MACHINE LEARNING-BASED POLYMER SURFACE ENERGY PREDICTION SYSTEM

A method includes determining a plurality of molecular descriptors, each molecular descriptor of the plurality of molecular descriptors associated with at least one of an atomic scale property, a molecular scale property, and a compound-scale property. The method further includes selecting, by a selection operator and based on a minimization of an error, a subset of the plurality of molecular descriptors that affect a polymer surface energy, training a machine learning model to predict a polymer surface energy of a given polymer based on the subset of molecular descriptors and predicting, via the trained machine learning model, a surface energy of an input polymer.

TECHNICAL FIELD

The disclosure relates to surface energy prediction.

BACKGROUND

Consideration of surface energies provide an understanding of articles, materials, and products for many applications, such as adhesives, coatings, repellent materials, and applications involving wetting of substrates by materials. Current methods for determining polymer surface energies usually involve a trade-off between cost and accuracy. Experimental determinations are accurate but time-intensive while the converse is true for conventional computational methods.

SUMMARY

In general, the disclosure describes systems and techniques for predicting or computationally determining surface energies of polymers. The systems and techniques disclosed may provide for computational prediction of polymer surface energies with improved accuracy and reduced cost.

In one example, this disclosure describes a method including determining a plurality of molecular descriptors, each molecular descriptor of the plurality of molecular descriptors associated with at least one of an atomic scale property, a molecular scale property, and a compound-scale property: selecting, by a selection operator and based on a minimization of an error, a subset of the plurality of molecular descriptors that affect a polymer surface energy: training a machine learning model to predict a polymer surface energy of a given polymer based on the subset of molecular descriptors; and predicting, via the trained machine learning model, a surface energy of an input polymer.

In another example, this disclosure describes a method including determining a plurality of molecular descriptors, each molecular descriptor of the plurality of molecular descriptors associated with at least one of an atomic scale property, a molecular scale property, and a compound-scale property: selecting, by a selection operator and based on a minimization of an error, a subset of the plurality of molecular descriptors that affect a polymer surface energy: predicting, via a trained machine learning model, a surface energy of an input polymer.

In another example, this disclosure describes a computer readable medium including instructions that when executed cause one or more processors to: determine a plurality of molecular descriptors, each molecular descriptor of the plurality of molecular descriptors associated with at least one of an atomic scale property, a molecular scale property, and a compound-scale property: select, by a selection operator and based on a minimization of an error, a subset of the plurality of molecular descriptors that affect a polymer surface energy: predict, via a trained machine learning model, a surface energy of an input polymer: and output the predicted surface energy.

In another example, this disclosure describes a means for determining plurality of molecular descriptors, each molecular descriptor of the plurality of molecular descriptors associated with at least one of an atomic scale property, a molecular scale property, or a compound-scale property: a means for selecting, based on a minimization of an error, a subset of the plurality of molecular descriptors that affect a polymer surface energy: a means for training a machine learning model to predict a polymer surface energy of a given polymer based on the subset of molecular descriptors: and a means for predicting, via the trained machine learning model, a surface energy of an input polymer.

DETAILED DESCRIPTION

In examples, the disclosure describes systems and techniques for predicting or computationally determining surface energies of polymers. In some examples, techniques and systems utilize a fingerprinting scheme for selecting a plurality of molecular descriptors that affect polymer surface energy, a selection operator to select a subset of the plurality of molecular descriptors based on minimization of an error value, and a material informatics machine learning (MI/ML) model trained to predict surface energies of a polymer based on the subset of molecular descriptors.

Rapid prediction of surface and interfacial energies with an MI/ML model streamlines the process to improve surface and interfacial energies for a variety of applications. Development and optimization of products, such as polymer products having particular surface and interfacial energies, may be slow due to the need to experimentally create the product and measure the surface and interfacial energies. Conventional computational prediction methods for polymer surface and interfacial energies suffer from poor prediction accuracy and offer only limited development improvements.

Surface energy (g) of solids, or surface tension of liquids, is generally defined as the work needed to create a surface at constant temperature, pressure, and composition. Surface energy is also related to interfacial energy (g12) which is generally defined as the energy required to create an interface between two surfaces, such as an adhesive and a substrate.

Surface energy and interfacial energy are design properties of materials in many applications and in adhesion science, as well as in the development of polymeric coatings with specific wetting properties, oleophobicity, hydrophobicity, and the like. Surface and interfacial energies may also be design properties for polymer processing, e.g., for release of polymeric materials from molds.

As an example, surface and interfacial energies may be important in designing adhesives for bonding to low surface energy substrates, such as polypropylene, or high surface energy substrates, such as metals. A generally observed tendency is that low surface energy adhesives bond well to low surface energy substrates while high surface energy adhesives bond well to high surface energy substrates.

The work of adhesion (Wadh) between two surfaces can be calculated from the surface energy and the interfacial energy: Wadh=g1+g2−g12. If Wadhis positive, the interface is stable and requires work to separate the two surfaces. If Wadhis negative, the interface is unstable and will separate spontaneously.

