Editorial Feature

Applications of Machine Learning to Design Polymer-Based Dielectrics

Polymer-based dielectrics are widely used in different electrical and electronic devices like capacitors, power transmission cables, and microchips. To adapt to different working conditions, a range of distinct properties like dielectric and thermal parameters are desired for polymers, which can be tuned by customizing the chemical and morphological structure or adding nanofillers/additives to form nanocomposites. This is discussed in the journal IET Nanodielectrics.

nanocomposites, machine learning, structure–property, algorithm

Study: Review of machine learning-driven design of polymer-based dielectrics. Image Credit: Michael Traitov/Shutterstock.com

Extensive efforts have been devoted to the design and development of polymer-based dielectrics to optimize their properties. As a result, new paradigms are expected to efficiently design polymer-based dielectrics with desired properties.

The emerging machine learning (ML) technique trained on massive amounts of data establishes linkages between input fingerprints and output properties, which provides a powerful surrogate model for the structure–property linkage analysis.

Moreover, inverse design methods such as evolution searching (ES) strategies and generative models can be employed to explore the large space of potential materials, greatly accelerating the discovery and development of new polymers. Figure 1 illustrates the workflow of ML methods for the rational design of polymer dielectrics.

The schematic of machine learning methods for the rational design of polymer-based dielectrics.

Figure 1. The schematic of machine learning methods for the rational design of polymer-based dielectrics. Image Credit: Zhu, et al., 2021

The study attempted to offer an overview of the application of ML-driven methods for the rational design of polymer or nanocomposite dielectrics.


The ML methods employed to design polymer-based dielectrics often involve supervised learning, where the reliability of these models is mainly governed by the amount and quality of samples in the training dataset. The key sources of training data are online libraries, high-throughput computations, and experiments.

As an effective alternative approach, high-throughput computations that involve first-principles theory, phase-filed model, molecular dynamics (MD), and finite-element method have been used to obtain property data. The researchers illustrate the DFT method used to estimate the charge injection barrier from the electrode to polymer and the trap depth in polymer, respectively.

The thermodynamic properties of nanocomposites or polymers, such as thermal conductivity and glass transmission temperature, can be readily calculated through MD simulations. For instance, the non-equilibrium MD has been extensively used to estimate thermal conductivity.

Phase-field models have been created to analyze the breakdown behavior and effective permittivity of polymer nanocomposites (Figure 2e), where the effect of the microstructure of nanocomposites, like the shape and orientation of nanofillers, can be considered.

ML-driven approaches involve two different steps: numerically representing the materials in the dataset (fingerprinting) and establishing a mapping between the target property and the fingerprinted input (learning).

The polymers were fingerprinted through the occurrence of various kinds of building fragments (including blocks like CO, CH2, CS, C6H4, O, C4H2S, and NH) in terms of their number fractions.

The aim of the ML algorithm is to establish a mapping between the target property and the fingerprinted input, which offers an effective surrogate for calculating the target property. At present, linear and non-linear regression algorithms are being used to build the model, of which artificial neural networks (ANNs) and kernel-based regression are the most popular algorithms.

Gaussian process regression (GPR) is a well-established method for developing ML models for polymer dielectrics. The mean and variance for objective values can be well estimated based on the calculation of the covariance matrix, the elements of which indicate the covariance between two features.

Different ML algorithms can be used for developing a surrogate model between the target property and the fingerprinted input. These techniques have their own benefits and drawbacks in terms of the size of applicable dataset, computational efficiency, and prediction capabilities. Table 1 depicts a brief comparison of these algorithms.

Table 1. Comparison of different ML algorithms. Source: Zhu, et al., 2021

ML algorithm Advantages Disadvantages
Linear regression Simplest method Neglect of non-linear linkage between descriptors and properties
KRR, SVM Low computational cost Unfeasible for large datasets as the size of the kernel matrix scales quadratically with the number of features
GPR The uncertainty for objective values can be well predicted Requires a manageable dataset size and does not have the capability to train multiple properties in one single model
RF Feasible for large datasets and provides an intrinsic metric to evaluate the importance of each descriptor Might create over-complex trees and cause overfitting
ANN Exhibits strong ability to capture non-linear complex relations from large-scale datasets Requires much more training data, is time-consuming, and lacks interpretability; also called ‘black boxes’.
Feasible for graphical representations of materials and learns representations with different abstraction levels Requires much more training data, is time-consuming, and lacks interpretability

Abbreviations: ANN, artificial neural network; GPR, Gaussian process regression; KRR, kernel ridge regression; ML, machine learning; RF, random forest; SVM, support vector machine.

