ABSTRACT Inverse design is an outstanding challenge in disordered systems with multiple length scales such as polymers, particularly when designing polymers with desired phase behavior. Here

we demonstrate high-accuracy tuning of poly(2-oxazoline) cloud point via machine learning. With a design space of four repeating units and a range of molecular masses, we achieve an

accuracy of 4 °C root mean squared error (RMSE) in a temperature range of 24–90 °C, employing gradient boosting with decision trees. The RMSE is >3x better than linear and polynomial

regression. We perform inverse design via particle-swarm optimization, predicting and synthesizing 17 polymers with constrained design at 4 target cloud points from 37 to 80 °C. Our approach

MULTIOBJECTIVE ACTIVE LEARNING FOR MATERIALS DESIGN AND DISCOVERY Article Open access 19 April 2021 DESIGN OF FUNCTIONAL AND SUSTAINABLE POLYMERS ASSISTED BY ARTIFICIAL INTELLIGENCE Article

19 August 2024 INTRODUCTION Polymers are ubiquitous in both structural and functional systems, owing to their highly tunable physical, chemical, and electrical properties.1,2,3,4 The

development of polymers has historically been based on an Edisonian approach. Herein, we develop a machine-learning framework to predict polymer structure (topology, composition,

functionality, and size), on the basis of target-phase properties, specifically the cloud point. This framework accommodates the complex disorder across multiple length scales that

distinguishes polymers from small molecules,5,6,7 inorganic crystals,8 and systems-structure optimization.9,10,11 Phase properties, which describe the order of a polymer across multiple

length scales, are determined by interactions of polymers with other polymers, the solution, and themselves. One such phase property is the cloud point, the temperature at which polymers are

no longer miscible in solution.12 Numerous studies tabulate simple relationships between cloud point and one or two experimental variables (e.g., structure13 and temperature14,15), or offer

polynomial fits to the data.16 Ramprasad et al. applied machine learning to density-functional theory (DFT) calculations to predict optoelectronic17,18 and physical19 bulk polymer

properties.4,19 However, this approach is computationally expensive,7,20 particularly for polymer systems,21 and does not enable scalable inverse design over a wide range of conditions with

high accuracy.22,23 In this study, we combine machine learning, domain expertise, and experiment to solve the inverse-design problem for polymers. Our framework (Fig. 1) has three parts: (1)

data curation (defining material descriptors) that relates poly(2-oxazolines) cloud point, size, and relative ratios of four different monomer units; (2) machine-learning algorithm

selection and hyperparameter tuning to enable fast forward prediction of cloud point based on the structure with the evaluation of algorithmic robustness over systematic error and differing

data quality; and (3) use of said algorithm for inverse design using particle-swarm optimization (PSO) with design selection using an ensemble of neural networks. We demonstrate the accuracy

of our inverse-design paradigm by predicting the compositions of, and synthesizing, 17 polymers, not previously reported in the literature, with cloud points between 37 and 80 °C, using a

modular combination of four repeating monomer units. We achieve ~4 °C error, nearly within experimental error (1–3 °C). RESULTS AND DISCUSSION We combine and curate literature and

experimental data to create the input into our machine-learning framework. Historical cloud-point data for poly(2-oxazoline)s16,24,25,26,27,28,29 were curated into a set of input variables

((1) molecular weight of the polymers; (2) polydispersity index; (3) polymer type (homo, statistical, or block); (4) the total number of each monomer unit in the final polymer (A: EtOx, B:

nPropOx, C: cPropOx, D: iPropOx, E: esterOx)) and output variables (cloud point in °C) (Table S1). We synthesized 87 poly(2-oxazoline)s by similar methods to augment this data (Table S2).

Cloud point was evaluated by dynamic-light scattering (DLS) in accordance with best practices,30 particularly since DLS affords greater weightage to the modal mass as a correction for the

asymmetric molecular weight distributions (MWD) of our synthesized polymers (details in Supplementary Materials under the heading _“Curation and synthesis of polymer library”_). Due to data

scarcity, esterOx was neither synthesized nor considered in inverse design. The relationships of individual input variables to the output cloud point are plotted in Fig. 2. We test whether

machine-learning methods have superior predictive accuracies to simple regression methods in this multi-variable parameter space.31,32,33 We compare the root-mean-squared errors (RMSE) of

simple linear and quadratic regressions against more robust machine-learning methods, including support vector regressions (SVR), (ensembles of) neural networks (NN), and gradient boosting

regression with decision trees (GBR) (Fig. 3; S3). The accuracies of the various models are determined by splitting the input data set into training, validation, and test sets, with training

and validation performed from the historical data, while testing is performed with the experimental data. The RMSE and inference times are reported in Table S3. Linear and polynomial