The interfacial energy between two surfaces can be calculated for non-polar or low-polar materials from the surface energies of the two materials via: g12=(g10.5−g20.5)2. This equation does not work well for strongly polar or hydrogen bonding materials. For strongly polar or hydrogen bonding types of materials, an approach that has been shown to work well is to express the surface energy as a sum of dispersive and polar/hydrogen bonding terms, namely g=gd+gx. The interfacial energy between two surfaces can then be calculated via g12=(gd10.5−gd20.5)2+(gx10.5−gx20.5)2.

Polar/hydrogen bonding surface energy components (gx) have been estimated by a number of methods and are available for many commonly used polymers. The polar/hydrogen bonding component may then be used to calculate the dispersive component from the overall surface energy of the material via g=gd+gx.

If the surface energies of two materials to be bonded are measured experimentally or predicted by computational theoretical methodologies, the surface energies can then be used to calculate the interfacial energies from the equations above for many material interfaces. However, experimental measurement is high cost (e.g., in terms of labor, time, materials, etc.) and conventional computational methods are low accuracy, also resulting in high cost.

The systems and techniques disclosed herein provide for computational prediction of polymer surface energies with improved accuracy and reduced cost. In some examples, a method of implementing a MI/ML model to rapidly predict surface energies for polymers is disclosed. The predicted surface energies may then be used to calculate interfacial energies, via the equations above.

FIG.1is a block diagram illustrating an example computing device configured to execute a polymer surface energy prediction technique, in accordance with the techniques of this disclosure. The architecture of computing device28illustrated inFIG.1is shown for exemplary purposes only and computing device28is not limited to this architecture. In other examples. computing device28may be configured in a variety of ways. Computing device28may be configured to execute a MI/ML model-based surface energy prediction method. for example. by executing surface energy prediction unit48.

As shown in the example ofFIG.1. computing device28includes one or more processors30. one or more user interface (UI) devices32. one or more communication units34. and one or more memory units36. Memory36of computing device28stores operating system38. user interface (UI) module40. telemetry module42. and surface energy prediction unit48. which are executable by processors30. Each of the components. units or modules of computing device28are coupled (physically, communicatively, and/or operatively) using communication channels for inter-component communications. In some examples, the communication channels may include a system bus, a network connection, an inter-process communication data structure, or any other technology for communicating data.

Processors30, in one example, may comprise one or more processors that are configured to implement functionality and/or process instructions for execution within computing device28. For example, processors30may be capable of processing instructions stored by memory36. Processors30may include, for example, microprocessors, a single-core processor, a multi-core processor. digital signal processors (DSPs). application specific integrated circuits (ASICs), field-programmable gate array (FPGAs), processing circuitry (e.g., fixed function circuitry. programmable circuitry, or any combination of fixed function circuitry and programmable circuitry) or equivalent discrete or integrated logic circuitry, or a combination of any of the foregoing devices or circuitry.

Memory36may be configured to store information (e.g., data and/or executable instructions) within computing device28during operation. Memory36may include a computer-readable storage medium or computer-readable storage device. In some examples, memory36may include one or more of a short-term memory or a long-term memory. Memory36may include, for example, one or more of random access memories (RAM). dynamic random access memories (DRAM), static random access memories (SRAM). on chip memory (e.g., in the case of SoC implementations). off chip memory, magnetic discs, optical discs, flash memories, or forms of electrically programmable memories (EPROM) or electrically erasable and programmable memories (EEPROM). In some examples, memory36is used to store program instructions for execution by processors30. Memory36may be used by software or applications running on computing device28(e.g., surface energy prediction unit48) to temporarily store information during program execution.

Computing device28may utilize communication units34to communicate with external devices via one or more networks and/or via wireless signals. Communication units34may be network interfaces, such as Ethernet interfaces, optical transceivers, radio frequency (RF) transceivers, or any other type of devices that can send and receive information. Other examples of interfaces may include Wi-Fi®, near field communication (NFC), or Bluetooth® radios. In some examples, computing device28utilizes communication units34to wirelessly communicate with an external device.

UI devices32may be configured to operate as both input devices and output devices. For example, UI devices32may be configured to receive tactile, audio, textual, or visual input from a user of computing device28. In addition to receiving input from a user, UI devices32may be configured to provide output to a user or machine via tactile, audio, digital, or visual means. In one example, UI devices32may be configured to output content such as a graphical user interface (GUI) for display at a display device. UI devices32may include a presence-sensitive display (e.g., a so-called “touchscreen”) that displays a GUI and receives input from a user using capacitive, inductive, and/or optical detection at or near the presence-sensitive display.

Other examples of UI devices32include a mouse, a keyboard, a voice responsive system, video camera, microphone, or any other type of device for detecting a command from a user, or a sound card, a video graphics adapter card, or any other type of device for converting a signal into an appropriate form understandable to humans or machines. Additional examples of UI devices32include a speaker, a cathode ray tube (CRT) monitor, a liquid crystal display (LCD), organic light emitting diode (OLED),. or any other type of device that can generate or relay output data in a manner that is intelligible to a user or a machine.

