Thermodynamic modeling by machine learning

Abstract

An example method of training a machine learning model to predict a solvation property of an adsorbate includes receiving an adsorbate dataset, generating a feature set from trajectories obtained by a plurality of molecular dynamics simulations, extracting, from the trajectories, a plurality of features, and training the machine learning model using the plurality of features, where the machine learning model is configured to predict the solvation property of the adsorbate.

Description

Docket Number: 103362-116WO1THERMODYNAMIC MODELING BY MACHINE LEARNINGCROSS-REFERENCE TO RELATED APPLICATIONS

[0001] This application claims the benefit of U. S. provisional patent application No. 63 / 791,120, filed on April 18, 2025, and titled “THERMODYNAMIC MODELING BY MACHINE LEARNING,’’ the disclosure of which is expressly incorporated herein by reference in its entirety.STATEMENT REGARDING FEDERALLY FUNDED RESEARCH

[0002] This invention was made with government support under DE-SC0025579 awarded by the Department of Energy. The government has certain rights in the invention.BACKGROUND

[0003] Catalysis refers to the increased rate of a chemical reaction in the presence of a catalyst. Heterogeneous catalysis refers to types of catalysis where the catalysts are different phases from the reagents / products of the reaction. In particular aqueous phase heterogeneous catalysis refers to such reactions carried out in water, where the catalyst is a different phase (e.g., a solid).

[0004] To model industrial processes including aqueous phase heterogeneous catalysis, solvation properties modeling can be performed. Modeling techniques include multi-scale modeling, where models are created at different scales (e.g., atomic, molecular, kinetic, and larger).

[0005] Improvements to modeling thermodynamics, including the modeling of aqueous phase heterogeneous catalysis, can improve industrial processes.SUMMARY

[0006] In some aspects, implementations of the present disclosure include a computer-implemented method of training a machine learning model predict a solvation property7of an adsorbate, the method including: receiving a multiscale modeling dataset; generating a feature set from trajectories obtained by a plurality of molecular dynamics simulations; extracting, from the trajectories, a plurality of features; and training the machine learning model using the plurality of features, wherein the machine learning model is configured to predict the solvation property of the adsorbate.Docket Number: 103362-116WO1

[0007] In some aspects, implementations of the present disclosure include a method, wherein the feature set includes one or more of adsorbate features, hydrogen bond features, or solvent features.

[0008] In some aspects, implementations of the present disclosure include a method, wherein the feature set includes molecular descriptors, a molecular fingerprint, or both.

[0009] In some aspects, implementations of the present disclosure include a method, wherein the molecular fingerprint includes an Ewald sum matrix fingerprint.

[0010] In some aspects, implementations of the present disclosure include a method, further including concatenating at least a portion of the feature set into a feature matrix, wherein training the machine learning model uses the feature matrix.

[0011] In some aspects, implementations of the present disclosure include a method, wherein training the machine learning model includes performing recursive feature elimination to select a subset of informative features.

[0012] In some aspects, implementations of the present disclosure include a method, wherein training the machine learning model further includes performing cross-validation to evaluate model performance on unseen adsorbates and tune hyper-parameters.

[0013] In some aspects, implementations of the present disclosure include a method, wherein the adsorbate dataset includes results from density functional theory simulations, results from multi-scale sampling simulations, or both.

[0014] In some aspects, implementations of the present disclosure include a method, wherein the adsorbate dataset includes interaction energies, solvation energies, solvation free energies, or any combination thereof.

[0015] In some aspects, implementations of the present disclosure include a method, wherein the solvation property includes an interaction energy, a solvation energy, a solvation free energy, or any combination thereof.

[0016] In some aspects, implementations of the present disclosure include a method, wherein the plurality of features includes at least one feature representing hydrogen bonding, van der Waals interactions, solvent density, or an electronic property of the adsorbate.

[0017] In some aspects, implementations of the present disclosure include a method, wherein the machine learning model includes a support vector regressor, a least absolute shrinkage and selection operator model, a ridge model, a stochastic gradient descent model, a Bayesian ridge model, a k-nearest neighbors model, a decision tree model, a randomDocket Number: 103362-116WO1forest model, a gradient boosting regressor, an extreme gradient boosting model, or a multilayer perceptron regression model.

[0018] In some aspects, implementations of the present disclosure include a computer-implemented method of predicting a solvation property of an adsorbate, the method including: performing a molecular dynamics simulation of the adsorbate; generating, based on the molecular dynamics simulation, a plurality of features for the adsorbate; inputting the plurality of features into a trained machine learning model; and outputting, by the trained machine learning model, the solvation property of the adsorbate.

[0019] In some aspects, implementations of the present disclosure include a method, wherein the plurality of features includes one or more of adsorbate features, hydrogen bond features, or solvent features.

[0020] In some aspects, implementations of the present disclosure include a method, wherein outputting the solvation property includes predicting interaction energies for a plurality of molecular-dynamics configurations and averaging the predicted interaction energies to obtain a solvation energy.

