Accelerating Liquid Simulation With an Improved Data-Driven Method

In physics-based liquid simulation for graphics applications, pressure projection consumes a significant amount of computational time and is frequently the bottleneck of the computational efficiency. How to rapidly apply the pressure projection and at the same time how to accurately capture the liquid geometry are always among the most popular topics in the current research trend in liquid simulations. In this paper, we incorporate an artificial neural network into the simulation pipeline for handling the tricky projection step for liquid animation. Compared with the previous neural-network-based works for gas flows, this paper advocates new advances in the composition of representative features as well as the loss functions in order to facilitate fluid simulation with free-surface boundary. Specifically, we choose both the velocity and the level-set function as the additional representation of the fluid states, which allows not only the motion but also the boundary position to be considered in the neural network solver. Meanwhile, we use the divergence error in the loss function to further emulate the lifelike behaviours of liquid. With these arrangements, our method could greatly accelerate the pressure projection step in liquid simulation, while maintaining fairly convincing visual results. Additionally, our neutral network performs well when being applied to new scene synthesis even with varied boundaries or scales.     

Representation of Nonlinear Random Transformations by Non-Gaussian Stochastic Neural Networks

The learning capability of neural networks is equivalent to modeling physical events that occur in the real environment. Several early works have demonstrated that neural networks belonging to some classes are universal approximators of input-output deterministic functions. Recent works extend the ability of neural networks in approximating random functions using a class of networks named stochastic neural networks (SNN). In the language of system theory, the approximation of both deterministic and stochastic functions falls within the identification of nonlinear no-memory systems. However, all the results presented so far are restricted to the case of Gaussian stochastic processes (SPs) only, or to linear transformations that guarantee this property. This paper aims at investigating the ability of stochastic neural networks to approximate nonlinear input-output random transformations, thus widening the range of applicability of these networks to nonlinear systems with memory. In particular, this study shows that networks belonging to a class named non-Gaussian stochastic approximate identity neural networks (SAINNs) are capable of approximating the solutions of large classes of nonlinear random ordinary differential transformations. The effectiveness of this approach is demonstrated and discussed by some application examples.     

字典神经网络方法快速湍流烟雾合成

目的 基于物理的烟雾模拟是计算机图形学的重要组成部分,渲染具有细小结构的高分辨率烟雾,需要大量的计算资源和高精度的数值求解方法。针对目前高精度湍流烟雾模拟速度慢,仿真困难的现状,提出了基于字典神经网络的方法,能够快速合成湍流烟雾,使得合成的结果增加细节的同时,保持高分辨率烟雾结果的重要结构信息。方法 使用高精度的数值仿真求解方法获得高分辨率和低分辨率的湍流烟雾数据,通过采集速度场局部块及相应的空间位置信息和时间特征生成数据集, 设计字典神经网络的网络架构,训练烟雾高频成分字典预测器,在GPU（graphic processing unit）上实现并行化,快速合成高分辨率的湍流烟雾结果。结果 实验表明,基于字典神经网络的方法能够在非常低分辨率的烟雾数据下合成空间和时间上连续的高分辨率湍流烟雾结果,效率比通过在GPU平台上直接仿真得到高分辨率湍流烟雾的结果快了一个数量级,且合成的烟雾结果与数值仿真方法得到的高分辨率湍流烟雾结果足够接近。结论 本文方法解决了烟雾的上采样问题,能够从非常低分辨率的烟雾仿真结果,通过设计基于字典神经网络结构以及特征描述符编码烟雾速度场的局部和全局信息,快速合成高分辨率湍流烟雾结果,且保持高精度烟雾的细节,与数值仿真方法的对比表明了本文方法的有效性。     

Nonlinear Systems Identification via Two Types of Recurrent Fuzzy CMAC

Normal fuzzy CMAC neural network performs well for nonlinear systems identification because of its fast learning speed and local generalization capability for approximating nonlinear functions. However, it requires huge memory and the dimension increases exponentially with the number of inputs. It is difficult to model dynamic systems with static fuzzy CMACs. In this paper, we use two types of recurrent techniques for fuzzy CMAC to overcome the above problems. The new CMAC neural networks are named recurrent fuzzy CMAC (RFCMAC) which add feedback connections in the inner layers (local feedback) or the output layer (global feedback). The corresponding learning algorithms have time-varying learning rates, the stabilities of the neural identifications are proven.     

