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

TL;DR

This paper reviews the mathematical foundations of convolutional neural networks (CNNs), emphasizing their connections to various scientific techniques, demystifying their computations, and exploring diverse applications beyond image processing.

Contribution

It provides a comprehensive overview of CNNs in chemical engineering, highlighting their mathematical basis, computational processes, and expanding their application scope to new scientific domains.

Findings

CNNs are connected to statistics, signal processing, and linear algebra.

They can be applied to diverse grid data beyond images.

CNNs effectively identify features for various scientific applications.

Abstract

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.