[0021] In some aspects, implementations of the present disclosure include a method, wherein the plurality of features includes ensemble-average features derived from a plurality of molecular-dynamics configurations, and wherein the solvation property includes a solvation energy or a solvation free energy.

[0022] In some aspects, implementations of the present disclosure include a method, wherein the trained machine learning model was trained using an adsorbate dataset including results from density functional theory simulations, multi-scale sampling simulations, or both.

[0023] In some aspects, implementations of the present disclosure include a system including: a molecular dynamics simulation module; and a machine learning module, wherein the machine learning module is configured to perform the method.

[0024] In some aspects, implementations of the present disclosure include a system, further including a density functional theory workflow designed to generate single-point density functional theory energy calculations for training the machine learning module.

[0025] In some aspects, implementations of the present disclosure include a non-transitory computer-readable medium storing instructions that, when executed by one or more processors, cause the one or more processors to perform the method.Docket Number: 103362-116WO1

[0026] It should be understood that the above-described subject matter may also be implemented as a computer-controlled apparatus, a computer process, a computing system, or an article of manufacture, such as a computer-readable storage medium.

[0027] Other systems, methods, features and / or advantages will be or may become apparent to one with skill in the art upon examination of the following drawings and detailed description. It is intended that all such additional systems, methods, features and / or advantages be included within this description and be protected by the accompanying claims.BRIEF DESCRIPTION OF THE DRAWINGS

[0028] The components in the drawings are not necessarily to scale relative to each other. Like reference numerals designate corresponding parts throughout the several views.

[0029] FIG. 1 A illustrates an example method of training a machine learning model to predict a solvation property of an adsorbate, according to implementations of the present disclosure.

[0030] FIG. IB illustrates an example method of predicting a solvation property of an adsorbate, according to implementations of the present disclosure.

[0031] FIG. 2 illustrates an example system according to implementations of the present disclosure.

[0032] FIG. 3 illustrates an example computing device.

[0033] FIG. 4 illustrates an example implementation of the present disclosure where MD trajectory and configurations are used to generate features for machine learning, while single-point DFT calculations provide the interaction energies as labels for machine learning training.

[0034] FIG. 5A illustrates study results showing distribution of 450ΔEintDFTvalues for individual configurations, ranging from -1.18 to +0.08 eV, according to a study of an example implementation of the present disclosure.

[0035] FIG. 5B illustrates study results showing distribution of 90ΔEsolDFTvalues for adsorbates, ranging from -0.94 to -0.02 eV, according to a study of an example implementation of the present disclosure.

[0036] FIG. 5C illustrates a distribution of 90ΔFsolMSSvalues for adsorbates, ranging from -0.45 to +0.05 eV, according to a study of an example implementation of the present disclosure.Docket Number: 103362-116WO1

[0037] FIG. 6 illustrates a composition of features in the predictive model, which includes adsorbate features, hydrogen bond features, and solvent features, all concatenated to form the final feature matrix for ML model input.

[0038] FIG. 7 A illustrates recursive feature elimination with cross-validation (RFECV) results using the gradient boosting regressor including the mean CV RMSE score vs the number of features selected, and the standard deviation across five folds, according to a study of an example implementation of the present disclosure.

[0039] FIG. 7B illustrates a performance comparison of the gradient boosting regressor using different groups of features, according to a study of an example implementation of the present disclosure.

[0040] FIG. 8A illustrates an example method of model performance evaluation: predicting ΔEintfor each configuration and averaging the predictions across multiple configurations to assess configuration model performance, and directly predicting ΔEsolto assess trajectory model performance, according to a study of an example implementation of the present disclosure.

[0041] FIG. 8B illustrates an overview of the nested cross-validation process, according to a study of an example implementation of the present disclosure.

[0042] FIG. 9A illustrates performance of various machine learning algorithms in predicting ΔEintand ΔEsol, using three evaluation metrics: R2, RMSE, and MAE, according to a study of an example implementation of the present disclosure.

[0043] FIG. 9B illustrates performance of various machine learning algorithms in predicting AEintand AEsol, using three evaluation metrics: R2, RMSE, and MAE and configuration model predictions for A£’mtfor a configuration model and trajectory model's predictions for AEsoi.

[0044] FIG. 10A illustrates parity plots of the ML configuration model using GBR algorithm, (a) ML predicted vs DFT calculated AEintfor individual configurations, according to a study of an example implementation of the present disclosure.

[0045] FIG. 10B illustrates machine-learning-predicted vs DFT calculated AEsolfor adsorbates, according to a study of an example implementation of the present disclosure.

[0046] FIG. 10C illustrates a comparison of ΔEsolMLand ΔEsolMDagainst ΔEsolDFTvalues, according to a study of an example implementation of the present disclosure.Docket Number: 103362-116WO1

[0047] FIG. I 1 A illustrates parity plots of the ML trajectory model using GBR algorithm for predicting ΔEsolwith ML predicted vs DFT calculated ΔEsolfor adsorbates, according to a study of an example implementation of the present disclosure.

[0048] FIG. 1 IB illustrates parity plots of the ML trajectory model using GBR algorithm for predicting Esojwith a comparison of AES“Land AF^,0against AE°Tvalues, according to a study of an example implementation of the present disclosure.