regressions, while significantly faster than the others, performed poorly when compared with SVR, NN, and GBR. Of the latter three, GBR was the more accurate out-of-the-box without extensive

hyperparameter tuning. Moreover, it possesses fast inference speed, which is essential for efficient exploration of the parameter space in inverse design. We chose GBR as our primary

forward model to balance fast inference speed and good test RMSE. The predictive accuracy was further improved by tuning via a cross-validation grid search on hyperparameters. We used both

historic and experimental data, with a test set of 10%, to validate our choice of hyper-parameters with the test error on three randomly split training and test sets (Fig. 3). We now observe

improved performance with an increased data set and thorough tuning. This algorithm is shown to generalize well across the variation in polymer data set of varying polydispersity. The

historical data sets had narrow polydispersity indices with the assumption of symmetrical MWDs, while the synthesized polymers had broad and unsymmetrical MWD. Nevertheless, the model

trained on the historical data still performed adequately on data from our synthesized polymers. The robustness of this algorithm in handling variations in the data renders this far more

powerful than less sophisticated algorithms, which may require highest quality of data. With a sufficiently accurate model, we finally retrain (using the tuned hyper-parameters) on the

entire data set to produce a finalized forward model that we use for subsequent inverse design. The feature importance ranking based on Gini importance or gain (roughly the mean improvement

in objective due to splits in the chosen feature, see the Ref. 34 for more details) (Fig. S4) indicates that “units of A” and “molecular mass” are the two most important features defining

cloud point. We note that these insights are not trivially derived from Fig. 2, which indicates similarly strong dependences of variables a–c on cloud point. Also, the molecular mass

correlating most strongly with cloud point is the mode, not the median or mean (Fig. S2), which we speculate could indicate a critical threshold, e.g., of polymers with molecular mass above

a certain concentration necessary to induce globule formation. However, we note that this statistical relationship depends on the model and fitting algorithm employed, and certainly does not

imply the presence of causal relationships, for which more rigorous theoretical and experimental studies must be conducted. While a forward predictive models in machine-learning approaches

for materials science are fairly common, inverse design is far more challenging. This is because the descriptors, which are usually high dimensional, are difficult to predict from outputs

which are low dimensional. In the case of our polymer data set, the output of cloud point is a single number, attributed to the five numbers representing molecular mass and composition of

the polymer. Inverse design would provide the ability to design polymers based on a desired final property, and accelerate the synthesis process of target polymers based on design

constraints to meet desired cloud points. To further realize new material discovery, we propose to extrapolate from our training data set by designing terpolymers, which are nonexistent in

our training set, and limiting EtOx composition, which is common. Typically, inverse optimization on piecewise constant functions provides a large number of different predicted designs.

These may achieve our optimization and constraint target according to the fitted GBR model. However, the quality of these designs vary, particularly in the case of extrapolation. By

extrapolation, we mean designs that are different in class from the training data set (e.g., binary vs. ternary systems), or in a more precise sense, those that lie outside of the convex

hull of the training data points, which is the smallest convex set containing all the points. Validating all of produced designs experimentally would be inefficient and so a filtering method

with an ensemble of _M_ three-layer fully connected neural networks (NN) was employed to select the most promising design candidates for experimental validation. Each NN’s trainable

parameters are initialized with distinct, random values, resulting in different fitted predictors \(\{ \hat f_1, \ldots ,\hat f_M\}\), due to the non-convex nature of the objective function

and random initialization. Note that this is even the case when a deterministic training algorithm is used (e.g., full-batch gradient descent), hence this heterogeneity is inherent in our

model choice. For each design _x_, we then compared the ensemble of NN-predicted cloud points \(\{ \hat f_1(x), \ldots ,\hat f_M(x)\}\) with the GBR prediction \(\hat f(x)\) and only

experimentally validated designs where \(\hat f\left( x \right) \approx \frac{1}{M}\mathop {\sum }\nolimits_{i = 1}^M \hat f_i(x)\)(NN predictions agree with GBR) and \(Var\{ \hat f_1(x),

\ldots ,\hat f_M(x)\}\) was small. This ensures that _x_ is predicted with high confidence and not an ad-hoc extrapolation. As far as we are aware, there is no concrete theory analyzing the

relationship between generalization properties of neural networks with the variance of the ensemble predictions, in which each network is trained with random initial conditions. However, we

found experimentally that this is an effective filtering strategy. Figure 4 illustrates the principle of this approach. Although the NNs are also good approximators for the cloud point, they

were not used as the forward model for producing inverse-design candidates because the feed-forward step of the NN ensemble is still too slow compared with GBR, which consists of simple

summing of piecewise constant functions. Using this technique, we downselected 17 polymers over our four desired cloud points (37, 45, 60, 80 °C) designing polymers with more than two

