Multi-fidelity modeling approach for polymer property prediction

Abstract

According to embodiments, a method predicting at least one property of a polymer includes acquiring data from sources to produce experimental data relating to the polymer, performing a second number of molecular simulations, and combining the experimental data and the simulation data into a model for predicting the property of the polymer. The at least one property of the polymer may be a glass transition temperature (Tg). The experimental data provides high fidelity data while simulation data provides low fidelity data. The multi-fidelity model may be a machine learning model. Selecting design alternatives for polymer structures based on the predicted value of at least one property made by the model. The model may be a linear gaussian process surrogate model. A quantitative measure of prediction uncertainty of the model may be calculated, allowing the determination of optimal locations in a design space of the polymer for further experimentation or simulation.

Description

202303330 MULTI-FIDELITY MODELING APPROACH FOR POLYMER PROPERTY PREDICTION TECHNICAL FIELD

[0001] This application relates to materials engineering. BACKGROUND

[0002] Predicting material physico-chemical properties for polymers, such as the glass transition temperature (Tg) is an important consideration in polymer design for a target application. For example, with respect to Tg, Tg affects almost all polymer properties related to processing the material performance as the polymer properties change significantly when the polymer undergoes glass transition. Synthesizing and testing new polymer chemistries for their corresponding properties, e.g., Tg, through experimentation is costly and time-consuming. Further, a significant number of possible polymer chemistries exist, creating a large design space that must be explored.

[0003] Conventionally, researchers use physical experiments to determine the physico-chemical properties of polymers and often perform blind iterations of experiments to identify the molecular structure that has the desired properties. However, such experiments are costly and time consuming. For these reasons, researchers also use molecular simulations and machine learning techniques to predict the material properties and direct the exploration of the molecular structure design space in a more cost and time efficient manner.

[0004] Another approach to aid polymer design is molecular simulation, as the polymer properties can be determined in silico without requiring the costly synthesis of new polymer chemistries. Conventional methods using molecular simulation typically have202303330 some degree of error in the prediction of polymer properties, for example, molecular simulation overpredicts the Tg due to differences in time scales between experiments and simulations. Specifically, the simulation timeframe is much shorter than those of experiments and this affects the Tgprediction. To overcome this, researchers typically fine-tune simulation parameters for a specific subset of polymers to account for simulation errors, but this requires additional expertise and development effort.

[0005] Machine learning (ML) techniques have shown some benefits for predicting properties like Tg in polymers when there is an abundant amount of experimental and polymer characterization data available. However, for polymers with little experimental and characterization data, machine learning can fall short of expectations.

[0006] Some recent studies have focused on multi-fidelity models to predict some polymer properties by combining values determined from theoretical models, such as group contribution theory, with experimental data. However, these methods may not be applicable to properties determined through molecular dynamics simulations. SUMMARY

[0007] According to embodiments described in this disclosure, a method for predicting at least one physico-chemical property of a polymer includes obtaining data from a small number of experiments (by either performing the relevant experiments or obtaining the values from other resources such as literature or available databases) to produce sparse experimental data relating to the polymer, obtaining a second number of molecular simulation data (or performing molecular simulations to produce simulation data), and combining the experimental data and the simulation data into a model for predicting at least one property of the polymer. The at least one property of the polymer may be a202303330 glass transition temperature (Tg). The experimental data provides high fidelity data while the simulation data provides low fidelity data. The model is a multi-fidelity model. The multi-fidelity model may be a machine learning model. A design property for a polymer is defined as a target physico-chemical property to be optimized with regards to an application and may be based on the prediction of at least one property made by the model. This definition will be used thereafter. The model may be a linear gaussian process surrogate model. A quantitative measure of a prediction uncertainty of the model may be calculated, allowing the determination of optimal locations in a design space of the polymer for further experimentation or simulation.

[0008] The molecular simulation data is either obtained from available resources or created by performing at least one molecular simulation to determine the design property of the polymer. This data may be evaluated by the model using available experimental data and the molecular simulation data. The polymer structure may be put into a format useable by a machine learning model which may be achieved by constructing a molecular fingerprint as a numerical description of one or more repeat units in the polymer structure and producing a vector representative of the molecular fingerprint for input to the ML model.