[0049] FIG. 12A illustrates parity plots of the ML trajectory model using MLP algorithm for predicting ΔFsolwith the ML predicted vs MSS calculated ΔFsolfor adsorbates, according to a study of an example implementation of the present disclosure.

[0050] FIG. 12B illustrates parity plots of the ML trajectory model using MLP algorithm for predicting AFsolwith a comparison of AFs^ljand AF^Dagainst AFS”SS, according to a study of an example implementation of the present disclosure.

[0051] FIG. 13 illustrates relative feature importance of the features in the gradient boosting regressor (GBR) for the prediction of ΔEint, according to a study of an example implementation of the present disclosure.

[0052] FIG. 14A illustrates the number of hydrogen bonds vs ΔEintDFTfor individual configurations, according to a study of an example implementation of the present disclosure.

[0053] FIG. 14B illustrates the average number of hydrogen bonds across 501 MD frames vs ΔEsolDFT, according to a study of an example implementation of the present disclosure.

[0054] FIG. 14C illustrates the average number of hydrogen bonds across 501 MD frames vs ΔFsolMSS, according to a study of an example implementation of the present disclosure.DETAILED DESCRIPTION

[0055] Unless defined otherwise, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art. Methods and materials similar or equivalent to those described herein can be used in the practice or testing of the present disclosure. As used in the specification, and in the appended claims, the singular forms “a,” “an,” “the” include plural referents unless the context clearly dictates otherwise. The term “comprising” and variations thereof as used herein is used synonymously with the term “including” and variations thereof and are open, non-limiting terms. The terms “optional” or “optionally” used herein mean that the subsequently describedDocket Number: 103362-116WO1feature, event or circumstance may or may not occur, and that the description includes instances where said feature, event or circumstance occurs and instances where it does not. Ranges may be expressed herein as from "about" one particular value, and / or to "about" another particular value. When such a range is expressed, an aspect includes from the one particular value and / or to the other particular value. Similarly, when values are expressed as approximations, by use of the antecedent "about," it will be understood that the particular value forms another aspect. It will be further understood that the endpoints of each of the ranges are significant both in relation to the other endpoint, and independently of the other endpoint. While implementations will be described for aqueous phase heterogeneous catalysis, it will become evident to those skilled in the art that the implementations are not limited thereto, but are applicable for any type of thermodynamic or chemical modeling.

[0056] As used herein, the terms "about" or "approximately" when referring to a measurable value such as an amount, a percentage, and the like, is meant to encompass variations of ±20%, ±10%, ±5%, or ±1% from the measurable value.

[0057] Conventional techniques for determining solvation thermodynamic properties of adsorbates can provide accurate results, but they are computationally expensive because they rely on repeated evaluation of multiple liquid solvent configurations and in many instances quantum mechanical energy calculations. The systems and methods of the present disclosure overcome these limitations of conventional methods by generating a feature set from molecular dynamic trajectories and using a machine learning model trained on those features to predict interaction energy, solvation energy, and / or free energy of an adsorbate. Because the prediction is driven by physically meaningful molecular-dynamic-derived features, the system can provide solvation property estimates without requiring additional density functional theory calculations for new inferences. Accordingly, the systems and methods described herein improve the operation of computational thermodynamic modeling systems by reducing the computational resources required and by reducing the elapsed time required to obtain solvation property7estimates while maintaining accuracy comparable to multi-scale sampling approaches, as shown by the example described herein,

[0058] With reference to FIG. 1A, an example method of training a machine learning model to predict a solvation property of an adsorbate according to implementations of the present disclosure.

[0059] At step 110, the method includes receiving an adsorbate dataset. Optionally, the adsorbate dataset can include results from density functional theory simulations, results from multi-scale sampling simulations, or both. Alternatively or additionally, the adsorbateDocket Number: 103362-116WO1dataset can include interaction energies, solvation energies, solvation free energies, or any combination thereof.

[0060] At step 120, the method includes generating a feature set from trajectories obtained by a set of molecular dynamics simulations. Optionally, the feature set includes one or more of adsorbate features, hydrogen bond features, or solvent features. Alternatively or additionally the feature set comprises molecular descriptors, a molecular fingerprint, or both. A non-limiting example of a molecular fingerprint is an Ewald sum matrix fingerprint.

[0061] At step 130, the method includes extracting, from the trajectories, a plurality of features. In some implementations, the features include at least one feature representing hydrogen bonding, van der Waals interactions, solvent density, or an electronic property of the adsorbate.

[0062] At step 140, the method includes training the machine learning model using the plurality of features, wherein the machine learning model is configured to predict the solvation property of the adsorbate. Non-limiting examples of a solvation property include an interaction energy, a solvation energy, a solvation free energy, or any combination thereof.

[0063] Example machine learning models that can be used include a support vector regressor, a least absolute shrinkage and selection operator model, a ridge model, a stochastic gradient descent model, a Bayesian ridge model, a k-nearest neighbors model, a decision tree model, a random forest model, a gradient boosting regressor, an extreme gradient boosting model, or a multi-layer perceptron regression model.