components—unseen in the training data. Several design constraints were imposed in order to narrow the search space, based on a weightage to minimize EtOx and also to limit the polymer

design within the bounds of what could be made with our laboratory resources. From this series of design and downselection, we observe that a significant proportion of the target and

obtained designs (~35%) lie strictly outside the convex hull of the training data (see Table S4). Hence, some of these designs are also extrapolations in a precise mathematical sense. These

polymers were synthesized, although an average of three iterations were required to achieve the target mass and composition of the designs, owing to the difficulties with terpolymer

synthesis, where the Mayo–Lewis equation does not apply in calculating required feed ratio of monomer for desired final copolymer composition. The mass and composition of the synthesized

polymers are reported in Table S4, showing minimal deviation from algorithmic design, along with their cloud points (an average of three measurements). The RMSE of the obtained cloud points

was 3.9 °C, however, when the polymer structure of the new polymers is fed back into the NN ensemble, a larger RMSE is observed (6.1 °C) (Fig. 4). Deviation from the target cloud points was

within test RMSE between 37 and 60 °C, but above it at 80 °C, and can be attributed to sparseness of the data set at higher temperatures (Fig. 2f)—an in-depth analysis is provided in

Supplementary Materials under the heading _“Machine-Learning Validation”_. These results show that our combination of slow and fast algorithms are able to design polymers with unique

compositions with control over the desired physical property and structural design. Overall, a significant conceptual advance in polymer design has been achieved via judicious application of

machine-learning methods. This was done in three important steps. First, we curated and categorized historical and new data. Second, we selected and fine-tuned a machine-learning model

based on gradient boosting regression with decision trees, resulting in a cloud point predictive accuracy of 3.9 °C (RMSE). The model was able to generalize well with both well-defined

historic data sets as well as newly synthesized polymers of unsymmetrical MWDs. Third, polymer inverse design by particle-swarm optimization which predicted the design of new polymers based

on desired cloud points spread over the range of the cloud points of the training data (37, 45, 60, 80 °C). We discuss how our inverse-design methodology is scalable to more than one

objective function. We also demonstrated how we could extrapolate beyond the training set via an ensemble of neural networks as a cross-validation technique to downselect 17 polymers with

the lowest variance across predictions. The RMSE of predicted polymers were similar to those of the forward model. This methodology offers unprecedented control of polymer design, which may

significantly accelerate polymer design for one or more objective properties well beyond cloud points. METHODS MATERIALS 2-_n_-propyl-2-oxazoline (nPropOx),1 2-cyclopropyl-2-oxazoline

(cPropOx),2 and 2-isopropyl-2-oxazoline (iPropOx)3 were synthesized as described in the literature, and distilled over calcium hydride and stored with molecular sieves (size 5 Å) in a

glovebox. In all, 2-ethyl-2-oxazoline (EtOx, Sigma-Aldrich) was distilled over calcium hydride and stored with molecular sieves (size 5 Å) in glovebox. All other reagents were used as

supplied unless otherwise stated. ANALYTICAL METHODS NUCLEAR MAGNETIC RESONANCE (NMR) The compositions of the polymers were determined using 1H NMR spectroscopy. 1H NMR spectra were on JEOL

500 -MHz NMR system (JMN-ECA500IIFT) in CDCl3. The residual protonated solvent signals were used as reference. SIZE EXCLUSION CHROMATOGRAPHY (SEC) Gel permeation chromatography (GPC)

measurements were performed in THF (flowrate: 1 mL/min) on a Viscotek GPC Max module equipped with Phenogel columns (10−3 and 10−5 Å) (size: 300 × 7.80 mm) in series heated to 40 °C. The

average molecular weights and polydispersities were determined with a Viscotek TDA 305 detector calibrated with poly(methyl methacrylate) standards. DYNAMIC-LIGHT SCATTERING (DLS)

Measurements at various temperatures were conducted using a Malvern Instruments Zetasizer Nano ZS instrument equipped with a 4 mV He–Ne laser operating at l = 633 nm, an avalanche photodiode

detector with high quantum efficiency, and an ALV/LSE-5003 multiple tau digital correlator electronics system. on Malvern Nano ZS. Solutions of polymers (5 mg/mL) were prepared by

dissolving polymer in deionized water at room temperature. The solutions were then heated to 100 °C and cooled down to remove thermal memory, before measurements were taken. EXPERIMENTAL

METHODS For all polymerizations, the polymerization mixture was prepared in vials that were dried in 100 °C oven overnight before use, and crimped air-tight in a glovebox. The mixture

contained the monomers (EtOx, nPropOx, cPropOx, iPropOx) of desired ratios, with a total monomer concentration of 4 M, anhydrous acetonitrile (ACN) and methyl tosylate (MeOTs) as initiator.

