Kang Yang

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.

Qigong Sun, Xiufang Li, Fanhua Shang et al.

The training of deep neural networks (DNNs) always requires intensive resources for both computation and data storage. Thus, DNNs cannot be efficiently applied to mobile phones and embedded devices, which severely limits their applicability in industrial applications. To address this issue, we propose a novel encoding scheme using {-1, +1} to decompose quantized neural networks (QNNs) into multi-branch binary networks, which can be efficiently implemented by bitwise operations (i.e., xnor and bitcount) to achieve model compression, computational acceleration, and resource saving. By using our method, users can achieve different encoding precisions arbitrarily according to their requirements and hardware resources. The proposed mechanism is highly suitable for the use of FPGA and ASIC in terms of data storage and computation, which provides a feasible idea for smart chips. We validate the effectiveness of our method on large-scale image classification (e.g., ImageNet), object detection, and semantic segmentation tasks. In particular, our method with low-bit encoding can still achieve almost the same performance as its high-bit counterparts.

Yangchun Yan, Rongzuo Guo, Chao Li et al.

Channel pruning has demonstrated its effectiveness in compressing ConvNets. In many related arts, the importance of an output feature map is only determined by its associated filter. However, these methods ignore a small part of weights in the next layer which disappears as the feature map is removed. They ignore the phenomenon of weight dependency. Besides, many pruning methods use only one criterion for evaluation and find a sweet spot of pruning structure and accuracy in a trial-and-error fashion, which can be time-consuming. In this paper, we proposed a channel pruning algorithm via multi-criteria based on weight dependency, CPMC, which can compress a pre-trained model directly. CPMC defines channel importance in three aspects, including its associated weight value, computational cost, and parameter quantity. According to the phenomenon of weight dependency, CPMC gets channel importance by assessing its associated filter and the corresponding partial weights in the next layer. Then CPMC uses global normalization to achieve cross-layer comparison. Finally, CPMC removes less important channels by global ranking. CPMC can compress various CNN models, including VGGNet, ResNet, and DenseNet on various image classification datasets. Extensive experiments have shown CPMC outperforms the others significantly.

Jianrong Xu, Boyu Diao, Bifeng Cui et al.

Deep learning has achieved impressive results in many areas, but the deployment of edge intelligent devices is still very slow. To solve this problem, we propose a novel compression and acceleration method based on data distribution characteristics for deep neural networks, namely Pruning Filter via Gaussian Distribution Feature (PFGDF). Compared with previous advanced pruning methods, PFGDF compresses the model by filters with insignificance in distribution, regardless of the contribution and sensitivity information of the convolution filter. PFGDF is significantly different from weight sparsification pruning because it does not require the special accelerated library to process the sparse weight matrix and introduces no more extra parameters. The pruning process of PFGDF is automated. Furthermore, the model compressed by PFGDF can restore the same performance as the uncompressed model. We evaluate PFGDF through extensive experiments, on CIFAR-10, PFGDF compresses the convolution filter on VGG-16 by 66.62% with more than 90% parameter reduced, while the inference time is accelerated by 83.73% on Huawei MATE 10.

Qigong Sun, Fanhua Shang, Kang Yang et al.

The training of deep neural networks (DNNs) requires intensive resources both for computation and for storage performance. Thus, DNNs cannot be efficiently applied to mobile phones and embedded devices, which seriously limits their applicability in industry applications. To address this issue, we propose a novel encoding scheme of using {-1,+1} to decompose quantized neural networks (QNNs) into multi-branch binary networks, which can be efficiently implemented by bitwise operations (xnor and bitcount) to achieve model compression, computational acceleration and resource saving. Based on our method, users can easily achieve different encoding precisions arbitrarily according to their requirements and hardware resources. The proposed mechanism is very suitable for the use of FPGA and ASIC in terms of data storage and computation, which provides a feasible idea for smart chips. We validate the effectiveness of our method on both large-scale image classification tasks (e.g., ImageNet) and object detection tasks. In particular, our method with low-bit encoding can still achieve almost the same performance as its full-precision counterparts.