Kaixuan Zhang

Jianing Huang, Kaixuan Zhang, Youjia Wu et al.

Neural operators have become increasingly popular in solving \textit{partial differential equations} (PDEs) due to their superior capability to capture intricate mappings between function spaces over complex domains. However, the data-hungry nature of operator learning inevitably poses a bottleneck for their widespread applications. At the core of the challenge lies the absence of transferability of neural operators to new geometries. To tackle this issue, we propose operator learning with domain decomposition, a local-to-global framework to solve PDEs on arbitrary geometries. Under this framework, we devise an iterative scheme \textit{Schwarz Neural Inference} (SNI). This scheme allows for partitioning of the problem domain into smaller subdomains, on which local problems can be solved with neural operators, and stitching local solutions to construct a global solution. Additionally, we provide a theoretical analysis of the convergence rate and error bound. We conduct extensive experiments on several representative PDEs with diverse boundary conditions and achieve remarkable geometry generalization compared to alternative methods. These analysis and experiments demonstrate the proposed framework's potential in addressing challenges related to geometry generalization and data efficiency.

Kaixuan Zhang, Hu Wang, Minxian Li et al.

High Dynamic Range Novel View Synthesis (HDR-NVS) aims to establish a 3D scene HDR model from Low Dynamic Range (LDR) imagery. Typically, multiple-exposure LDR images are employed to capture a wider range of brightness levels in a scene, as a single LDR image cannot represent both the brightest and darkest regions simultaneously. While effective, this multiple-exposure HDR-NVS approach has significant limitations, including susceptibility to motion artifacts (e.g., ghosting and blurring), high capture and storage costs. To overcome these challenges, we introduce, for the first time, the single-exposure HDR-NVS problem, where only single exposure LDR images are available during training. We further introduce a novel approach, Mono-HDR-3D, featuring two dedicated modules formulated by the LDR image formation principles, one for converting LDR colors to HDR counterparts, and the other for transforming HDR images to LDR format so that unsupervised learning is enabled in a closed loop. Designed as a meta-algorithm, our approach can be seamlessly integrated with existing NVS models. Extensive experiments show that Mono-HDR-3D significantly outperforms previous methods. Source code will be released.

Zheng Wang, Kaixuan Zhang, Wanfang Chen et al.

Time series forecasting remains a critical challenge across numerous domains, yet the effectiveness of complex models often varies unpredictably across datasets. Recent studies highlight the surprising competitiveness of simple linear models, suggesting that their robustness and interpretability warrant deeper theoretical investigation. This paper presents a systematic study of linear models for time series forecasting, with a focus on the role of characteristic roots in temporal dynamics. We begin by analyzing the noise-free setting, where we show that characteristic roots govern long-term behavior and explain how design choices such as instance normalization and channel independence affect model capabilities. We then extend our analysis to the noisy regime, revealing that models tend to produce spurious roots. This leads to the identification of a key data-scaling property: mitigating the influence of noise requires disproportionately large training data, highlighting the need for structural regularization. To address these challenges, we propose two complementary strategies for robust root restructuring. The first uses rank reduction techniques, including Reduced-Rank Regression and Direct Weight Rank Reduction, to recover the low-dimensional latent dynamics. The second, a novel adaptive method called Root Purge, encourages the model to learn a noise-suppressing null space during training. Extensive experiments on standard benchmarks demonstrate the effectiveness of both approaches, validating our theoretical insights and achieving state-of-the-art results in several settings. Our findings underscore the potential of integrating classical theories for linear systems with modern learning techniques to build robust, interpretable, and data-efficient forecasting models.

Kaixuan Zhang, Zhipeng Xiong, Minxian Li et al.

High Dynamic Range Novel View Synthesis (HDR NVS) seeks to learn an HDR 3D model from Low Dynamic Range (LDR) training images captured under conventional imaging conditions. Current methods primarily focus on static scenes, implicitly assuming all scene elements remain stationary and non-living. However, real-world scenarios frequently feature dynamic elements, such as moving objects, varying lighting conditions, and other temporal events, thereby presenting a significantly more challenging scenario. To address this gap, we propose a more realistic problem named HDR Dynamic Novel View Synthesis (HDR DNVS), where the additional dimension ``Dynamic'' emphasizes the necessity of jointly modeling temporal radiance variations alongside sophisticated 3D translation between LDR and HDR. To tackle this complex, intertwined challenge, we introduce HDR-4DGS, a Gaussian Splatting-based architecture featured with an innovative dynamic tone-mapping module that explicitly connects HDR and LDR domains, maintaining temporal radiance coherence by dynamically adapting tone-mapping functions according to the evolving radiance distributions across the temporal dimension. As a result, HDR-4DGS achieves both temporal radiance consistency and spatially accurate color translation, enabling photorealistic HDR renderings from arbitrary viewpoints and time instances. Extensive experiments demonstrate that HDR-4DGS surpasses existing state-of-the-art methods in both quantitative performance and visual fidelity. Source code will be released.