[0009] According to other embodiments, a system for predicting at least one property of a polymer includes a computer processor and a non-transitory computer memory in communication with the computer processor. The non-transitory computer memory stores machine readable instructions executed by the computer processor causing the computer processor to perform a small number of experiments to access sparse experimental data relating to the polymer, perform a second number of molecular simulations to produce202303330 simulation data, and combine the experimental data and the simulation data into a model for predicting the at least one property of the polymer. The at least one property of the polymer may be a glass transition temperature (Tg). The experimental data provides high fidelity data while the simulation data provides low fidelity data, making the model a multi- fidelity model. The multi-fidelity model may be a machine learning model. The model may be implemented as a linear gaussian process surrogate model. According to some embodiments, a quantitative measure of a prediction uncertainty of the model may be determined and used to determine optimal locations in a design space of the polymer for further experimentation or simulation. The model includes a representation of the polymer structure in a format useable for machine learning, molecular simulation data, for example performing a molecular simulation to determine the Tg of the polymer, and the available experimental data.

[0010] The polymer structure may be represented in a format useable by a machine learning model. ., Several methods have been reported and utilized such as graph representations, grammar based representations eg., SMILES, SELFIES,expert-based molecular fingerprints. For example, the polymer molecular structure can be encodedby constructing a molecular fingerprint as a numerical description of one or more repeat units in the polymer structure and by combining the numerical descriptions to produce a vector representative of the molecular fingerprint for input to the ML model. BRIEF DESCRIPTION OF THE DRAWINGS

[0011] The foregoing and other aspects of the present invention are best understood from the following detailed description when read in connection with the accompanying drawings. For the purpose of illustrating the invention, there is shown in the drawings202303330 embodiments that are presently preferred, it being understood, however, that the invention is not limited to the specific instrumentalities disclosed. Included in the drawings are the following Figures:

[0012] FIG.1 is an illustration of mapping a polymer structure to a molecular fingerprint according to aspects of embodiments of this disclosure.

[0013] FIG.2 is a graphical depiction of the density curve of a polymer.

[0014] FIG.3 is a graphical depiction comparing simulations of different fidelities to a reference function.

[0015] FIG.4 is a block diagram for building a multi-fidelity model according to aspects of embodiments of this disclosure.

[0016] FIG.5 is a block diagram of a computer system, which may be used to make and use aspects of embodiments described in this disclosure. DETAILED DESCRIPTION

[0017] Embodiments described in this disclosure provide systems and methods for optimally combining experimental and molecular simulation data for polymers, which aid in the prediction of physio-chemical properties where limited experimental data is available. This may include data that is sparse, data that is too similar to other data in the same dataset, and biased datasets. When applied to intricate or unique polymers where little historical information is available regarding these polymers, as described in embodiments, these methods further provide guidance on the design process by indicating the most likely productive areas for future experimentation and synthesis of target polymer molecular structures. This guidance increases the speed of development202303330 while reducing the associated costs and number of experiments needed to optimize a property of interest.

[0018] The embodiments of this disclosure are particularly useful when applied to intricate or unique polymers where little is known about these polymers. By providing guidance on the ongoing design process by speeding up development and optimizing the property of interest.

[0019] The following systems and methods combine experimental and simulation data through application of a multi-fidelity Gaussian Process (GP) surrogate modeling approach. This technique has demonstrated an improvement in prediction accuracy and a reduction of uncertainty of the prediction of a polymer physico-chemical property (e.g., Tg) as compared to surrogate models that are built directly on sparse datasets either experimental or obtained from simulation. Additionally, the described embodiments integrate various low-fidelity data sources in a hierarchical manner along with molecular simulations for estimating various physio-chemical properties.

[0020] An exemplary embodiment will now be described for using multi-fidelity modeling to determine the Tgof a polymer. It will be understood that the methods and techniques described are not limited to this example and may be used for simulating other properties relating to a given polymer or other object being evaluated.

[0021] Multi-fidelity modeling includes the following steps:

[0022] 1. Representing the polymer structure in a suitable manner for machine learning;

[0023] 2. performing molecular simulations to determine Tg; and202303330

[0024] 3. building the multi-fidelity model with the simulations from step 2 and available experimental data.