Operating system38provides a multitasking operating environment for the operation of components of computing device28. For example, operating system38facilitates the communication of UI module40, telemetry module42, and surface energy prediction unit48with processors30, UI devices32, communication units34, and memory36. UI module40, telemetry module42, and surface energy prediction unit48may each include program instructions and/or data stored in memory36that are executable by processors30. For example, surface energy prediction unit48may include instructions that cause computing device28to perform one or more of the techniques described in this disclosure.

Computing device28may include additional components that, for clarity, are not shown inFIG.1. For example, computing device28may include a battery to provide power to the components of computing device28. Similarly, the components of computing device28shown inFIG.1may not be necessary in every example of computing device28that is consistent with this disclosure.

In the example illustrated inFIG.1, surface energy prediction unit48includes descriptor unit50, machine learning unit52, training datasets database54, and descriptor database56. Descriptor unit50may comprise instructions for executing a hierarchical fingerprinting method to capture chemical and/or molecular descriptors that affect polymer surface energy. A molecular descriptor may be the final result of a logical and/or mathematical procedure which determines a numerical value and/or an experimental result based on chemical information encoded within a symbolic representation of a molecule. Descriptor unit50may be configured to execute feature engineering methods and/or processes to determine features and/or descriptors of a molecule, chemical, polymer, and the like, that are most relevant to surface energy. Descriptor unit50may provide structure and/or property information associated with the molecule, chemical, polymer, and the like. In some examples. descriptor unit50may be software, hardware, or a combination thereof configured to execute descriptor selection instructions, e.g., via execution of descriptor unit50by processors30. Descriptor unit50may be configured to select a subset of molecular descriptors from a larger initial set of molecular descriptors relevant to polymers. In some examples, descriptor unit50may retrieve at least a portion of the larger initial set of molecular descriptors from molecular descriptor database56. Molecular descriptor database56may be stored in memory36and/or retrieved from the memory of another device, such as a server, via communication units34. In some examples, descriptor unit50may be configured to generate at least a portion of the larger initial set of molecular descriptors, e.g., via cheminformatics software such as RDKit (www.rdkit.org). Descriptor unit50may be configured to select the subset of molecular descriptors based on their effects on polymer surface energy.

For example, a user may select a plurality of polymers from which descriptor unit50may capture and/or select one or more molecular descriptors that affect polymer surface energy. The user may provide a polymer identifier, such as a polymer specification in the form of a line notation (e.g., an American Standard Code for Information Interchange (ASCII) character string) for describing the structure of a polymer that may be used with a simplified molecular-input line-entry system (SMILES). In some examples, the user may input the SMILE specification to computing device28. In other examples the user may input a polymer identifier to computing device28, and descriptor unit50may form the SMILE specification using the polymer identifier. Descriptor unit50may then retrieve one or more descriptors for each polymer, e.g., from a database, or generate one or more descriptors for each polymer, e.g., via cheminformatics software such as RDKit. Descriptor unit50may store the retrieved and/or generated descriptors as a large initial set of molecular descriptors, e.g., in descriptor database56.

Descriptor unit50may be configured to categorize each molecular descriptor of the larger initial set of molecular descriptors as at least one of an atomic scale molecular descriptor, a molecular scale molecular descriptor, or a compound-scale molecular descriptor. For example. an atomic scale molecular descriptor may be a count of relevant atoms of a polymer, e.g., a count of halogen atoms, a count of oxygen atoms, a count of three-fold coordinated carbons, a count of four-fold coordinated carbons, and the like. Table 1 below includes a non-limiting list of relevant atoms. e.g., of a polymer and/or polymer fragment.

TABLE 1Example polymer fragments including relevant atomsAliphatic_COONhpyrrolefuranoximeAliphatic_OHSHguanidopara_hydroxylationAliphatic_OH_noTertaldehydehalogenphenolAromaticNalkyl_carbamatehdrzinephenol_noOrthoHbondAromatic_COOalkyl_halidehdrzonephos_acidAromatic_Nallylic_oxidimidazolephos_esterAromatic_NHamideimidepiperdineAromatic_OHamidineisocyanpiperzineCOOanilineisothiocyanpriamideCOO2aryl_methylketoneprisulfonamdC_Oazideketone_ToplisspyridineC_O_noCOOazolactamquatNC_SbarbiturlactonesulfideHOCCNbenzenemethoxysulfonamdIminebenzodiazepinemorpholinesulfoneNH0bicyclicnitrileterm_acetyleneNH1diazonitrotetrazoleNH2dihydropyridinenitro_aromthiazoleN_Oepoxidenitro_arom_nonorthiocyanNdealkylation1esternitrosothiopheneNdealkylation2etheroxazoleunbrch_alkaneureaindicates data missing or illegible when filed