[0064] Optionally, the method of FIG. 1 A can further include concatenating at least a portion of the feature set into a feature matrix and training the machine learning model using the feature matrix. Alternatively or additionally, training the machine learning model can include performing recursive feature elimination to select a subset of informative features.

[0065] Alternatively or additionally, training the machine learning model can further include performing cross-validation to evaluate model performance and tune hyperparameters.

[0066] With reference to FIG. IB, implementations of the present disclosure include methods of predicting a solvation property of an adsorbate using the trained machine learning models described herein.

[0067] At step 150, the method includes performing a molecular dynamics simulation of the adsorbate.Docket Number: 103362-116WO1

[0068] At step 160, the method includes generating, based on the molecular dynamics simulation, a plurality of features for the adsorbate.

[0069] At step 170, the method includes inputting the plurality of features into a trained machine learning model. The trained machine learning model can be trained according to any of the methods described herein. The features can optionally include one or more of adsorbate features, hydrogen bond features, or solvent features. Alternatively or additionally, the features can include ensemble-average features derived from a plurality of molecular-dynamics configurations, and the solvation property can include a solvation energy or a solvation free energy.

[0070] At step 180, the method includes outputting, by the trained machine learning model, the solvation property of the adsorbate. Optionally, outputting the solvation property can include predicting interaction energies for a set of molecular-dynamics configurations and averaging the predicted interaction energies to obtain a solvation energy.

[0071] FIG. 2 illustrates an example computing environment 200 for implementing machine-leaming-based prediction of solvation properties according to the methods described herein. The computing environment 200 can include a molecular dynamics simulation module 202, a machine learning module 204, and a display 206.

[0072] The machine learning module 204 can include a feature extraction module 208, a feature matrix generation module 210, and an optional density functional theory module 212. The molecular dynamics simulation module 202 can generate molecular-dynamics trajectories and configurations for an adsorbate system. The feature extraction module 208 can extract adsorbate features, hydrogen-bond features, solvent features, descriptors, fingerprints, or any combination thereof from simulation input data and / or trajectory data. The feature matrix generation module 210 can concatenate at least a portion of the extracted features into a feature matrix for input to the machine learning module 204. The optional density functional theory module 212 can generate single-point interaction-energy calculations usable as labels for training. The machine learning module 204 can train and / or execute a machine learning model configured to predict a solvation property of an adsorbate, including an interaction energy, a solvation energy, or a solvation free energy, and the display 206 can present predicted values and related output.

[0073] As shoyvn in FIG. 4, implementations of the present disclosure can include systems for implementing the methods described herein and evaluating the claimed systems and methods as compared to density functional theory. FIG. 4 illustrates a system for calculating energies by DFT and by machine learning as described herein. The systemDocket Number: 103362-116WO1includes a molecular dynamics simulation module 402, a machine learning module 404, and a density functional theory module 406. The density functional theory module 406 can optionally be used to generate single-point DFT energy calculations for training the machine learning module 404, The machine learning module 404 can optionally be configured to perform machine learning training and / or inference, according to the methods described herein.

[0074] As used herein, the term "‘feature set” refers to a collection of features generated from trajectories obtained by one or more molecular-dynamics simulations and extracted from the molecular-dynamics simulations for use by the machine-learning model. The feature set can include adsorbate features, hydrogen bond features, solvent features, or any combination thereof. In some embodiments, the feature set includes features derived from descriptors, fingerprints, or both.

[0075] As used herein, the term “feature matrix” refers to an arrangement of features used as input to the machine-learning model. In some embodiments, the feature set, including descriptors and / or fingerprints, is concatenated to form the feature matrix.

[0076] As used herein, the term “fingerprint” refers to a matrix representation of an adsorbate for use as a feature in the machine-learning model. In some embodiments, the fingerprint is related to geometric structure, electronic structure, or both, and can comprise an Ewald sum matrix fingerprint.

[0077] It should be appreciated that the logical operations described herein with respect to the various figures may be implemented (1) as a sequence of computer implemented acts or program modules (i.e., software) running on a computing device (e.g., the computing device described in Fig. 3), (2) as interconnected machine logic circuits or circuit modules (i.e., hardware) within the computing device and / or (3) a combination of software and hardware of the computing device. Thus, the logical operations discussed herein are not limited to any specific combination of hardware and software. The implementation is a matter of choice dependent on the performance and other requirements of the computing device. Accordingly, the logical operations described herein are referred to variously as operations, structural devices, acts, or modules. These operations, structural devices, acts and modules may be implemented in software, in firmware, in special purpose digital logic, and any combination thereof. It should also be appreciated that more or fewer operations may be performed than shown in the figures and described herein. These operations may also be performed in a different order than those described herein.Docket Number: 103362-116WO1

[0078] Referring to Fig. 3, an example computing device 300 upon which the methods described herein may be implemented is illustrated. It should be understood that the example computing device 300 is only one example of a suitable computing environment upon which the methods described herein may be implemented. Optionally, the computing device 300 can be a well-known computing system including, but not limited to, personal computers, servers, handheld or laptop devices, multiprocessor systems, microprocessorbased systems, network personal computers (PCs), minicomputers, mainframe computers, embedded systems, and / or distributed computing environments including a plurality of any of the above systems or devices. Distributed computing environments enable remote computing devices, which are connected to a communication network or other data transmission medium, to perform various tasks. In the distributed computing environment, the program modules, applications, and other data may be stored on local and / or remote computer storage media.