[0025] First, the polymer structure is represented in a manner that can be utilized by machine learning. This is accomplished by creating a molecular fingerprint 130 that provides a numerical description of the chemical structure of the polymer repeat units 101, 103. Repeat units 101, 103 are the building blocks to form a polymer 120 of which 110 is an example of a section of polymer 120. FIG. 1 is an illustration of achieving a molecular fingerprint 130 from a polymer structure where the polymer 120 includes two repeat units 101, 103 arranged in random order sequence 110. The chemical structure of the repeat units 101, 103 are represented as molecular fingerprints that are combined with the polymer chain 120 to form a vector that is suitable for use as in input to a surrogate model.

[0026] Next, Molecular dynamics simulations are performed to determine Tg for a variety of polymer structures. The molecular simulations include simulating polymers at various temperatures and calculating the density at each temperature. The Tg is determined from a distinct change in slope of the density as a function of temperature as shown in FIG.2.

[0027] FIG.2 is a graphical representation of a polymer's density versus temperature according to embodiments of this disclosure. At lower temperatures, the polymer exhibits a glassy state in region 205. At the temperature point characterizing Tg 210, the slope changes significantly to a steeper curve in density 200 and goes to the rubbery state region 215 at temperatures above the Tg. Then when the polymer reaches even higher temperatures, a transition from the rubbery state 215 to a liquid state 225 occurs at202303330 transition temperature 215. At each transition 210, 220, an abrupt change in the slope of the density curve 200 may be observed.

[0028] Finally, a multi-fidelity GP model is used to combine the experimental and simulation data. According to an embodiment, a linear multi-fidelity GP model is used and in this case the high-fidelity portion is modelled as a linear sum of the low fidelity function and an additional bias term is introduced that accounts for differences between the high and low fidelities. The high-fidelity model is a gaussian process based on experimental data and the low fidelity model is a gaussian process based on simulation data according to: ^^ℎ ^^ ^^ℎ(^^)= ^^ ^^ ^^ ^^ ^^(^^)+ ^^ ^^ ^^ ^^ ^^(^^)

[0029] As shown in FIG.3 on an academic example, the multi-fidelity model is built on 6 high-fidelity datapoints and 10 low-fidelity datapoints from a high- and low-fidelity versions of the Forrester function, respectively.

[0030] The high-fidelity function is: ^^ℎ ^^ ^^ℎ( ^^) = 2 (6 ^^ − 2)2sin(12 ^^ − 4)

[0031] The low-fidelity function is an approximation of the high-fidelity function: ^^^^ ^^ ^^(^^)= 0.5 ^^ℎ ^^ ^^ℎ(^^)+ 10(^^ − 0.5)+ 5

[0032] In FIG.3, it may be seen that the single-fidelity GP trained on only the high- fidelity data 301 does not accurately capture the features of the function 310 such as the local and global optima in the observed range. However, the multi-fidelity function 303 accurately captures the high-fidelity function behavior over the range, except for high values of x, where there are not datapoints at either fidelity.202303330

[0033] Lastly, we apply the multi-fidelity GP to predict the Tg for polymers. The experimental data was obtained from the CROW polymer property database and the simulations were performed for a selection of the polymers and some additional polymers derived from the dataset.

[0034] The results for a selection of chemical structures are shown in FIG.4, where it may be seen that the single-fidelity GP surrogate model 415 (built only on experimental 410 or simulation data 430) has large error and uncertainty in the Tg prediction 420, while the multi-fidelity model 440 significantly reduces the error and uncertainty of the predictions 450.

[0035] Additionally, the multi-fidelity Gaussian Process surrogate model 440 provides a quantitative measure of the prediction uncertainty, which can be used to determine the optimal locations in the design space where further simulations and / or experiments could be performed to optimize the Tg for a set of polymer chemistries of interest.

[0036] The combination of improved prediction accuracy and information on which follow-up simulations / experiments would be most beneficial to conduct (informed by the uncertainty estimates provided by the model), makes the multi-fidelity Gaussian Process surrogate model a powerful tool to navigate polymer design spaces when only limited experimental results are available. Additionally, as the molecular simulations are still relatively computationally expensive, the approach also informs which combination of simulations and / or experiments would be most beneficial to perform next in the design space as opposed to a more costly traditional exploration of the design space.

