2023 AIChE Annual Meeting

(165b) Fast Computational Topology for the Real-Time Analysis of Chemical Sensor Data

Authors

Laky, D. - Presenter, Purdue University
Jiang, S., University of Wisconsin-Madison
Zavala, V., University of Wisconsin-Madison
Liquid crystals (LCs) are a class of materials that can be designed to elicit optical responses in the presence of target chemical contaminants. Data analysis techniques can be used to identify features of LC responses that correlate to different contaminants and their concentrations; as such, this provides an avenue to design chemical sensors. Supervised machine-learning algorithms such as convolutional neural networks (Bao et al. 2022a; Smith et al. 2020; Cao et al. 2018) provide capabilities to extract feature information from response data (images) but these tools are difficult to train and interpret. As an alternative, response features can be summarized in the form of topological descriptors such as the Euler characteristic (EC), which have been shown to correlate to the presence and concentration of a contaminant and are also easier to interpret (Smith et al. 2021). However, in order to use these techniques in real-time applications, it is necessary to develop fast and scalable methods that can process images at high resolutions.

In this work, we present computational topology tools that enable real-time analysis of liquid crystal responses. Specifically, we present a Python implementation of a bitmap method (Gray, 1971; Lorenson and Cline 1987; Toriwaki and Yonekura, 2002; Snidaro and Foresti, 2003) that can compute the EC on megapixel images in seconds and at least 4x faster than state-of-the-art software packages (The GUDHI project 2023). Also, due to the bitmap nature of the solution, binary measures of other topological descriptors (perimeter, area, and volume) can be computed from the same output. The implemented method can leverage parallel computing hardware by exploiting the inclusion-exclusion property of the EC. In addition, because the method can operate on small domains of an image (4 pixels in 2D, 8 voxels in 3D), it is possible to process large images without the need to store them in dynamic memory. Our implementation also uses advanced image pre-processing techniques, which enables analysis of data that is collected from high-throughput experiments. This allows us to build large databases that can be used to train machine learning models and benchmark diverse methodologies. Our results aim to provide a stepping stone towards the use of computational topology tools in chemical engineering applications.

Bao, N., Jiang, S., Smith, A., Schauer, J.J., Mavrikakis, M., Van Lehn, R.C., Zavala, V.M., and Abbott, N.L. (2022a) Sensing gas mixtures by analyzing the spatiotemporal optical responses of liquid crystals using 3D convolutional neural networks, ACS sensors, 7, 9, 2545-2555

Smith, A., Abbott, N.L., and Zavala, V.M. (2020) Convolutional network analysis of optical micrographs for liquid crystal sensors, Journal of Physical Chemistry C, 124(28), 15152-15161

Cao, Y., Yu, H., Abbott, N.L., and Zavala, V.M. (2018) Machine learning algorithms for liquid crystals-based sensors, ACS Sensors, 3, 2237-2245

Smith, A., and Zavala, V.M. (2021) The euler characteristic: a general topological descriptor for complex data, Computers & Chemical Engineering, 154

Jiang, S., Noh, J., Park, C., Smith, A., Abbott, N., and Zavala, V.M. (2021) Identification of endotoxins from bacterial species using liquid crystal droplets and machine learning, Analyst, 4

Bao, N., Gold, J.I., Sheavly, J.K.., Schauer, J.J., Zavala, V.M., Van Lehn, R.C., Mavrikakis, M., and Abbott, N.L. (2022b) Ordering transition of liquid crystals triggered by metal oxide-catalyzed reactions of sulfur oxide species, J. Am. Chem. Soc., 144, 36, 16378-16388

Gray, S.B. (1971) Local properties of binary images in two dimensions, IEEE Trans. on C, C-20, 5, 551–561

Lorenson, W.E., and Cline, H.E. (1987) Marching cubes: a high resolution 3D surface construction algorithm, Computer Graphics, 21(4), 163-169

Toriwaki, J., and Yonekura, T. (2002) Euler number and connectivity indexes of a three dimensional digital picture, Forma, 17, 183-209

Snidaro, L., and Foresti, G.L. (2003) Real-time thresholding with Euler numbers, Pattern Recognition Letters, 23, 1533-1544

The GUDHI Project (2023) GUDHI user and reference manual, GUDHI editorial board, 3.7.1,
https://gudhi.inria.fr/doc/3.7.1/