基于函数正交基展开的过程神经网络学习算法

过程神经网络的输入和连接权均可为时变函数，过程神经元增加了一个对于时间的聚合算子，使网络同时具有时空二维信息处理能力．该文在考虑过程神经网络对时间聚合运算的复杂性的基础上，提出了一种基于函数正交基展开的学习算法．在网络输入函数空间中选择一组适当的函数正交基，将输入函数和网络权函数都表示为该组正交基的展开形式，利用基函数的正交性．简化过程神经元对时间的聚合运算．应用表明，算法简化了过程神经网络的计算复杂度，提高了网络学习效率和对实际问题求解的适应性．以旋转机械故障诊断问题和油藏开发过程采收率的模拟为例验证了算法的有效性．     

Fuzzy wavelet networks for function learning

Inspired by the theory of multiresolution analysis (MRA) of wavelet transforms and fuzzy concepts, a fuzzy wavelet network (FWN) is proposed for approximating arbitrary nonlinear functions. The FWN consists of a set of fuzzy rules. Each rule corresponding to a sub-wavelet neural network (WNN) consists of single-scaling wavelets. Through efficient bases selection, the dimension of the approximated function does not cause the bottleneck for constructing FWN. Especially, by learning the translation parameters of the wavelets and adjusting the shape of membership functions, the model accuracy and the generalization capability of the FWN can be remarkably improved. Furthermore, an algorithm for constructing and training the fuzzy wavelet networks is proposed. Simulation examples are also given to illustrate the effectiveness of the method     

边收缩池化的网格变分自编码器

目的 3D形状分析是计算机视觉和图形学的一个重要研究课题。虽然现有方法使用基于图的卷积将基于图像的深度学习推广到3维网格,但缺乏有效的池化操作限制了其网络的学习能力。针对具有相同连通性,但几何形状不同的网格模型数据集,本文利用网格简化的边收缩操作建立网格层次结构,提出了一种新的网格池化操作。方法 本文改进了传统的网格简化方法,以避免生成高度不规则的三角形,利用改进的网格简化方法定义了新的网格池化操作。网格简化的边收缩操作建立的网格层次结构之间存在对应关系,有利于网格池化的定义。新定义的池化操作有效地编码了层次结构中较粗糙和较稠密网格之间的对应关系。最后提出了一种带有边收缩池化和图卷积的变分自编码器（variational auto-encoder,VAE）结构,以探索3D形状的隐空间并用于3D形状的生成。结果 由于引入了新定义的池化操作和图卷积操作,提出的网络结构比原始MeshVAE需要的参数更少,因此可以处理更稠密的网格模型。结论 实验表明提出的方法具有更好的泛化能力,并且在各种应用中更可靠,包括形状生成、形状插值和形状嵌入。     

一类基于神经网络非线性观测器的鲁棒故障检测

针对一类仿射非线性动态系统,提出了一种基 于神经网络非线性观测器的鲁棒故障检测与隔离的新方法．该方法采用神经网络逼近观测器 系统中的非线性项,提高了状态估计的精度,并从理论上证明了状态估计误差稳定且渐近收 敛到零;另一方面引入神经网络分类器进行故障的模式识别,通过在神经网络输入端加入噪 声项来进行训练,提高神经网络的泛化逼近能力,从而保证对被监测系统的建模误差和外部 扰动具有良好的鲁棒性．最后,利用本文方法针对某型歼击机结构故障进行仿真验证,仿真 结果表明本文方法是有效的．     

基于Chebyshey神经网络的非线性预测应用研究

将Chebyshev神经网络作为非线性时间序列的辨识模型,通过对过去序列样本的学习,调整网络的权值,然后预测和推断未来的序列,仿真结果表明,Chebyshev神经网络具有优良的泛化能力和预测功能。     

Constructive neural networks with piecewise interpolationcapabilities for function approximations

This paper proposes a constructive neural network with a piecewise linear or nonlinear local interpolation capability to approximate arbitrary continuous functions. This neural network is devised by introducing a space tessellation which is a covering of the Euclidean space by nonoverlapping hyperpolyhedral convex cells. In the proposed neural network, a number of neural network granules (NNG's) are processed in parallel and repeated regularly with the same structures. Each NNG does a local mapping with an interpolation capability for a corresponding hyperpolyhedral convex cell in a tessellation. The plastic weights of the NNG can be calculated to implement the mapping for training data; consequently, this reduces training time and alleviates the difficulties of local minima in training. In addition, the interpolation capability of the NNG improves the generalization for the new data within the convex cell. The proposed network requires additional neurons for tessellation over the standard multilayer neural networks. This increases the network size but does not slow the retrieval response when implemented by parallel architecture.     