A molecular scale molecular descriptor may comprise a population of pre-defined chemical building blocks, e.g., aldehydes, acids, aromatics, and the like. A compound-scale molecular descriptor may comprise quantitative structure-property relationship (QSPR) descriptors, e.g., van der Waals surface area, topological surface area, fraction of rotatable bonds, and the like. In some examples, descriptor unit50may be configured to categorize molecular descriptors hierarchically based on length scale. In some examples, descriptor unit50may be configured to categorize hundreds of molecular descriptors from the larger initial set of molecular descriptors. In some examples, descriptor unit50may be configured to categorize molecular descriptors by the length scale of a polymer or polymers. In some examples, descriptor unit50may be configured to categorize and/or classify ID molecular descriptors across the length scale of one or more polymers.

Descriptor unit50may be configured to select a subset of molecular descriptors based on each descriptor's effects on polymer surface energy from the larger, categorized set of molecular descriptors. For example, descriptor unit50may be configured to select the subset of molecular descriptors by executing regression methods including shrinkage (e.g., coefficient elimination) to select descriptors with the greatest effects on polymer surface energy. One example of such a technique that descriptor nit50may use is a least absolute shrinkage and selection operator (LASSO) that minimizes the sum of squared errors (between calculated and experimentally determined surface energies) with a bound on the sum of the absolute values of the LASSO coefficients. in this case. the descriptors. In the example ofFIG.3below. descriptor unit50is configured to categorize a set of150descriptors from a larger initial set of molecular descriptors relating to a training dataset of301chemically diverse polymers (e.g., from training datasets database54described below) and select a subset of descriptors (e.g.,30descriptors. although greater or fewer numbers of descriptors may be used in examples consistent with this disclosure) relevant to polymer surface energy via executing LASSO.

In some examples, a user may select and/or deselect one or more descriptors of the larger initial set of descriptors. For example, a user may know that one or more descriptors of the larger initial set of descriptors have an effect on polymer surface energy, and the user may select those one or more descriptors for inclusion with the subset of descriptors before and/or without either of categorization or selection (e.g., via regression methods) by descriptor unit50. In other examples. a user may know that one or more descriptor of the large initial set of descriptors has little or no effect on polymer surface energy and a user may omit those one or more descriptors from the subset of descriptors before and/or without either of categorization or selection by descriptor unit50, or may deselect those one or more descriptors if selected by descriptor unit50. In other words, a user may modify the larger initial set of descriptors retrieved and/or generated, and/or may modify the selected subset of descriptors.

Training datasets database54may include a plurality of polymers and the respective surface energies or each of the plurality of polymers. The surface energies may be known. measured. or otherwise reliably determined. Training datasets database54may further include details regarding the polymers, such as molecular composition, class, type, and/or categorization. and physical, electrical, and/or chemical properties. In some examples. training datasets database54may be curated from a chemical or polymer database. built via experimentally making polymers and measuring their physical, electrical. and/or chemical properties and inputting the measured properties and any other polymer information (e.g., composition, structure, experimental or formulation details. and the like) by a user to training datasets database54, or both. In some examples, training datasets database54may include the example dataset ofFIG.3described below. For example, training datasets database54may include301chemically diverse polymers, each of which may be numerically presented via one or more relevant molecular descriptors. In other words, each polymer may be associated with one or more molecular descriptors retrieved and/or generated as described above, each descriptor comprising a numerical value representing an aspect of the polymer, e.g., a chemical composition, a structure, a property, and the like.

Descriptor database56may include a plurality of molecular descriptors suitable for predicting the surface energies of polymers. For example, descriptor database56may include any of the larger initial set of molecular descriptors, a set of descriptors categorized by descriptor unit50into atomic, molecular, and/or compound-scale molecular descriptors, and/or a selected subset of molecular descriptors, e.g., selected via descriptor unit50as described above. Descriptor database56may include a plurality of molecular descriptors retrieved and/or generated and selected by descriptor unit50based on one or more training datasets of training datasets database54. Descriptor database56may include updated descriptors and/or new descriptors added. e.g., via machine learning unit52.

Machine learning unit52may be configured to predict a surface energy of a polymer based on one or more descriptors, e.g., from descriptor database56. In some examples. machine learning unit52may be a single-fidelity machine learning model. In some examples, machine learning unit52may implement Gaussian Process Regression (GPR) with a radial basis function (RBF) kernel configured to map one or more polymers to respective surface energies. GPR uses a Bayesian framework in which a Gaussian process is used to obtain the mapping from a polymer to its surface energy based on an available training dataset of polymers and associated descriptors and a Bayesian prior, which is incorporated using the kernel function. In some examples, machine learning unit52may implement GPR with cross-validation, e.g., GPR comprising a five-fold cross-validation.