[0037] FIG. 5 illustrates an exemplary computing environment 500 within which embodiments of the invention may be implemented. Computers and computing202303330 environments, such as computer system 510 and computing environment 500, are known to those of skill in the art and thus are described briefly here.

[0038] As shown in FIG.5, the computer system 510 may include a communication mechanism such as a system bus 521 or other communication mechanism for communicating information within the computer system 510. The computer system 510 further includes one or more processors 520 coupled with the system bus 521 for processing the information.

[0039] The processors 520 may include one or more central processing units (CPUs), graphical processing units (GPUs), or any other processor known in the art. More generally, a processor as used herein is a device for executing machine-readable instructions stored on a computer readable medium, for performing tasks and may comprise any one or combination of, hardware and firmware. A processor may also comprise memory storing machine-readable instructions executable for performing tasks. A processor acts upon information by manipulating, analyzing, modifying, converting or transmitting information for use by an executable procedure or an information device, and / or by routing the information to an output device. A processor may use or comprise the capabilities of a computer, controller or microprocessor, for example, and be conditioned using executable instructions to perform special purpose functions not performed by a general-purpose computer. A processor may be coupled (electrically and / or as comprising executable components) with any other processor enabling interaction and / or communication there-between. A user interface processor or generator is a known element comprising electronic circuitry or software or a combination of both202303330 for generating display images or portions thereof. A user interface comprises one or more display images enabling user interaction with a processor or other device.

[0040] Continuing with reference to FIG.5, the computer system 510 also includes a system memory 530 coupled to the system bus 521 for storing information and instructions to be executed by processors 520. The system memory 530 may include computer readable storage media in the form of volatile and / or nonvolatile memory, such as read only memory (ROM) 531 and / or random-access memory (RAM) 532. The RAM 532 may include other dynamic storage device(s) (e.g., dynamic RAM, static RAM, and synchronous DRAM). The ROM 531 may include other static storage device(s) (e.g., programmable ROM, erasable PROM, and electrically erasable PROM). In addition, the system memory 530 may be used for storing temporary variables or other intermediate information during the execution of instructions by the processors 520. A basic input / output system 533 (BIOS) containing the basic routines that help to transfer information between elements within computer system 510, such as during start-up, may be stored in the ROM 531. RAM 532 may contain data and / or program modules that are immediately accessible to and / or presently being operated on by the processors 520. System memory 530 may additionally include, for example, operating system 534, application programs 535, other program modules 536 and program data 537.

[0041] The computer system 510 also includes a disk controller 540 coupled to the system bus 521 to control one or more storage devices for storing information and instructions, such as a magnetic hard disk 541 and a removable media drive 542 (e.g., floppy disk drive, compact disc drive, tape drive, and / or solid-state drive). Storage devices may be added to the computer system 510 using an appropriate device interface (e.g., a202303330 small computer system interface (SCSI), integrated device electronics (IDE), Universal Serial Bus (USB), or FireWire).

[0042] The computer system 510 may also include a display controller 565 coupled to the system bus 521 to control a display or monitor 566, such as a cathode ray tube (CRT) or liquid crystal display (LCD), for displaying information to a computer user. The computer system includes an input interface 560 and one or more input devices, such as a keyboard 562 and a pointing device 561, for interacting with a computer user and providing information to the processors 520. The pointing device 561, for example, may be a mouse, a light pen, a trackball, or a pointing stick for communicating direction information and command selections to the processors 520 and for controlling cursor movement on the display 566. The display 566 may provide a touch screen interface which allows input to supplement or replace the communication of direction information and command selections by the pointing device 561. In some embodiments, an augmented reality device 567 that is wearable by a user, may provide input / output functionality allowing a user to interact with both a physical and virtual world. The augmented reality device 567 is in communication with the display controller 565 and the user input interface 560 allowing a user to interact with virtual items generated in the augmented reality device 567 by the display controller 565. The user may also provide gestures that are detected by the augmented reality device 567 and transmitted to the user input interface 560 as input signals.

