Bei Hua

Xiang Huang, Zhuoyuan Li, Hongsheng Liu et al.

Recently, using neural networks to simulate spatio-temporal dynamics has received a lot of attention. However, most existing methods adopt pure data-driven black-box models, which have limited accuracy and interpretability. By combining trainable difference operators with black-box models, we propose a new hybrid architecture explicitly embedded with partial prior knowledge of the underlying PDEs named PDE-Net++. Furthermore, we introduce two distinct options called the trainable flipping difference layer (TFDL) and the trainable dynamic difference layer (TDDL) for the difference operators. Numerous numerical experiments have demonstrated that PDE-Net++ has superior prediction accuracy and better extrapolation performance than black-box models.

Yu Sheng, Jiajun Deng, Xinran Zhang et al.

A major breakthrough in 3D reconstruction is the feedforward paradigm to generate pixel-wise 3D points or Gaussian primitives from sparse, unposed images. To further incorporate semantics while avoiding the significant memory and storage costs of high-dimensional semantic features, existing methods extend this paradigm by associating each primitive with a compressed semantic feature vector. However, these methods have two major limitations: (a) the naively compressed feature compromises expressiveness, affecting the model's ability to capture fine-grained semantics, and (b) the pixel-wise primitive prediction introduces redundancy in overlapping areas, causing unnecessary memory overhead. To this end, we introduce \textbf{SpatialSplat}, a feedforward framework that produces redundancy-aware Gaussians and capitalizes on a dual-field semantic representation. Particularly, with the insight that primitives within the same instance exhibit high semantic consistency, we decompose the semantic representation into a coarse feature field that encodes uncompressed semantics with minimal primitives, and a fine-grained yet low-dimensional feature field that captures detailed inter-instance relationships. Moreover, we propose a selective Gaussian mechanism, which retains only essential Gaussians in the scene, effectively eliminating redundant primitives. Our proposed Spatialsplat learns accurate semantic information and detailed instances prior with more compact 3D Gaussians, making semantic 3D reconstruction more applicable. We conduct extensive experiments to evaluate our method, demonstrating a remarkable 60\% reduction in scene representation parameters while achieving superior performance over state-of-the-art methods. The code is available at https://github.com/shengyuuu/SpatialSplat.git

Xiang Huang, Zhanhong Ye, Hongsheng Liu et al.

Many important problems in science and engineering require solving the so-called parametric partial differential equations (PDEs), i.e., PDEs with different physical parameters, boundary conditions, shapes of computation domains, etc. Recently, building learning-based numerical solvers for parametric PDEs has become an emerging new field. One category of methods such as the Deep Galerkin Method (DGM) and Physics-Informed Neural Networks (PINNs) aim to approximate the solution of the PDEs. They are typically unsupervised and mesh-free, but require going through the time-consuming network training process from scratch for each set of parameters of the PDE. Another category of methods such as Fourier Neural Operator (FNO) and Deep Operator Network (DeepONet) try to approximate the solution mapping directly. Being fast with only one forward inference for each PDE parameter without retraining, they often require a large corpus of paired input-output observations drawn from numerical simulations, and most of them need a predefined mesh as well. In this paper, we propose Meta-Auto-Decoder (MAD), a mesh-free and unsupervised deep learning method that enables the pre-trained model to be quickly adapted to equation instances by implicitly encoding (possibly heterogenous) PDE parameters as latent vectors. The proposed method MAD can be interpreted by manifold learning in infinite-dimensional spaces, granting it a geometric insight. Extensive numerical experiments show that the MAD method exhibits faster convergence speed without losing accuracy than other deep learning-based methods. The project page with code is available: https://gitee.com/mindspore/mindscience/tree/master/MindElec/.

Xiang Huang, Hongsheng Liu, Beiji Shi et al.

In recent years, deep learning technology has been used to solve partial differential equations (PDEs), among which the physics-informed neural networks (PINNs) emerges to be a promising method for solving both forward and inverse PDE problems. PDEs with a point source that is expressed as a Dirac delta function in the governing equations are mathematical models of many physical processes. However, they cannot be solved directly by conventional PINNs method due to the singularity brought by the Dirac delta function. We propose a universal solution to tackle this problem with three novel techniques. Firstly the Dirac delta function is modeled as a continuous probability density function to eliminate the singularity; secondly a lower bound constrained uncertainty weighting algorithm is proposed to balance the PINNs losses between point source area and other areas; and thirdly a multi-scale deep neural network with periodic activation function is used to improve the accuracy and convergence speed of the PINNs method. We evaluate the proposed method with three representative PDEs, and the experimental results show that our method outperforms existing deep learning-based methods with respect to the accuracy, the efficiency and the versatility.