[0079] In its most basic configuration, computing device 300 typically includes at least one processing unit 306 and system memory 304. Depending on the exact configuration and type of computing device, system memory 304 may be volatile (such as random access memory (RAM)), non-volatile (such as read-only memory (ROM), flash memory, etc.), or some combination of the two. This most basic configuration is illustrated in FIG. 3 by box 302. The processing unit 306 may be a standard programmable processor that performs arithmetic and logic operations necessary for operation of the computing device 300. The computing device 300 may also include a bus or other communication mechanism for communicating information among various components of the computing device 300.

[0080] Computing device 300 may have additional features / functionality. For example, computing device 300 may include additional storage such as removable storage 308 and non-removable storage 310 including, but not limited to, magnetic or optical disks or tapes. Computing device 300 may also contain network connection(s) 316 that allow the device to communicate with other devices. Computing device 300 may also have input device(s) 314 such as a keyboard, mouse, touch screen, etc. Output device(s) 312 such as a display, speakers, printer, etc. may also be included. The additional devices may be connected to the bus in order to facilitate communication of data among the components of the computing device 300. All these devices are well known in the art and need not be discussed at length here.

[0081] The processing unit 306 may be configured to execute program code encoded in tangible, computer-readable media. Tangible, computer-readable media refers toDocket Number: 103362-116WO1any media that is capable of providing data that causes the computing device 300 (i.e., a machine) to operate in a particular fashion. Various computer-readable media may be utilized to provide instructions to the processing unit 306 for execution. Example tangible, computer- readable media may include, but is not limited to, volatile media, non-volatile media, removable media and non-removable media implemented in any method or technology for storage of information such as computer readable instructions, data structures, program modules or other data. System memory 304, removable storage 308, and non-removable storage 310 are all examples of tangible, computer storage media. Example tangible, computer-readable recording media include, but are not limited to, an integrated circuit (e.g., field-programmable gate array or application-specific IC), a hard disk, an optical disk, a magneto-optical disk, a floppy disk, a magnetic tape, a holographic storage medium, a solidstate device, RAM, ROM, electrically erasable program read-only memory (EEPROM), flash memory or other memory technology, CD-ROM, digital versatile disks (DVD) or other optical storage, magnetic cassettes, magnetic tape, magnetic disk storage or other magnetic storage devices.

[0082] In an example implementation, the processing unit 306 may execute program code stored in the system memory 304. For example, the bus may carry data to the system memory 304, from which the processing unit 306 receives and executes instructions. The data received by the system memory 304 may optionally be stored on the removable storage 308 or the non-removable storage 310 before or after execution by the processing unit 306.

[0083] It should be understood that the various techniques described herein may be implemented in connection with hardware or software or, where appropriate, with a combination thereof. Thus, the methods and apparatuses of the presently disclosed subject matter, or certain aspects or portions thereof, may take the form of program code (i.e., instructions) embodied in tangible media, such as floppy diskettes, CD-ROMs, hard drives, or any other machine-readable storage medium wherein, when the program code is loaded into and executed by a machine, such as a computing device, the machine becomes an apparatus for practicing the presently disclosed subject matter. In the case of program code execution on programmable computers, the computing device generally includes a processor, a storage medium readable by the processor (including volatile and non-volatile memory and / or storage elements), at least one input device, and at least one output device. One or more programs may implement or utilize the processes described in connection with the presently disclosed subject matter, e.g., through the use of an application programming interface (API),Docket Number: 103362-116WO1reusable controls, or the like. Such programs may be implemented in a high level procedural or object-oriented programming language to communicate with a computer system. However, the program(s) can be implemented in assembly or machine language, if desired. In any case, the language may be a compiled or interpreted language and it may be combined with hardware implementations.

[0084] Examples

[0085] The following examples are put forth so as to provide those of ordinary skill in the art with a complete disclosure and description of how the compounds, compositions, articles, devices and / or methods claimed herein are made and evaluated, and are intended to be purely exemplary and are not intended to limit the disclosure. Efforts have been made to ensure accuracy with respect to numbers (e.g., amounts, temperature, etc.), but some errors and deviations should be accounted for. Unless indicated otherwise, parts are parts by weight, temperature is in °C or is at ambient temperature, and pressure is at or near atmospheric.

[0086] An example implementation of the present disclosure was implemented in a study described herein.