ZerNet: Convolutional Neural Networks on Arbitrary Surfaces Via Zernike Local Tangent Space Estimation

In this paper, we propose a novel formulation extending convolutional neural networks (CNN) to arbitrary two-dimensional manifolds using orthogonal basis functions called Zernike polynomials. In many areas, geometric features play a key role in understanding scientific trends and phenomena, where accurate numerical quantification of geometric features is critical. Recently, CNNs have demonstrated a substantial improvement in extracting and codifying geometric features. However, the progress is mostly centred around computer vision and its applications where an inherent grid-like data representation is naturally present. In contrast, many geometry processing problems deal with curved surfaces and the application of CNNs is not trivial due to the lack of canonical grid-like representation, the absence of globally consistent orientation and the incompatible local discretizations. In this paper, we show that the Zernike polynomials allow rigourous yet practical mathematical generalization of CNNs to arbitrary surfaces. We prove that the convolution of two functions can be represented as a simple dot product between Zernike coefficients and the rotation of a convolution kernel is essentially a set of 2 × 2 rotation matrices applied to the coefficients. The key contribution of this work is in such a computationally efficient but rigorous generalization of the major CNN building blocks.     

An extended functional network model and its application for a gas sensing system

Functional networks (FNs) are a promising numerical scheme that produces accurate solutions for several problems in science and engineering with less computational effort than other conventional numerical techniques such as neural networks. By using domain knowledge in addition to data knowledge, functional networks can be regarded as a generalization of neural networks: they allow to design arbitrary functional models without neglecting possible functional constraints involved by the model. The computational efficiency of functional networks can be improved by combining this scheme with finite differences when highly oscillating systems have to be considered. The main focus of this paper is on the possible questions arising from the application of this combined scheme to an identification problem when non-smooth functions are involved and noisy data are possible. These issues are not covered by the current literature. An extended version, based on a piecewise approach, and a stability criterion are proposed and applied to the quantitative identification problem in a gas sensing system in its transient state. Numerical simulations show that our scheme allows good accuracy, avoiding the error accumulation and the sensitivity to noisy data by means of the stability criterion.     

基于范例的神经网络模型

引言 无论采用何种学习算法,神经网络一旦投入使用其性能主要体现在泛化能力上,泛化能力是指训练过的神经网络对测试样本或工作样本作出正确反应的能力,或推广应用能力.没有泛化能力的网络是没有实用价值的,如何将其有效地提高已成为神经网络领域最受关注的问题之一为此,国内外学者开展了大量的研究工作,并提出了诸多方法或措施,     

输入输出均为时变函数的过程神经网络及应用

为了解决实际系统中输入、输出经常是时变连续函数的问题,提出了一类基于基函数展开的过程神经元网络模型.该模型利用过程神经元网络所具有的对时间变量的非线性映射能力,实现系统的输入、输出之间的连续映射关系.另外,还给出了一种学习算法.为了简化计算,选择正交函数作为基函数,并以油藏开发仿真为例,验证了模型和算法的有效性.     

Improving signal prediction performance of neural networks through multiresolution learning approach.

In this paper, we extend the original work on multiresolution learning for neural networks, and present new developments on the multiresolution learning paradigm. The contributions of this paper include: (1) proposing a new concept and method of adjustable neural activation functions in multiresolution learning to improve neural network learning efficacy and generalization performance for signal predictions; (2) providing new insightful explanations for the multiresolution learning paradigm from a multiresolution optimization perspective; (3) exploring underlying ideas why the multiresolution learning scheme associated with adjustable activation functions would be more appropriate for the multiresolution learning paradigm; and (4) providing rigorous validations to evaluate the multiresolution learning paradigm with adjustable activation functions and comparing it with the schemes of multiresolution learning with fixed activation functions and traditional learning. This paper presents systematically new analytical and experimental results on the multiresolution learning approach for training an individual neural network model, demonstrates our integral solution on neural network learning efficacy, and illustrates the significant improvements on neural networks' generalization performance and robustness for nonlinear signal predictions.     

