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.

At present, SOILD-STATE Fermentation (SSF) is mainly controlled by artificial experience, and the product quality and yield are not stable. Accurately predicting the quality and yield of SSF is of great significance for improving human food security and supply. In this paper, we propose an Intelligent Utility Prediction (IUP) scheme for SSF in 5G Industrial Internet of Things (IoT), including parameter collection and utility prediction of SSF process. This IUP scheme is based on the environmental perception and intelligent learning algorithms of the 5G Industrial IoT. We build a workflow model based on rewritable petri net to verify the correctness of the system model function and process. In addition, we design a utility prediction model for SSF based on the Generative Adversarial Networks (GAN) and Fully Connected Neural Network (FCNN). We design a GAN with constraint of mean square error (MSE-GAN) to solve the problem of few-shot learning of SSF, and then combine with the FCNN to realize the utility prediction (usually use the alcohol) of SSF. Based on the production of liquor in laboratory, the experiments show that the proposed method is more accurate than the other prediction methods in the utility prediction of SSF, and provide the basis for the numerical analysis of the proportion of preconfigured raw materials and the appropriate setting of cellar temperature.

This paper concerns the a priori generalization analysis of the Deep Ritz Method (DRM) [W. E and B. Yu, 2017], a popular neural-network-based method for solving high dimensional partial differential equations. We derive the generalization error bounds of two-layer neural networks in the framework of the DRM for solving two prototype elliptic PDEs: Poisson equation and static Schr\"odinger equation on the $d$-dimensional unit hypercube. Specifically, we prove that the convergence rates of generalization errors are independent of the dimension $d$, under the a priori assumption that the exact solutions of the PDEs lie in a suitable low-complexity space called spectral Barron space. Moreover, we give sufficient conditions on the forcing term and the potential function which guarantee that the solutions are spectral Barron functions. We achieve this by developing a new solution theory for the PDEs on the spectral Barron space, which can be viewed as an analog of the classical Sobolev regularity theory for PDEs.

Large size models are implemented in recently ASR system to deal with complex speech recognition problems. The num- ber of parameters in these models makes them hard to deploy, especially on some resource-short devices such as car tablet. Besides this, at most of time, ASR system is used to deal with real-time problem such as keyword spotting (KWS). It is contradictory to the fact that large model requires long com- putation time. To deal with this problem, we apply some sparse algo- rithms to reduces number of parameters in some widely used models, Deep Neural Network (DNN) KWS, which requires real short computation time. We can prune more than 90 % even 95% of parameters in the model with tiny effect decline. And the sparse model performs better than baseline models which has same order number of parameters. Besides this, sparse algorithm can lead us to find rational model size au- tomatically for certain problem without concerning choosing an original model size.

Hypernymy identification aims at detecting if isA relationship holds between two words or phrases. Most previous methods are based on lexical patterns or the Distributional Inclusion Hypothesis, and the accuracy of such methods is not ideal. In this paper, we propose a simple yet effective supervision framework to identify hypernymy relations using distributed term representations (a.k.a term embeddings). First, we design a distance-margin neural network to learn term embeddings based on some pre-extracted hypernymy data. Then, we apply such embeddings as term features to identify positive hypernymy pairs through a supervision method. Experimental results demonstrate that our approach outperforms other supervised methods on two popular datasets and the learned term embeddings has better quality than existing term distributed representations with respect to hypernymy identification.