[0087] Aqueous phase heterogeneous catalysis is important to various industrial processes, including biomass conversion, Fischer-Tropsch synthesis, and electrocatalysis. Accurate calculation of solvation thermodynamic properties is essential for modeling the performance of catalysts for these processes. Explicit solvation methods employing multiscale modeling, e.g., involving density functional theory and molecular dynamics have emerged for this purpose. Although accurate, these methods are computationally intensive. This study introduces example machine learning models to predict solvation thermodynamics for adsorbates on a Pt(111) surface, aiming to enhance computational efficiency without compromising accuracy. In particular, ML models are developed using a combination of molecular descriptors and fingerprints and trained on previously published water-adsorbate interaction energies, energies of solvation, and free energies of solvation of adsorbates bound to Pt(111). These models achieve root mean square error values of 0.09 eV for interaction energies, 0.04 eV for energies of solvation, and 0.06 eV for free energies of solvation, demonstrating accuracy within the standard error of multi-scale modeling. Feature importance analysis reveals that hydrogen bonding, van der Waals interactions, and solvent molecular density, together with the properties of the adsorbate, are critical factors influencing solvation thermodynamics. These findings suggest that ML models can provideDocket Number: 103362-116WO1rapid and reliable predictions of solvation properties. This approach not only reduces computational costs but also offers insights into the solvation characteristics of adsorbates at Pt(111)-water interfaces.

[0088] This study discloses ML models to predict energies and free energies of solvation for adsorbates on a metal catalyst surface. To achieve this, the study used ML to fit a variety of descriptors and fingerprints to previously published energies and free energies of solvation for adsorbates bound to a Pt(l 11) surface. In particular, energies and free energies of solvation are taken from a method of multi-scale sampling (MSS) to compute these values. MSS is an explicit solvation method that employs a combination of MD and DFT to generate adsorbate configurations and compute energies and free energies of solvation. The study chose ML for its computational efficiency and ability to handle the complexity of MSS data. To achieve the predictive model, the present disclosure introduces a featurization strategy that includes a combination of molecular descriptors and fingerprints. The features in this study are derived from the MD simulations performed during the final step of the MSS simulations and include information about adsorbate properties, hy drogen bonding, and solvent molecule distributions. Importantly, they do not require any additional DFT calculations.

[0089] The ML training and evaluation processes are designed to minimize overfitting and ensure robust model performance. Strategies include the use of separate test sets for model evaluation, feature selection techniques, and regularization techniques to limit model complexity. The workflow of the example implementation used in the study is shown in FIG. 4. The example implementation achieves root mean square error (RMSE) values of 0.09, 0.04, and 0.06 eV on the ML test sets for water-adsorbate interaction energies, adsorbate energies of solvation, and adsorbate free energies of solvation, respectively. These RMSE values are within the standard error of the MSS method and represent a notable reduction in computational cost. Finally, by enabling examination of the feature importance of the predictive models, the example implementation enables a deeper understanding of the solvation characteristics of adsorbates in this environment.

[0090] Dataset Preparation

[0091] An example dataset was acquired from prior data collection works including: X. Zhang, R. S. DeFever, S. Sarupria, and R. B. Getman, ‘‘Free energies of catalytic species adsorbed to Pt(l 11) surfaces under liquid solvent calculated using classical and quantum approaches,” J. Chem. Inf. Model. 59(5), 2190-2198 (2019); C. J.Bodenschatz, X. Zhang, T. Xie, J. Arvay, S. Sarupria, and R. B. Getman, “Multi-scaleDocket Number: 103362-116WO1sampling of a heterogeneous water / metal catalyst interface using density functional theory and force-field molecular dynamics,” J. Visualized Exp. 146, e59284 (2019); X. Zhang, ‘‘Development of improved models for simulating adsorption kinetics and solvation free energies of catalytic species at Pt(l 11 ) / liquid water interfaces,” Ph D. dissertation (Clemson University, 2021); and R. A. Garcia Carcamo, X. Zhang, A. Estejab, J. Zhou, B. J. Hare, C. Sievers, S. Sarupria, and R. B. Getman, “Differences in solvation thermodynamics of oxygenates at Pt / A12O3 perimeter versus Pt( 111) terrace sites,” iScience 26(2), 105980 (2023).

[0092] The example dataset included 90 adsorbates on a Pt(l ll) surface, which comprise water (H2O), methane (CH4), methanol (CH3OH), ethane (CH3CH3), formic acid (HCOOH), ethanol (CH3CH2OH), ethylene glycol (HOCH2CH2OH), and glycerol (CH2OHCHOHCH2OH) and / or their decomposition products. The adsorbates have been hydrated using explicit liquid H2O using classical MD simulations. The MD simulations result in 501 configurations of H2O molecules around each adsorbate. In the example dataset, the input raw data are a subset of these configurations as well as solvent properties (i.e., ensemble averages) derived using all 501 configurations. In particular, for each adsorbate, a subset of five configurations is selected and the water-adsorbate interaction energies ( ΔEintDFT) are calculated in DFT, i.e.,

[0093] where Ep^J+ adsis the electronic energy of the Pt surface with the adsorbate in the presence of the configuration of liquid H2O molecules; Ep“+adsis the electronic energy of the Pt surface with the adsorbate in the absence of the liquid H2O molecules; E^ is the electronic energy of the Pt surface in the presence of the configuration of liquid H2O molecules but with the adsorbate removed; and Ep is the electronic energy of the Pt surface with no adsorbate or H2O molecules. The labels in the dataset are these values as well as the energies of solvation ( Asol) for each adsorbate:

[0094] which are averaged over the five values of ΔEintDFTfor each adsorbate, as well as the associated free energies of solvation.A pMSS _ pDFT ’ A CM LJ ZQAAr sol ~ CSoi — 1 sol ’Docket Number: 103362-116WO1

[0095] where MSS is an abbreviation for multi-scale sampling to compute AESoTand (as we[]asAES^Dand AFS^D, see in the following). The study used five configurations to calculate AE°Tfor computational tractability. In general, these methods show good agreement, suggesting that free energies of solvation calculated using MSS are within the current state-of-the-art for computing such values. In all, the dataset provides a total of 450 values of ΔEintDFTand 90 values of AE°fFTand AS“jD. The study additionally compared ML predictions of ΔEsoland ΔFsol, i.e., AEs^tLand AFS^Lwith the values obtained using classical MD simulations, i.e., AES^Dand AFS”D. For these calculations, AE^15are taken directly from the dataset, while AFS^Dare computed asAF«P = AESM0? - T S^. (4)

[0096] A temperature of 300 K is used to obtain all values. In the dataset, DFT calculations are performed with the Vienna Ab initio Simulation Package (VASP) with the Perdew, Burke, Ernzerhof (PBE) electron exchange and correlation functional along with projector augmented wave (PAW) pseudopotentials and D2 dispersion corrections. MD simulations are performed at 300 K using the Large-scale Atomic / Molecular Massively Parallel Simulator (LAMMPS) using the canonical (NVT) ensemble with the Transferable Intermolecular Potential with 3 Points-Chemistry at Harvard Macromolecular Mechanics (TIP3P / CHARMM) force field for H2O molecules, the optimized potentials for liquid simulations-all atom (OPLS-AA) force field for adsorbate species, and the universal force field (UFF) for Pt surface atoms.

[0097] The distribution of the label values for ΔEintDFT, AEs^T, and AF“SSin the dataset are shown in FIGS. 5A-5C. FIG. 5A show's ΔEintDFTranging from -1.18 to +0.08 eV; FIG. 5B shows ΔE7ranging from -0.94 to -0.02 eV; and FIG. 5C shows ΔFsolMSSranging from -0.45 to +0.05 eV. All three distributions are approximately unimodal, with a slight skew- toward higher values.

[0098] Example Featurization Methods

[0099] Features are derived from molecular descriptors (i.e., adsorbate property values) and fingerprints (matrix representations of the adsorbates), which are processed into a set of inputs for the machine learning models in the example implementation of the present disclosure. In general, it is preferable to use computationally efficient descriptors; hence, the study avoided using descriptors that require additional quantum chemistry calculations beyond the initial DFT calculations used to obtain the adsorbate's configuration and charges (which can be inputs to MD). Instead, the remaining information needed to computeDocket Number: 103362-116WO1descriptors is based on information from MD input and trajectory files. The example implementation adopted 103 descriptors inspired by various literatures, which are calculated for each simulated system. Descriptors are selected based on hypotheses related to the properties driving solvation thermodynamics and are broken into three groups: adsorbate descriptors, water enrichment descriptors, and hydrogen bond descriptors. Adsorbate descriptors include properties such as surface area, volume, charge, and various other features derived from atomic coordinates and partial charges. They additionally include the previously established 3D directional moment descriptors and "3D weighted holistic invariant molecular" (3D-WHIM) descriptors, which describe an adsorbate's size, shape, symmetry, and atomic distribution. These descriptors are adopted from the literature on structure¬ property relationships of organic compounds. Solvent descriptors characterize the enrichment around the adsorbate, as this can influence interactions with the adsorbate and hence solvation thermodynamics. These descriptors include information about the distances of various atoms within water molecules from the adsorbate, as well as the water coordination numbers around the adsorbate. To represent the local solvent structure, radial distribution function (RDF) descriptors are employed. In addition, pairwise van der Waals and electrostatic interactions between the adsorbate and individual water molecules are included. Solvent descriptors related to the hydrogen bonds formed between the solvent and the adsorbate are also incorporated.

[0100] The various descriptors are calculated using various Python packages, including MD Analysis, Open Babel, PyMOL, Chemistry Development Kit, Morfeus, and DScribe, as well as scripts written in-house, which reduce the tedium of calculating various descriptors using multiple software packages.

[0101] Fingerprints have been shown to exhibit strong predictive capabilities for thermodynamic properties of adsorbates on surfaces. Hence, the study evaluated fingerprints in addition to features. The specifically evaluated fingerprints related to geometric and electronic structures as calculated with the open-source DScribe package. The atomic coordinates and electronic structure information used to construct the fingerprints (matrices) are obtained from DFT. The study found that Ewald sum matrices yield the best performance of the fingerprints that were tested. This fingerprint was evaluated in the feature set (while excluding the remaining fingerprints calculated with DScribe). As fingerprint arrangement depends on the atom orders in the adsorbate, which may affect machine learning model performance, the fingerprint matrix is permuted by sorting the rows and columns by their L2 norms. In addition, different adsorbates have different numbers of atoms, leading toDocket Number: 103362-116WO1adsorbate fingerprints of different sizes; this issue is addressed by zero-padding the matrices to the largest atom number in the dataset to ensure uniform matrix dimensions. In the dataset, the largest adsorbate has 14 atoms, resulting in a flattened vector of size 196. Given the high dimensionality of the flattened fingerprint vectors, principal component analysis (PCA) is used for dimensionality reduction, retaining the most important components and reducing the risk of overfitting. The study found that reducing the dimensionality of the Ewald sum matrix to 15 components captures 95% of the total variance, preserving the essential variability in the original data.