The techniques, devices, and systems disclosed herein may provide an improvement in accuracy at a reduced cost, e.g., relative to conventional computational methods of predicting, and/or experimental methods of determining, polymer surface energy. For example, descriptor unit50and machine learning unit52may be configured to provide computational prediction according to methods with a greater emphasis and/or focus on polymer attributes relevant to polymer surface energy. By way of contrast, conventional computational methods for polymer surface energy prediction may approximate surface energy property/structure relationships by correlating a relatively small number (e.g., one, two, five, ten) of inherent properties to semi-empirical equations by fitting to experimental data, or approximate group contribution surface energy property/structure relationships by correlating chemical groups to experimental data, which requires a database of chemical fragments with group contributions to properties. The techniques, devices, and systems disclosed herein are predictive based on polymer composition and do not require a database of chemical group contributions. The techniques, devices, and systems disclosed may provide fast (e.g., within hours, within minutes, or within seconds) or potentially even substantially instantaneous polymer surface energy prediction with improved accuracy.

FIG.2Ais a flowchart of an example method200of training a machine informatics/machine learning (MI/ML) model for polymer surface energy prediction. in accordance with one or more techniques of this disclosure. Although method200is discussed using computing device28ofFIG.1, it is to be understood that the methods discussed herein may include and/or utilize other systems and methods in other examples.

Computing device28may select a set of polymers and/or polymer compositions (202). For example, computing device28may receive a selection input via one or more of UI devices32. For example, a user may select a population of chemically diverse polymers having a range of polymer surface energies. In the examples ofFIGS.4-8,301chemically diverse polymers are selected.

Computing device28may determine a plurality of molecular descriptors that control a polymer surface energy (204). Computing device28may retrieve, receive, and/or generate a plurality and/or a set of molecular descriptors, e.g., a large initial set of molecular descriptors. For example, computing device28may generate a large initial set of molecular descriptors via cheminformatics software and based on a plurality of polymers and their respective surface energies. In other examples, computing device28may retrieve and/or receive the larger initial set of molecular descriptors from a database, such as descriptor database56. Computing device28may categorize each molecular descriptor of the larger initial set of molecular descriptors as at least one of an atomic scale molecular descriptor, a molecular scale molecular descriptor, or a compound-scale molecular descriptor. In some examples, the plurality of molecular descriptors affect a homopolymer surface energy.

Computing device28may categorize a polymer according to an atomic scale property including a count of relevant atoms, the relevant atoms including at least one of a halogen, oxygen, a three-fold coordinated carbon, or a four-fold coordinated carbon. Computing device28may categorize a polymer according to a molecular scale property including a count of functional groups, the functional groups including a count of at least one of an aldehyde group, an acid group, or an aromatic group. Computing device28may categorize a polymer according to a compound scale property including at least one of a van der Waals surface area, a topological surface area, or a fraction of rotatable bonds.

Computing device28may select a subset of molecular descriptors that affect a polymer surface energy based on a minimization of an error (206). For example, computing device28may execute a hierarchical fingerprinting method to capture chemical and/or molecular descriptors that affect polymer surface energy. In some examples, computing device28may select a subset of molecular descriptors based on each descriptor's effects on polymer surface energy from the larger, categorized set of molecular descriptors. In some examples, computing device28may execute a LASSO to select the subset of molecular descriptors.

In some examples, computing device28may process user input data received via one or more of UI devices32to select and/or deselect one or more descriptors of the larger initial set of descriptors. For example, one or more descriptors of the large initial set of descriptors may be known to have an effect on polymer surface energy, and a user may select those one or more descriptors for inclusion within the subset of descriptors before and/or without either of categorization or selection (e.g., via regression methods) at blocks (204) and/or (206). In other examples, one or more descriptors of the larger initial set of descriptors may be known to have little or no effect on polymer surface energy, and a user may omit those one or more descriptor from the subset of descriptors before and/or without either of categorization or selection by computing device28, or may deselect those one or more descriptors if previously selected by computing device28. In other words, a user may modify the large initial set of descriptors retrieved and/or generated, and/or may modify the selected subset of descriptors.

Computing device28may train a machine learning (ML) model to predict a polymer surface energy of a given polymer based on the subset of molecular descriptors (208). For example, computing device28may train a GPR ML model with an RBF kernel to map one or more polymers to respective surface energies using a training dataset of training datasets database54. In some examples, the one or more training polymers may be homopolymers. In examples describe below, a dataset includes301distinct and chemically diverse polymers having known or determined surface energies ranging from 7 mN/m to 72 mN/m (e.g., as illustrated inFIG.3). Computing device28may use241of the polymers of the dataset to train the GPR ML model, and reserve60of the polymers for testing and/or validation of the trained GPR ML model, e.g., five-fold cross-validation.

Computing device28may train a ML model with a training dataset comprising a plurality of polymers. each polymer including a plurality of polymer classes. For example, computing device28may train the ML model with a training dataset including at least one of a polyoxide, a polyvinyl, a polyolefin, a polyamide, or a polyether. Computing device28may train a ML model with a training dataset that further includes a plurality of chemical moieties including at least one of hydrogen, carbon, nitrogen, oxygen, sulfur, silicon, fluorine, chlorine, or bromine. In some examples, computing device28may train the ML model with a training dataset including at least one experimentally determined surface energy of at least one of the plurality of polymers of the training dataset.

