Machine Learning Inversion from Scattering for Mechanically Driven Polymers

TL;DR

This work addresses the challenge of extracting molecular-level parameter information from scattering data of mechanically driven polymers. It combines Monte Carlo simulations to generate a labeled dataset of scattering functions $I_{xz}(oldsymbol{Q})$ and associated features ($κ$, $f$, $γ$, $R^2$, $R_g^2$, $R_{xz}$), with PCA/SVD to establish a feasible, well-behaved inversion landscape. A Gaussian Process Regressor is trained to map $I_{xz}(oldsymbol{Q})$ to the feature targets, achieving high-precision predictions on a held-out test set (r^2 near 1). The approach enables rapid, noninvasive interpretation of scattering data in terms of both external mechanical inputs and polymer conformations, with potential extensions to more complex interactions and flow environments.

Abstract

We develop a Machine Learning Inversion method for analyzing scattering functions of mechanically driven polymers and extracting the corresponding feature parameters, which include energy parameters and conformation variables. The polymer is modeled as a chain of fixed-length bonds constrained by bending energy, and it is subject to external forces such as stretching and shear. We generate a data set consisting of random combinations of energy parameters, including bending modulus, stretching, and shear force, along with Monte Carlo-calculated scattering functions and conformation variables such as end-to-end distance, radius of gyration, and the off-diagonal component of the gyration tensor. The effects of the energy parameters on the polymer are captured by the scattering function, and principal component analysis ensures the feasibility of the Machine Learning inversion. Finally, we train a Gaussian Process Regressor using part of the data set as a training set and validate the trained regressor for inversion using the rest of the data. The regressor successfully extracts the feature parameters.

Figures (7)

• Figure 1: $I_{xz}(\vb{Q})$ of a semiflexible chain with $L = 200$ in its quiescent state with bending modulus $\kappa=5, 10$ and $15$.
• Figure 2: Sample configurations of a semiflexible chain with $L = 200$ and $\kappa=10$ with various combinations of stretching and shear $(f,\gamma)=(0,0.1,0.2)\times(0,0.6,0.9)$, color corresponds to end-to-end orientation in the $xz$ plane. The system is symmetric about $\pm xz$ for (b) and (c) where $f=0, \gamma\neq 0$, these configurations are flipped to the $xz$ direction for better visualization.
• Figure 3: Scattering function $I_{xz}(\vb{Q})$ of a semiflexible chain with $L = 200$ and $\kappa=10$ with various combinations of stretching and shear $(f,\gamma)=(0,0.1,0.2)\times(0,0.3,0.9)$.
• Figure 4: Singular value decomposition (SVD) of scattering function data set. (a) Singular value $\Sigma$ versus Singular Value Rank (SVR), value with top 3 rank are highlighted in red circle. (b)-(d) First 3 singular vectors.
• Figure 5: Distribution of various inversion features of training data in the singular value space. (a) Bending modulus $\kappa$. (b) Stretching force $f$. (c) Contour length normalized shear $\gamma L$. (d) End-to-end distance scaled by Contour length square $R^2/L^2$. (e) Radius of Gyration square scaled by Contour length $R_g^2/L$. (f) Off-diagonal, $xz$, component of gyration tensor $R_{xz}$