[0043] The computer system 510 may perform a portion or all of the processing steps of embodiments of the invention in response to the processors 520 executing one or more sequences of one or more instructions contained in a memory, such as the system202303330 memory 530. Such instructions may be read into the system memory 530 from another computer readable medium, such as a magnetic hard disk 541 or a removable media drive 542. The magnetic hard disk 541 may contain one or more datastores and data files used by embodiments of the present invention. Datastore contents and data files may be encrypted to improve security. The processors 520 may also be employed in a multi- processing arrangement to execute the one or more sequences of instructions contained in system memory 530. In alternative embodiments, hard-wired circuitry may be used in place of or in combination with software instructions. Thus, embodiments are not limited to any specific combination of hardware circuitry and software.

[0044] As stated above, the computer system 510 may include at least one computer readable medium or memory for holding instructions programmed according to embodiments of the invention and for containing data structures, tables, records, or other data described herein. The term “computer readable medium” as used herein refers to any medium that participates in providing instructions to the processors 520 for execution. A computer readable medium may take many forms including, but not limited to, non- transitory, non-volatile media, volatile media, and transmission media. Non-limiting examples of non-volatile media include optical disks, solid state drives, magnetic disks, and magneto-optical disks, such as magnetic hard disk 541 or removable media drive 542. Non-limiting examples of volatile media include dynamic memory, such as system memory 530. Non-limiting examples of transmission media include coaxial cables, copper wire, and fiber optics, including the wires that make up the system bus 521. Transmission media may also take the form of acoustic or light waves, such as those generated during radio wave and infrared data communications.202303330

[0045] The computing environment 500 may further include the computer system 510 operating in a networked environment using logical connections to one or more remote computers, such as remote computing device 580. Remote computing device 580 may be a personal computer (laptop or desktop), a mobile device, a server, a router, a network PC, a peer device or other common network node, and typically includes many or all of the elements described above relative to computer system 510. When used in a networking environment, computer system 510 may include modem 572 for establishing communications over a network 571, such as the Internet. Modem 572 may be connected to system bus 521 via user network interface 570, or via another appropriate mechanism.

[0046] Network 571 may be any network or system generally known in the art, including the Internet, an intranet, a local area network (LAN), a wide area network (WAN), a metropolitan area network (MAN), a direct connection or series of connections, a cellular telephone network, or any other network or medium capable of facilitating communication between computer system 510 and other computers (e.g., remote computing device 580). The network 571 may be wired, wireless or a combination thereof. Wired connections may be implemented using Ethernet, Universal Serial Bus (USB), RJ-6, or any other wired connection generally known in the art. Wireless connections may be implemented using Wi-Fi, WiMAX, and Bluetooth, infrared, cellular networks, satellite or any other wireless connection methodology generally known in the art. Additionally, several networks may work alone or in communication with each other to facilitate communication in the network 571.

[0047] An executable application, as used herein, comprises code or machine- readable instructions for conditioning the processor to implement predetermined202303330 functions, such as those of an operating system, a context data acquisition system or other information processing system, for example, in response to user command or input. An executable procedure is a segment of code or machine-readable instruction, sub- routine, or other distinct section of code or portion of an executable application for performing one or more particular processes. These processes may include receiving input data and / or parameters, performing operations on received input data and / or performing functions in response to received input parameters, and providing resulting output data and / or parameters.

[0048] A graphical user interface (GUI), as used herein, comprises one or more display images, generated by a display processor and enabling user interaction with a processor or other device and associated data acquisition and processing functions. The GUI also includes an executable procedure or executable application. The executable procedure or executable application conditions the display processor to generate signals representing the GUI display images. These signals are supplied to a display device which displays the image for viewing by the user. The processor, under control of an executable procedure or executable application, manipulates the GUI display images in response to signals received from the input devices. In this way, the user may interact with the display image using the input devices, enabling user interaction with the processor or other device.

[0049] The functions and process steps herein may be performed automatically or wholly or partially in response to user command. An activity (including a step) performed automatically is performed in response to one or more executable instructions or device operation without user direct initiation of the activity.202303330

[0050] The system and processes of the figures are not exclusive. Other systems, processes and menus may be derived in accordance with the principles of the invention to accomplish the same objectives. Although this invention has been described with reference to particular embodiments, it is to be understood that the embodiments and variations shown and described herein are for illustration purposes only. Modifications to the current design may be implemented by those skilled in the art, without departing from the scope of the invention. As described herein, the various systems, subsystems, agents, managers and processes can be implemented using hardware components, software components, and / or combinations thereof. No claim element herein is to be construed under the provisions of 35 U.S.C.112, sixth paragraph, unless the element is expressly recited using the phrase “means for.”