FIG.2Bis a flowchart of an example method250of predicting a polymer surface energy via a trained MI/ML model, in accordance with one or more techniques of this disclosure. Although method250is discussed using computing device28ofFIG.1, it is to be understood that the methods discussed herein may include and/or utilize other systems and methods in other examples.

Computing device28may select a polymer and/or polymer composition (252). For example, computing device28may generate, retrieve, and/or receive. e.g., from a user or another computing device, a new polymer, and/or a specification of a new polymer, for surface energy prediction, and may provide information relating to the new polymer to computing device28.

Computing device28may determine a plurality of molecular descriptors (254). For example, computing device28may retrieve, receive, and/or generate a plurality and/or a set of molecular descriptors, e.g., a large initial set of molecular descriptors, as described above with respect toFIG.2A. for the user-selected polymer and/or polymer composition.

Computing device28may select a subset of descriptors that affect a polymer surface energy (256). In some examples, computing device28may select one or more of the same descriptors as the subset of molecular descriptors determined at block (206) of method200ofFIG.2A. For example, if computing device28determines molecular descriptors that includes all of the subset of molecular descriptors that affect polymer surface energy selected at block (206) of method200ofFIG.2A, computing device28might select the same subset of descriptors relating to the new polymer and/or polymer composition, e.g., the same subset of descriptors but having descriptor values relating to the new polymer and/or polymer composition. If computing device28determines molecular descriptors that do not include all of the subset of molecular descriptors that affect polymer surface energy selected at block (206) of method200ofFIG.2A. e.g., if there is not enough information regarding a new polymer to retrieve and/or generate all of the subset of molecular descriptors, computing device28may select at least a portion of the same descriptors as the subset of molecular descriptors selected at block (206) of method200ofFIG.2A.

Computing device28may predict a surface energy of an input polymer via the trained machine learning model (266). For example, computing device28may execute the trained GPR ML model to predict the surface energy of a polymer. In the examples described inFIGS.3-6below, computing device28may predict the surface energies of the60reserved polymers. e.g., to validate and/or test the performance of the trained GPR ML model. In some examples, the input polymer may be a homopolymer. In some examples, computing device28may predict a surface energy of an input polymer using a machine learning model without group contribution surface energy property/structure relation methods. without group additive contribution methods, and/or without a database of chemical group contributions. In some examples, computing device28may execute the trained GPR ML model with cross-validation. e.g., a five-fold cross-validation.

In some examples, training the machine learning model at block (208) of the method200ofFIG.2Amay be optional. For example, computing device28may predict a surface energy of an input polymer without training the machine learning model. In some examples, the machine learning model may have been previously trained. may not require training, or may be trained “on the fly” and over time via predicting a plurality of input polymers and receiving information related to the surface energy and/or accuracy of the predictions of the surface energies of at least a portion of the input polymers.

FIG.3is a histogram300of an example dataset for training and validation of a material informatics machine learning (MI/ML) model, in accordance with the techniques described in this disclosure. In the example shown, the dataset includes301distinct polymers. The surface energies of each of the301polymers are experimentally determined and/or measured. The dataset of the example is curated from a database from National Institute for Materials Science (NIMS) of Tsukuba, Japan, https://mits.nims.go.jp/en/. The dataset comprises several polymer classes including polyoxides, polyvinyls, polyolefins, polyamides, and polyethers and includes a plurality of diverse chemical moieties that include at least one of hydrogen, carbon, nitrogen, oxygen, sulfur, silicon, fluorine, chlorine, or bromine.

FIG.4is a set of four plots402-408illustrating example root-mean squared errors of a MI/ML model as a function of training dataset size. in accordance with the techniques described in this disclosure. Plots402-208represent learning curves of the MI/ML model (e.g., a GPR ML model with a RBF kernel). Plots402-408illustrate the average training and cross-validation root-mean-squared-error (RMSE) of the ML/MI model as a function of training set size. e.g., as a decimal percentage from 0.0-1.0 where 1.0 is 100%. of the 241 polymers. The validation set ofFIG.4refers to fractions of the241polymer training set as shown on the horizontal (x-) axis, all of which are distinct from the60polymers used for ML/MI model testing. The error bars represent1standard deviation of the average RMSE values over20iterations of the ML/MI model. In the example shown, plots402and406are learning curves of the ML/MI model trained using a set of descriptors selected according to the fingerprinting method described above, e.g., categorized via atomic, molecular, and compound-scale descriptors but without reduction via LASSO. Plots404and408are learning curves of the ML/MI model trained using a set of descriptors selected according to the fingerprinting method described above, e.g., with reduction of the descriptors used to via LASSO to a subset of the categorized set of descriptors.