A GPR-based ML model was employed to screen potential polymer nanocomposites with desired breakdown strength, permittivity, and energy density, leading to different kinds of nanocomposites with preferred properties.

Active learning algorithms that iteratively fill the chosen optimal point into the training dataset were shown to be effective in materials design.

Active learning algorithms include three interwoven steps: (1) training the ML-based surrogate model for predicting the target property, (2) choosing the optimal sample based on the prediction results such as values and uncertainties, and (3) supplementing the most ideal sample into the training dataset.

Pure exploration, pure exploitation, and balanced exploration and exploitation principles were used to choose the most ideal sample.

The GA method was used in tandem with ML models to develop polymers with a large bandgap and high glass transition temperature. An inverse design by PSO and trained ML algorithm was demonstrated, estimating 17 polymer structures from user-defined cloud points.

In the case of an autoencoder, the encoder figures out how to map the polymers to a lower-dimension space called the latent space, and the decoder tries to regain the original representation from the latent space. For GAN, the generator tries to produce samples from a distribution, while the discriminator forecasts whether the probability of a data is real or synthetic.

Pearson correlation coefficients (PCCs) between different target properties and features can be estimated to represent the variable importance, where PCC with −1 represents high negative correlations and 1 represents high positive correlations.

CNN gradient analysis was used to identify the composition–structure–property relationships for an array of BiVO4 alloys. DeepLIFT was applied to probe the contribution of various molecular structures to thermal conductivity of polymer chains.


Polymer-based dielectrics have found extensive applications in different electrical and electronic devices. It has been shown that the ML-driven approach is an effective means for rationally designing polymer-based dielectrics.

Table 2 summarizes certain examples of the ML-driven approach used to design polymers and nanocomposites, where the fingerprints, target properties, data sources, inverse design techniques, and ML models are provided.

Table 2. Some examples of the ML-driven approach applied in designing polymers and nanocomposites. Source: Zhu, et al., 2021

Fingerprint ML
Polymers: Bandgap of the polymer and electron injection barrier (proxies for breakdown strength) DFT computation Hierarchical fingerprint in [53] GPR Enumeration [53]
SMILES in [43] [43]
Polymers: Bandgap and dielectric constant (proxies
for energy density)
DFT computation Fingerprints based on singles, doubles and triples components  KRR Enumeration [22]
Polymers: Frequency-dependent dielectric constant Experimental data in
Hierarchical fingerprint GPR Enumeration [34]
Polymers: Dielectric constant Experimental data in
Hierarchical fingerprint Interval support vector regression - [86]
Polymers: Bandgap, glass transition temperature Experimental data in
SMILES GPR GA in [102] [102]
VAE in [104] [104]
Polymers: Glass transition temperature Experimental data in
SMILES GPR Active learning [88]
Polymers: Specific heat of polymers Experimental data Hierarchical fingerprint constructed using the Materials Studio software Decision tree - [66]
Polymers: Thermal conductivity MD simulations SMILES CNN - [25]
Polymers: Thermal conductivity Online database SMILES Bayesian method Enumeration [39]
Nanocomposites: Breakdown strength, permittivity and energy density Experimental data in
Descriptor-based fingerprint GPR Enumeration [26]
Nanocomposites: Breakdown strength Monte Carlo multi-scale simulation MCR methods GPR GA [79]
Nanocomposites: Energy density Phase-field simulations Descriptor-based fingerprint NN Enumeration [60]
Nanocomposites: Thermal
FEM simulation 2D cross-sectional
CNN - [61]

Abbreviations: CNN, convolutional neural network; DFT, density functional theory; FEM, finite-element model; GA, genetic algorithm; GPR, Gaussian process regression; KRR, kernel ridge regression; MCR, microstructure characterization and reconstruction MD, molecular dynamic; ML, machine learning; NN, neural network; SMILES, Simplified Molecular-Input Line-Entry System; VAE, variational autoencoder.


The ML-driven approach trained on enormous amounts of data has been demonstrated to be a robust technique for structure–property linkage analysis and the quick design of polymer-based dielectrics. The training data were largely gathered from online polymer libraries, high-throughput computations, and experiments in the literature.

Increasing knowledge of the connection between microstructures of polymers/nanocomposites and preferred properties should make way for incorporating other vital descriptors like the morphologies, trap state, and processing conditions to more precisely estimate the dielectric properties.

More sophisticated inverse design methods and neural network algorithms can be used for structure–property analysis, polymer dielectrics discovery, and property prediction.

Journal Reference:

Zhu, M.-X., Deng, T., Dong, L., Chen, J.-M., Dang, Z.-M. (2021) Review of machine learning-driven design of polymer-based dielectrics. IET Nanodielectrics. doi.org/10.1049/nde2.12029.

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