOOL) method, a novel unsupervised framework for solving dissipative equations. Rooted in the Onsager variational principle (OVP), DOOL trains a deep operator network by directly minimizing the OVP-defined Rayleighian functional, requiring no labeled data, and then proceeds in time explicitly through conservation/change laws for the solution. Another key innovation here lies in the spatiotemporal decoupling strategy: the operator's trunk network processes spatial coordinates exclusively, thereby enhancing training efficiency, while integrated external time stepping enables temporal extrapolation. Numerical experiments on typical dissipative equations validate the effectiveness of the DOOL method, and systematic comparisons with supervised DeepONet and MIONet demonstrate its enhanced performance. Extensions are made to cover the second-order wave models with dissipation that do not directly follow OVP.

Pedestrain detection for low-light vision proposal

The demand for pedestrian detection has created a challenging problem for various visual tasks such as image fusion. As infrared images can capture thermal radiation information, image fusion between infrared and visible images could significantly improve target detection under environmental limitations. In our project, we would approach by preprocessing our dataset with image fusion technique, then using Vision Transformer model to detect pedestrians from the fused images. During the evaluation procedure, a comparison would be made between YOLOv5 and the revised ViT model performance on our fused images

Linear features segmentation from aerial images

The rapid development of remote sensing technologies have gained significant attention due to their ability to accurately localize, classify, and segment objects from aerial images. These technologies are commonly used in unmanned aerial vehicles (UAVs) equipped with high-resolution cameras or sensors to capture data over large areas. This data is useful for various applications, such as monitoring and inspecting cities, towns, and terrains. In this paper, we presented a method for classifying and segmenting city road traffic dashed lines from aerial images using deep learning models such as U-Net and SegNet. The annotated data is used to train these models, which are then used to classify and segment the aerial image into two classes: dashed lines and non-dashed lines. However, the deep learning model may not be able to identify all dashed lines due to poor painting or occlusion by trees or shadows. To address this issue, we proposed a method to add missed lines to the segmentation output. We also extracted the x and y coordinates of each dashed line from the segmentation output, which can be used by city planners to construct a CAD file for digital visualization of the roads.