In the example shown, the cross-validation RMSE of the ML/MI model trained with all initial descriptors (e.g., plots402and406) and LASSO reduced descriptors (e.g., plots404and408) decrease with increasing training set size. The ML/MI model trained with LASSO-reduced descriptors, on average, have lower test RMSE than the ML/MI model trained without reducing the set of descriptors via LASSO. By way of these examples. LASSO regression is shown to be an effective method for eliminating irrelevant and/or less relevant descriptors, thereby simplifying and reducing the time and/or computing power consumed by the ML/MI model. For example, LASSO may identify descriptors pertinent to the surface energy of a polymer, such as polar chemical moieties like halogens, functional groups like nitrile, carbonyl, amide, and amine. LASSO may also identify large-scale descriptors like the total polar surface area (TPSA) and log P of a polymer as important and/or relevant descriptors for determining surface energy.

FIG.5is a plot500of an example comparison of the measured surface energy of each of a plurality of polymers of the dataset ofFIG.3versus the surface energy of each of the plurality of polymers predicted by an example MI/ML model in accordance with the techniques described in this disclosure. In the example shown, data points502correspond to the241training polymers, and data points504correspond to the60test polymers.

In the example shown, an ML/MI model trained on the training set of241polymers predicted. e.g., according to method200described above, the surface energies of the241training polymers with an average RMSE of 4.21 mN/m and results in a linear correlation R-squared value of 0.90 with respect to the experimentally measured surface energies of the241training polymers. The ML/MI model predicted the surface energies of the test polymers with an average RMSE of 6.95 mN/m and a linear correlation R-squared value is 0.77 with respect to the experimentally measured surface energies of the60reserved test polymers. In the example shown, the error bars illustrate the ML/MI model (e.g., the GPR) uncertainty. In the example shown, predictions for polymers with higher surface energies, e.g., greater than 60 mN/m. are less accurate due to underrepresentation of higher surface energy polymers in the training data set, e.g., as illustrated inFIG.3. In some examples. including a greater number of training polymers to the training data set may increase the prediction accuracy of the ML/MI model.

FIGS.6A-6Care plots of an example measured surface energy of each of a plurality of polymers versus the surface energy of each of the plurality of polymers predicted by an example computational model and illustrate a comparison of three different polymer surface energy computation models.FIG.6Ais a plot600of measured polymer surface energy versus polymer surface energy predicted by a ML/MI model. in accordance with the techniques described in this disclosure.FIG.6Bis a plot610of measured polymer surface energy versus polymer surface energy predicted by a first example conventional computation model. andFIG.6Cis a plot620of measured polymer surface energy versus polymer surface energy predicted by a second conventional computation model. The measured versus predicted surface energies are of all301polymers of the example dataset described above.

In the example shown inFIG.6B. the first example conventional computation model is a Dow Synthia model for predicting surface energies uses the polymer property/structure prediction methodology developed by J. Bicerano of Dow Chemical as implemented in the program Synthia from Dassault Systemes/Biovia. https://www.3ds.com/fileadmin/PRODUCTS-SERVICES/BIOVIA/PDF/BIOVIA-Material-Studio-synthia.pdf. In the example shown inFIG.6C. the second example conventional computation model is a Van Krevelen model for predicting surface energies uses the polymer properties group additive predictive method developed by D.W. van Krevelen as implemented in the program Molecular Modeling Plus from Norgwyn Montgomery Software, http://www.norgwyn.com/mmpplus.html.

In the example ofFIG.6A, which illustrates the performance of a ML/MI model trained according to aspects of this disclosure, the ML/MI model average prediction RMSE is 4.93 mN/m and linear correlation R-squared value is 0.90 with respect to the experimentally measured polymer surface energies. The ML/MI model in the examples shown provides a greater prediction accuracy than the Dow Synthia and Van Krevelen predictions, with average RMSEs of 17.2 mN/m and 18.2 mN/m and linear correlation R-squared values of 0.12 and.02. respectively.

FIGS.7A-7Care plots of a plurality of example surface energy absolute differences (e.g., difference magnitude) between measured polymer surface energies and predicted polymer surface energies predicted by the three different polymer surface energy computation models ofFIGS.6A-6C.FIG.7Ais a plot700of a plurality of example surface energy absolute differences between measured polymer surface energies and polymer surface energies predicted by a ML/MI model, in accordance with the techniques described in this disclosure.FIG.7Bis a plot710of a plurality of example surface energy absolute differences between measured polymer surface energies and polymer surface energies predicted by a first example conventional computation model, andFIG.7Cis a plot720of a plurality of example surface energy absolute differences between measured polymer surface energies and polymer surface energies predicted by a second conventional computation model. Plots7A-7C illustrate the same measured/predicted polymer surface energies as plots6A-6C. but plotted as a magnitude of the difference between the measured and predicted values as a function of polymer (e.g., the x-axis) rather than the measured vs. predicted plots ofFIGS.6A-6C.

