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We report how analysis of the spatial and temporal optical responses of liquid crystal (LC) films to targeted gases, when per-formed using a machine learning methodology, can advance the sensing of gas mixtures and provide important insights into the physical processes that underlie the sensor response. We develop the methodology using O3 and Cl2 mixtures (representative of an important class of analytes) and LCs supported on metal perchlorate-decorated surfaces as a model system. Whereas O3 and Cl2¬ both diffuse through LC films and undergo redox reactions with the supporting metal perchlorate surfaces to generate similar ini-tial and final optical states of the LCs, we show that a 3-dimensional convolutional neural network (3D CNN) can extract feature information that is encoded in the spatiotemporal color patterns of the LCs to detect the presence of both O3 and Cl2 species in mixtures as well as to quantify their concentrations. Our analysis reveals that O3 detection is driven by the transition time over which the brightness of the LC changes, while Cl2 detection is driven by color fluctuations that develop late in the optical response of the LC. We also show that we can detect the presence of Cl2 even when the concentration of O3 is orders of magnitude greater than the Cl2 concentration. The proposed methodology is generalizable to a wide range of analytes, reactive surfaces and LCs, and has the potential to advance the design of portable LC monitoring devices (e.g., wearable devices) for analyzing gas mixtures us-ing spatiotemporal color fluctuations. 

Detection and quantification of bacterial endotoxins is important in a range of health-related contexts, including during pharmaceutical manufacturing of therapeutic proteins and vaccines. Here we combine experimental measurements based on nematic liquid crystalline droplets and machine learning methods to show that it is possible to classify bacterial sources ( Escherichia coli , Pseudomonas aeruginosa , Salmonella minnesota ) and quantify concentration of endotoxin derived from all three bacterial species present in aqueous solution. The approach uses flow cytometry to quantify, in a high-throughput manner, changes in the internal ordering of micrometer-sized droplets of nematic 4-cyano-4′-pentylbiphenyl triggered by the endotoxins. The changes in internal ordering alter the intensities of light side-scattered (SSC, large-angle) and forward-scattered (FSC, small-angle) by the liquid crystal droplets. A convolutional neural network (Endonet) is trained using the large data sets generated by flow cytometry and shown to predict endotoxin source and concentration directly from the FSC/SSC scatter plots. By using saliency maps, we reveal how EndoNet captures subtle differences in scatter fields to enable classification of bacterial source and quantification of endotoxin concentration over a range that spans eight orders of magnitude (0.01 pg mL −1 to 1 μg mL −1 ). We attribute changes in scatter fields with bacterial origin of endotoxin, as detected by EndoNet, to the distinct molecular structures of the lipid A domains of the endotoxins derived from the three bacteria. Overall, we conclude that the combination of liquid crystal droplets and EndoNet provides the basis of a promising analytical approach for endotoxins that does not require use of complex biologically-derived reagents ( e.g. , Limulus amoebocyte lysate). 

The rates of liquid-phase, acid-catalyzed reactions relevant to the upgrading of biomass into high-value chemicals are highly sensitive to solvent composition and identifying suitable solvent mixtures is theoretically and experimentally challenging. We show that the complex atomistic configurations of reactant–solvent environments generated by classical molecular dynamics simulations can be exploited by 3D convolutional neural networks to enable accurate predictions of Brønsted acid-catalyzed reaction rates for model biomass compounds. We develop a 3D convolutional neural network, which we call SolventNet, and train it to predict acid-catalyzed reaction rates using experimental reaction data and corresponding molecular dynamics simulation data for seven biomass-derived oxygenates in water–cosolvent mixtures. We show that SolventNet can predict reaction rates for additional reactants and solvent systems an order of magnitude faster than prior simulation methods. This combination of machine learning with molecular dynamics enables the rapid, high-throughput screening of solvent systems and identification of improved biomass conversion conditions. 

In this article, 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.