arXiv subjects

Zhipeng Chang

Publications and source records attributed to Zhipeng Chang.

8 recordsLinked to original sources

arXiv2026

PatternFormer: Learning Multiple Solution Patterns in Reaction--Diffusion Systems

Many nonlinear models across physics, chemistry, and biology exhibit multiple solutions for the same parameters, and capturing this entire solution set is essential for understanding pattern-forming systems. Yet existing learned surrogates are fundamentally single-valued: neural operators map each parameter to a single output, and physics-informed neural networks converge to one branch. We develop \textbf{PatternFormer} (PF), a large language model-based framework for learning the multiple solutions of nonlinear partial differential equations. By transforming unordered coexisting solutions into canonical sequences, PF produces structured solution sets in a single autoregressive pass, terminating automatically for finite families and enforcing physical residual constraints for unbounded ones. On nonlinear elliptic problems it recovers all solution branches in one inference step; on Gray--Scott it generates coexisting Turing patterns, including physically valid states absent from the reference data and beyond training. PF can also be sequentially fine-tuned across multistable systems, toward general foundation models for solution landscapes.

math-ph↗

arXiv2026

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.

math.NA↗

arXiv2026

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.

cs.LG↗

arXiv2025

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.

cs.LG↗

arXiv2025

A Kolmogorov High Order Deep Neural Network for High Frequency Partial Differential Equations in High Dimensions

This paper proposes a Kolmogorov high order deep neural network (K-HOrderDNN) for solving high-dimensional partial differential equations (PDEs), which improves the high order deep neural networks (HOrderDNNs). HOrderDNNs have been demonstrated to outperform conventional DNNs for high frequency problems by introducing a nonlinear transformation layer consisting of $(p+1)^d$ basis functions. However, the number of basis functions grows exponentially with the dimension $d$, which results in the curse of dimensionality (CoD). Inspired by the Kolmogorov superposition theorem (KST), which expresses a multivariate function as superpositions of univariate functions and addition, K-HOrderDNN utilizes a HOrderDNN to efficiently approximate univariate inner functions instead of directly approximating the multivariate function, reducing the number of introduced basis functions to $d(p+1)$. We theoretically demonstrate that CoD is mitigated when target functions belong to a dense subset of continuous multivariate functions. Extensive numerical experiments show that: for high-dimensional problems ($d$=10, 20, 50) where HOrderDNNs($p>1$) are intractable, K-HOrderDNNs($p>1$) exhibit remarkable performance. Specifically, when $d=10$, K-HOrderDNN($p=7$) achieves an error of 4.40E-03, two orders of magnitude lower than that of HOrderDNN($p=1$) (see Table 10); for high frequency problems, K-HOrderDNNs($p>1$) can achieve higher accuracy with fewer parameters and faster convergence rates compared to HOrderDNNs (see Table 8).

math.NA↗

arXiv2024

Computing ground states of Bose-Einstein condensation by normalized deep neural network

We propose a normalized deep neural network (norm-DNN) for computing ground states of Bose-Einstein condensation (BEC) via the minimization of the Gross-Pitaevskii energy functional under unitary mass normalization. Compared with the traditional deep neural network for solving partial differential equations, two additional layers are added in training our norm-DNN for solving this kind of unitary constraint minimization problems: (i) a normalization layer is introduced to enforce the unitary mass normalization, and (ii) a shift layer is added to guide the training to non-negative ground state. The proposed norm-DNN gives rise to an efficient unsupervised approach for learning ground states of BEC. Systematical investigations are first carried out through extensive numerical experiments for computing ground states of BEC in one dimension. Extensions to high dimensions and multi-component are then studied in details. The results demonstrate the effectiveness and efficiency of norm-DNN for learning ground states of BEC. Finally, we extend the norm-DNN for computing the first excited states of BEC and discuss parameter generalization issues as well as compare with some existing machine learning methods for computing ground states of BEC in the literature.

cond-mat.quant-gas↗

arXiv2023

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

cs.CV↗

arXiv2022

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.

cs.CV↗