The amount of methyl tosylate added was determined by the various [M]/[I] ratios. Temperature controlled polymerizations were performed in sealed vials in a microwave reactor equipped with

IR temperature sensor at 140 °C for different length of time. The mixture was then cooled to ambient temperature and quenched by addition of tetramethylammonium hydroxide (2.5 wt% in

methanol, 2 equivalence relative to initiator). The solutions were concentrated by removing some of the solvent under reduced pressure, then precipitated in cold diethyl ether. The product

was collected and dried under reduced pressure overnight. All polymers were redissolved in THF for SEC, CDCl3 for 1H NMR and deionized water for DLS. 1H NMR of

P((EtOx)w(nPropOx)x(cPropOx)y(iPropOx)z) (500 MHz, CDCl3, _δ_, ppm): 0.8 (_d_, 66.5 Hz, 4 _y_H, CHC_H__2_ C_H__2_), 0.96 (_s_, 3_x_ H, CH2CH2C_H__3_), 1.11 (_s_, 6_z_ H, CHC_H__3_C_H__3_),

1.12 (_s_, 3_w_ H, CH2C_H__3_), 1.64 (_s_, 2_x_ H, CH2C_H__2_CH3) 2.30 (_d_, 56.5 Hz, 2_x_ H, NCOC_H__2_CH2CH3), 2.38 (_s_, 2_w_ H, NCOC_H__2_CH3), 2.70 (_d_, 61.0 Hz, _y_ H, C_H_CH2CH2),

2.80 (_d_, 123.5 Hz, _z_ H, C_H_CH3CH3), 3.49 (s, 2(_w_+_x_+_y_+_z_) H, CH2 backbone). Whereby _w_, _x_, _y_, and _z_ are the mole ratio of EtOx, nPropOx, cPropOx, and iPropOx, respectively.

DATA AVAILABILITY The data generated and analyzed during the current study can be found in the Supplementary Materials (Figures S3–S5, Tables S1–S4), and also in our repository

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Friedman, J. _The Elements of Statistical Learning_, Vol. 1 (Springer, New York, 2001). Download references ACKNOWLEDGEMENTS We thank Kedar Hippalgaonkar for scientific and framing

discussions. J.N.K., Q.L. and T.B. are supported by the AME Programmatic Fund by the Agency for Science, Technology, and Research under Grant no. A1898b0043. AUTHOR INFORMATION Author notes

* These authors contributed equally: Jatin N. Kumar, Qianxiao Li AUTHORS AND AFFILIATIONS * Institute of Materials Research & Engineering, 2 Fusionopolis Way, #08-03, Singapore, 138634,

Singapore Jatin N. Kumar & Karen Y. T. Tang * Institute of High-Performance Computing, 1 Fusionopolis Way, #16-16, Singapore, 138632, Singapore Qianxiao Li, Anibal L. Gonzalez-Oyarce 

& Jun Ye * Massachussets Institute of Technology, Cambridge, MA, 02139, USA Tonio Buonassisi Authors * Jatin N. Kumar View author publications You can also search for this author

inPubMed Google Scholar * Qianxiao Li View author publications You can also search for this author inPubMed Google Scholar * Karen Y. T. Tang View author publications You can also search for

this author inPubMed Google Scholar * Tonio Buonassisi View author publications You can also search for this author inPubMed Google Scholar * Anibal L. Gonzalez-Oyarce View author

publications You can also search for this author inPubMed Google Scholar * Jun Ye View author publications You can also search for this author inPubMed Google Scholar CONTRIBUTIONS J.N.K_._

was responsible for the (1) ideation; (2) experiments in polymer synthesis and characterization; (3) data curation and application of machine learning; (4) collation of information and

representation of findings. Q.L_._ developed the machine-learning methodology, was involved in data curation, algorithm development, and was the architect of the multi-method strategy,

including particle-swarm optimization. K.Y.T.T_._ carried out experiments in polymer synthesis and characterization and data curation. T.B_._ was involved in the ideation, collation, and

representation of findings. A.L.G-O. developed the machine-learning methodology and algorithm development, as well as the application of inverse design. J.Y. was involved in ideation, data

curation, and the representation of findings. CORRESPONDING AUTHOR Correspondence to Jatin N. Kumar. ETHICS DECLARATIONS COMPETING INTERESTS The authors declare no competing interests.

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CITE THIS ARTICLE Kumar, J.N., Li, Q., Tang, K.Y.T. _et al._ Machine learning enables polymer cloud-point engineering via inverse design. _npj Comput Mater_ 5, 73 (2019).

https://doi.org/10.1038/s41524-019-0209-9 Download citation * Received: 17 January 2019 * Accepted: 20 June 2019 * Published: 12 July 2019 * DOI: https://doi.org/10.1038/s41524-019-0209-9

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