The examples shownFIGS.7A-7Cvisually illustrate the accuracy of each computation model for the entire data set of polymers, e.g., all301polymers of the example dataset described above. A perfect match between prediction and measurement would have all data points along the x-axis with an absolute difference of zero. The larger the distance of the datapoints from the x-axis. such as withFIGS.7B-7C. the less accurate the predictions given by the model.

As shown inFIG.7Ais, the accuracy of the predictions of the ML/MI model is greater than the conventional computation models ofFIGS.7B and7C. e.g., the absolute differences between the measure polymer surface energies and the polymer surface energies predicted by the ML/MI model are less than the absolute differences between the measured polymer surface energies and the polymer surface energies predicted by either conventional model ofFIGS.7B-7C.FIG.7Aalso illustrates that the absolute differences between measured and ML/MI model predicted polymer surface energies are clustered around low. e.g., 5 mN/m or less, absolute differences much more than the absolute differences between measured and conventional computation model predicted polymer surface energies as shown inFIGS.7B-7C.

The following examples may illustrate one or more aspects of the disclosure:

Example 1: A method includes determining a plurality of molecular descriptors, each molecular descriptor of the plurality of molecular descriptors associated with at least one of an atomic scale property, a molecular scale property, and a compound-scale property: selecting, by a selection operator and based on a minimization of an error, a subset of the plurality of molecular descriptors that affect a polymer surface energy: training a machine learning model to predict a polymer surface energy of a given polymer based on the subset of molecular descriptors: and predicting, via the trained machine learning model, a surface energy of an input polymer.

Example 2: The method of example 1, wherein the polymer is a homopolymer.

Example 3: The method of any of examples 1 and 2, wherein the atomic scale property comprises a count of relevant atoms.

Example 4: The method of example 3, wherein the relevant atoms comprise at least one of a halogen, oxygen, a three-fold coordinated carbon, or a four-fold coordinated carbon.

Example 5: The method of any of examples 1 through 4, wherein the molecular scale property comprises a count of functional groups.

Example 6: The method of example 5, wherein the count of functional groups comprises a count of at least one of an aldehyde group, an acid group, or an aromatic group.

Example 7: The method of any of examples 1 through 6, wherein the compound scale property comprises at least one of a van der Waals surface area, a topological surface area, or a fraction of rotatable bonds.

Example 8: The method of any of examples 1 through 7, wherein the selection operator comprises a least absolute shrinkage and selection operator (LASSO).

Example 9: The method of any of examples 1 through 8, wherein the machine learning model comprises a Gaussian Process Regression (GPR) comprising a radial basis function (RBF) kernel.

Example 10: The method of example 9, wherein the GPR further comprises a five-fold cross-validation.

Example 11: A method includes determining a plurality of molecular descriptors, each molecular descriptor of the plurality of molecular descriptors associated with at least one of an atomic scale property, a molecular scale property, and a compound-scale property: selecting, by a selection operator and based on a minimization of an error, a subset of the plurality of molecular descriptors that affect a polymer surface energy: predicting, via a trained machine learning model, a surface energy of an input polymer.

Example 12: The method of example 11, wherein the atomic scale property comprises a count of relevant atoms.

Example 13: The method of example 12, wherein the relevant atoms comprise at least one of a halogen, oxygen, a three-fold coordinated carbon, or a four-fold coordinated carbon.

Example 14: The method of any of examples 11 through 13, wherein the molecular scale property comprises a count of functional groups.

Example 15: The method of example 14, wherein the count of functional groups comprises a count of at least one of an aldehyde group, an acid group, or an aromatic group.

Example 16: The method of any of examples 11 through 15, wherein the compound-scale property comprises at least one of a van der Waals surface area, a topological surface area, or a fraction of rotatable bonds.

Example 17: The method of any of examples 11 through 16, wherein the selection operator comprises a least absolute shrinkage and selection operator (LASSO).

Example 18: The method of any of examples 11 through 17, wherein the machine learning model comprises a Gaussian Process Regression (GPR) comprising a radial basis function (RBF) kernel and a five-fold cross-validation.

Example 19: The method of any of examples 11 through 18, wherein the machine learning model is trained with a training dataset comprising a plurality polymers, wherein the plurality polymers comprises a plurality of polymer classes comprising at least one of a polyoxide, a polyvinyl, a polyolefin, a polyamide, or a polyether, wherein the training dataset further comprises a plurality of chemical moieties, wherein the plurality of chemical moieties includes at least one of hydrogen, carbon, nitrogen, oxygen, sulfur, silicon, fluorine, chlorine, or bromine, wherein the training dataset further comprises at least one experimentally determined surface energy of at least one of the plurality of polymers.

Example 20: A computer readable medium includes instructions that when executed cause one or more processors to: determine a plurality of molecular descriptors, each molecular descriptor of the plurality of molecular descriptors associated with at least one of an atomic scale property, a molecular scale property, and a compound-scale property: select, by a selection operator and based on a minimization of an error, a subset of the plurality of molecular descriptors that affect a polymer surface energy: predict, via a trained machine learning model, a surface energy of an input polymer; and output the predicted surface energy.