arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 2101.04869cs.LGcs.AI
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化学工程中的卷积神经网络:基础、计算与应用

Convolutional Neural Nets in Chemical Engineering: Foundations, Computations, and Applications

University of Wisconsin-Madison(威斯康星大学麦迪逊分校)

Shengli Jiang, Victor M. Zavala

摘要:

在本文中,我们回顾了卷积神经网络(CNN)的数学基础,目标是:i)突出与统计,信号处理,线性代数,微分方程和优化技术的联系,ii)揭开底层计算的神秘面纱,iii)识别新类型的应用。CNN是功能强大的机器学习模型,可以突出网格数据的特征以进行预测(回归和分类)。网格数据对象可以表示为矢量(1D)、矩阵(2D)或张量(3D或更高维度),并且可以包含多个通道(从而在输入数据表示中提供高度灵活性)。CNN通过使用不同类型的运算符执行卷积运算来突出网格数据中的特征。操作员突出显示不同类型的特征(例如,图案、梯度、几何特征),并且通过使用优化技术来学习。换句话说,CNN寻求识别最佳算子,将输入数据最佳地映射到输出数据。一个常见的误解是,CNN只能处理图像或视频数据,但它们的应用范围要广泛得多;具体来说,在各种应用中遇到的数据集可以表示为网格数据。在这里,我们展示了如何将CNN应用于新型应用,如最优控制、流式细胞术、多变量过程监控和分子模拟。

英文摘要:

In this paper we review the mathematical foundations of convolutional neural nets (CNNs) with the goals of: i) highlighting connections with techniques from statistics, signal processing, linear algebra, differential equations, and optimization, ii) demystifying underlying computations, and iii) identifying new types of applications. CNNs are powerful machine learning models that highlight features from grid data to make predictions (regression and classification). The grid data object can be represented as vectors (in 1D), matrices (in 2D), or tensors (in 3D or higher dimensions) and can incorporate multiple channels (thus providing high flexibility in the input data representation). CNNs highlight features from the grid data by performing convolution operations with different types of operators. The operators highlight different types of features (e.g., patterns, gradients, geometrical features) and are learned by using optimization techniques. In other words, CNNs seek to identify optimal operators that best map the input data to the output data. A common misconception is that CNNs are only capable of processing image or video data but their application scope is much wider; specifically, datasets encountered in diverse applications can be expressed as grid data. Here, we show how to apply CNNs to new types of applications such as optimal control, flow cytometry, multivariate process monitoring, and molecular simulations.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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