Neural networks that learn from fuzzy if-then rules

An architecture for neural networks that can handle fuzzy input vectors is proposed, and learning algorithms that utilize fuzzy if-then rules as well as numerical data in neural network learning for classification problems and for fuzzy control problems are derived. The learning algorithms can be viewed as an extension of the backpropagation algorithm to the case of fuzzy input vectors and fuzzy target outputs. Using the proposed methods, linguistic knowledge from human experts represented by fuzzy if-then rules and numerical data from measuring instruments can be integrated into a single information processing system (classification system or fuzzy control system). It is shown that the scheme works well for simple examples     

Shallow and deep learning for image classification

The paper is focused on the idea to demonstrate the advantages of deep learning approaches over ordinary shallow neural network on their comparative applications to image classifying from such popular benchmark databases as FERET and MNIST. An autoassociative neural network is used as a standalone program realized the nonlinear principal component analysis for prior extracting the most informative features of input data for neural networks to be compared further as classifiers. A special study of the optimal choice of activation function and the normalization transformation of input data allows to improve efficiency of the autoassociative program. One more study devoted to denoising properties of this program demonstrates its high efficiency even on noisy data. Three types of neural networks are compared: feed-forward neural net with one hidden layer, deep network with several hidden layers and deep belief network with several pretraining layers realized restricted Boltzmann machine. The number of hidden layer and the number of hidden neurons in them were chosen by cross-validation procedure to keep balance between number of layers and hidden neurons and classification efficiency. Results of our comparative study demonstrate the undoubted advantage of deep networks, as well as denoising power of autoencoders. In our work we use both multiprocessor graphic card and cloud services to speed up our calculations. The paper is oriented to specialists in concrete fields of scientific or experimental applications, who have already some knowledge about artificial neural networks, probability theory and numerical methods.     

基于recurrent neural networks的网约车供需预测方法

以网约车订单等真实数据为数据源,结合TensorFlow深度学习框架,利用循环神经网络（recurrent neural networks）方法,预测网约车在未来某时间某地点的订单需求量。提出改进LSTM RNN（长短时记忆循环神经网络）模型,经过对其优化和训练,能够有效预测网约车未来某时间某地点的供需量。对数据源进行可视化分析,排除不相关数据源干扰,以此为基础设计仿真实验。仿真实验表明,该模型的正确率比反向传播神经网络（BPNN）、回归决策树（DTR）、非线性回归支持向量机（SVR）以及随机漫步（RW）等模型高,同时,对长短间隔不同的历史数据有较好的记忆能力,在测试数据上有较强的泛化能力。     

Neural network-based robust adaptive control of nonlinear systems with unmodeled dynamics

A neural network-based robust adaptive control design scheme is developed for a class of nonlinear systems represented by input–output models with an unknown nonlinear function and unmodeled dynamics. By on-line approximating the unknown nonlinear functions and unmodeled dynamics by radial basis function (RBF) networks, the proposed approach does not require the unknown parameters to satisfy the linear dependence condition. It is proved that with the proposed control law, the closed-loop system is stable and the tracking error converges to zero in the presence of unmodeled dynamics and unknown nonlinearity. A simulation example is presented to demonstrate the method.     

An adaptive H/sup /spl infin// controller design for bank-to-turn missiles using ridge Gaussian neural networks

A new autopilot design for bank-to-turn (BTT) missiles is presented. In the design of autopilot, a ridge Gaussian neural network with local learning capability and fewer tuning parameters than Gaussian neural networks is proposed to model the controlled nonlinear systems. We prove that the proposed ridge Gaussian neural network, which can be a universal approximator, equals the expansions of rotated and scaled Gaussian functions. Although ridge Gaussian neural networks can approximate the nonlinear and complex systems accurately, the small approximation errors may affect the tracking performance significantly. Therefore, by employing the H/sup /spl infin// control theory, it is easy to attenuate the effects of the approximation errors of the ridge Gaussian neural networks to a prescribed level. Computer simulation results confirm the effectiveness of the proposed ridge Gaussian neural networks-based autopilot with H/sup /spl infin// stabilization.