Nonlinear Manifold Learning Determines Microgel Size from Raman Spectroscopy

TL;DR

The conformal autoencoders substantially outperform state‐of‐the‐art methods and results for the first time in a promising prediction of polymer size from Raman spectra.

Abstract

Polymer particle size constitutes a crucial characteristic of product quality in polymerization. Raman spectroscopy is an established and reliable process analytical technology for in-line concentration monitoring. Recent approaches and some theoretical considerations show a correlation between Raman signals and particle sizes but do not determine polymer size from Raman spectroscopic measurements accurately and reliably. With this in mind, we propose three alternative machine learning workflows to perform this task, all involving diffusion maps, a nonlinear manifold learning technique for dimensionality reduction: (i) directly from diffusion maps, (ii) alternating diffusion maps, and (iii) conformal autoencoder neural networks. We apply the workflows to a data set of Raman spectra with associated size measured via dynamic light scattering of 47 microgel (cross-linked polymer) samples in a diameter range of 208nm to 483 nm. The conformal autoencoders substantially outperform state-of-the-art methods and results for the first time in a promising prediction of polymer size from Raman spectra.

Figures (12)

• Figure 1: Schematic overview of the proposed machine learning approaches applied to low dimensional parameterization (provided by DMAPs) of measured Raman spectra: (i) in Approach 1 the polymer size is predicted directly from DMAPs, (ii) Approach 2 implements AltDMAPs to find the data-driven common variable that is one-to-one with the polymer size (2.a), and in (2.b) predicts the polymer size from this common variable, and (iii) Approach 3 implements a Y-shaped conformal autoencoder, that identifies a "designer" latent space (3.a) from which it is possible to predict the polymer size (3.b).
• Figure 2: Schematic representation of the prediction strategy directly from the DMAP coordinates that parsimoniously parameterize the spectra.
• Figure 3: Schematic of the offline steps: (a) Step 1: Finding a reduced representation of the spectra with DMAPs; (b) Step 2: Finding the common variable between spectra and polymer size with AltDMAPs.
• Figure 4: Schematic of the online application of size prediction: Given a measured (new) spectrum, the reduced description via DMAPs is determined (Step 1). Then, the common AltDMAP variable is inferred with NNs, DoubleDMAPs, or XGBOOST networks (Step 2). Finally, the polymer size is predicted from the common variable, with NNs or XGBOOST (Step 3).
• Figure 5: Schematic of the Y-shaped conformal autoencoder architecture: (a) Representation of the workflow; (b) Y-shaped autoencoder composition: NN1 is the encoder that maps the DMAP coordinates to the latent variables of the autoencoder; NN2 is the inverse transformation, from the latent space back to the DMAP coordinates; NN3 maps one of the latent variables to the output of interest: polymer size.