Claims

202303330 CLAIMS What is claimed is:

1. A method for predicting at least one property of a polymer comprising: acquiring data relating to at least a small number of physical experiments to produce experimental data relating to the polymer; performing or acquiring a second number of molecular simulations to produce simulation data; and combining the experimental data and the simulation data into a model for predicting at least one property of the polymer.

2. The method of Claim 1, further comprising: producing the simulation data using molecular dynamics simulations.

3. The method of Claim 1, wherein the experimental data is high fidelity data, and the simulation data is low fidelity data, and the model is a multi-fidelity model.

4. The method of Claim 3, wherein the multi-fidelity model is a machine learning model.

5. The method of Claim 1, further comprising: selecting design alternatives for polymer structures based on the predicted value of at least one property.

6. The method of Claim 1 wherein the model is a linear gaussian process surrogate model.

7. The method of Claim 6, further comprising:202303330 calculating a quantitative measure of a prediction uncertainty of the model; and determining design alternatives for further experimentation or simulation.

8. The method of Claim 2, further comprising: in the model, representing the polymer structure in a format useable by a machine learning method; performing at least one molecular simulation to determine the Tg of the polymer to create molecular simulation data; and building the model using available experimental data and the molecular simulation data.

9. The method of Claim 1, further comprising: in the model, representing the polymer structure in a format useable by a machine learning method; performing at least one molecular simulation to create molecular simulation data and to determine a property of the polymer; and building the model using available experimental data and the molecular simulation data.

10. The method of Claim 9, wherein representing the polymer structure in a format useable by a machine learning model comprises: constructing a molecular fingerprint as a numerical description of one or more repeat units in the polymer structure; and202303330 producing a vector representative of the molecular fingerprint for input to the ML model.

11. A system for predicting at least one property of a polymer comprising: a computer processor; a non-transitory computer memory in communication with the computer processor, the non-transitory computer memory storing machine readable instructions that when executed by the computer processor, cause the computer processor to perform the steps of: acquiring data relating to at least a small number of experiments to produce experimental data relating to the polymer; performing a second number of molecular simulations to produce simulation data; and combining the experimental data and the simulation data into a model for predicting at least one property of the polymer.

12. The system of Claim 11 producing the simulation data using molecular dynamics simulations.

13. The system of Claim 11, wherein the experimental data is high fidelity data, and the simulation data is low fidelity data, and the model is a multi-fidelity model.

14. The system of Claim 13, wherein the multi-fidelity model is a machine learning model.202303330 15. The system of Claim 11, the non-transitory computer memory further storing instructions that when executed with the computer processor cause the computer processor to perform the steps of: selecting design alternatives for polymer structures based on the predicted value of at least one property.

16. The system of Claim 11 wherein the model is a linear gaussian process surrogate model.

17. The system of Claim 16, the non-transitory computer memory further storing instructions that when executed with the computer processor cause the computer processor to perform the steps of: calculating a quantitative measure of a prediction uncertainty of the model; and determine design alternatives for further experimentation or simulation.

18. The system of Claim 12, the non-transitory computer memory further storing instructions that when executed with the computer processor cause the computer processor to perform the steps of: in the model, representing the polymer structure in a format useable by a machine learning method; performing at least one molecular simulation to determine the Tgof the polymer to create molecular simulation data; and building the model using available experimental data and the molecular simulation data.202303330 19. The system of Claim 11, the non-transitory computer memory further storing instructions that when executed with the computer processor cause the computer processor to perform the steps of: in the model, representing the polymer structure in a format useable by a machine learning method; performing at least one molecular simulation to determine a property of the polymer to create molecular simulation data; and building the model using available experimental data and the molecular simulation data.

20. The system of Claim 19, wherein representing the polymer structure in a format useable by a machine learning method comprises: constructing a molecular fingerprint as a numerical description of one or more repeat units in the polymer structure; and producing a vector representative of the molecular fingerprint for input to the ML model.

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