Chenchen Wan

Lei Li, Yunxiao Liu, Chenchen Wan

We propose a quasi-random operator splitting method for evolution equations driven by multiple mechanisms. The method uses a low-discrepancy sequence to generate the ordering of the subflows, while requiring only one application of each subflow per time step. In particular, for a decomposition into \(p\) operators, the classical multi-operator Strang splitting requires essentially \(2p-2\) subflow evaluations per step, whereas the present method uses only \(p\). In contrast to randomized splitting, the quasi-random scheme is deterministic once the underlying sequence is fixed, so its improved accuracy is achieved in a single run rather than through averaging over many independent realizations. To analyze this method, we develop a convergence framework that exploits the discrepancy structure of the induced ordering sequence and translates it into cancellation in the accumulated local errors. For two operators, this yields an essentially second-order global error bound of order \(O(τ^{2}|\log τ|)\) for bounded linear problems. We further extend the analysis to the Allen--Cahn equation and present numerical experiments, including bounded linear systems and the Allen--Cahn equation, which confirm the predicted convergence behavior and demonstrate that the proposed method achieves near-Strang accuracy at a substantially lower computational cost.

Jiayang Bai, Jie Guo, Chenchen Wan et al.

Lighting prediction from a single image is becoming increasingly important in many vision and augmented reality (AR) applications in which shading and shadow consistency between virtual and real objects should be guaranteed. However, this is a notoriously ill-posed problem, especially for indoor scenarios, because of the complexity of indoor luminaires and the limited information involved in 2D images. In this paper, we propose a graph learning-based framework for indoor lighting estimation. At its core is a new lighting model (dubbed DSGLight) based on depth-augmented Spherical Gaussians (SG) and a Graph Convolutional Network (GCN) that infers the new lighting representation from a single LDR image of limited field-of-view. Our lighting model builds 128 evenly distributed SGs over the indoor panorama, where each SG encoding the lighting and the depth around that node. The proposed GCN then learns the mapping from the input image to DSGLight. Compared with existing lighting models, our DSGLight encodes both direct lighting and indirect environmental lighting more faithfully and compactly. It also makes network training and inference more stable. The estimated depth distribution enables temporally stable shading and shadows under spatially-varying lighting. Through thorough experiments, we show that our method obviously outperforms existing methods both qualitatively and quantitatively.