[0102] The final set of descriptors and fingerprints is concatenated to form the feature matrix as shown in FIG. 6. To maintain consistency and eliminate potential scale differences among features, all features are rescaled between 0 and 1 using min-max scaling. This scaling method transforms each feature by subtracting its minimum value and dividing by its range.

[0103] Feature Engineering

[0104] Given the relatively large number of features, feature selection is performed to improve model training efficiency, avoid overfitting, and facilitate feature importance testing. Feature selection is performed using a hybrid process that combines recursive feature elimination (RFE) and RFE with cross-validation (RFECV), followed by Pearson correlation coefficient analysis to detect highly correlated pairs of features (correlation threshold >0.95). First, RFECV is used to explore the relationship between the number of features used and model performance. During the RFECV process, a model is trained and its RMSE is calculated using different subsets of features. The number of selected features is adjusted iteratively using different training and validation sets (folds). RMSE values are then averaged across all folds, and the optimal number of features is determined by minimizing the cross-validation RMSE score. The results of feature engineering for the gradient boosting regressor (GBR) algorithm, chosen for its strong performance and robustness in handling complex, non-linear relationships between features and target variables, are presented in FIG. 7 A. When adding features to the model, the model's RMSE decreases and stabilizes when ~ 25 features are selected. The addition of more features beyond this point does not lead to further improvement in the cross-validation score, suggesting that the model captures most of the predictive information with around 25 features. This indicates that adding more features does not significantly enhance the model's predictive capability, thus a relatively smaller number of features is selected to reduce the risk of overfitting.Docket Number: 103362-116WO1

[0105] RFE is then employed to recursively eliminate the least important features based on their importance rankings. Feature importance is assessed using the built-in feature importance method provided by the GBR algorithm. The least important features are removed, and this procedure is recursively repeated until the desired number of features determined by RFECV (e.g., ~ 25 ) is reached. For different iterations and splits, RFE analysis removes ~ 80% of the features from the feature set. Finally, Pearson correlation coefficient analysis is performed to identify pairs of correlated features. In this analysis, linear correlation coefficients between pairs of features are calculated. These values range from -1 to +1. The features with correlation coefficient greater than 0.95 are classified as highly correlated. For each pair of highly correlated features, the feature with lower importance is removed, and the model is retrained. The model scores did not significantly change; hence, all features selected by RFE are ultimately retained. Table I lists the top 25 features that most frequently appeared as highly important across the tested algorithms, ordered according to their feature importance. The features listed m this table include adsorbate features, along with solvent and hydrogen bond features calculated from specific MD configurations, which together are used to predict AEint. In addition, solvent and hydrogen bond features calculated by averaging over all 501 frames of the entire MD trajectory, along with the shared adsorbate descriptors, are used to predict A£'soland A7yol. Detailed information on all features calculated in this study is provided in the supplementary material, Table S5.

[0106] The performance of the different groups of features is shown in FIG.7B. In particular, when only adsorbate descriptors are included in the feature set, the average RMSE on the test set is 0.160 eV. When features describing solvent structure and hydrogen bonding properties are additionally included, the RMSE decreases to 0.114 eV. When the adsorbate's Ewald sum matrix molecular fingerprint features are added to the feature set, the RMSE decreases to 0, 105 eV. When feature selection and Pearson correlation analysis for feature elimination are applied, the RMSE decreases to ~ O.lOeV. These results suggest that the strategy of incorporating additional feature sets to represent the complete solvation environment is effective, as features capturing both the adsorbate and solvent properties significantly enhance the model's performance. However, feature elimination through importance selection has only a limited impact on further improving the model's accuracy.

[0107] Example Machine Learning MethodsDocket Number: 103362-116WO1

[0108] Supervised machine learning algorithms are carried out by training two types of models. The first type, referred to as the "configuration model," uses adsorbate and solvent features extracted from the 450 configurations of H2O molecules for which AE^fvalues are available ( 90 adsorbates each with five values of AE^ ), and labels these data with the corresponding values of ΔEintDFT. The second type, termed the "trajectory model," employs adsorbate features along with the ensemble averages calculated over the 501 configurations of H2O molecules for each adsorbate ( 90 adsorbates each with 501 snapshots of H2O configurations from MD) and labels them with the corresponding values of AE°Tand AE.^33. These models and their performance evaluation processes are summarized in FIG. 8 A. Notably, while the configuration model and the trajectory model use different solvent features, they share the same adsorbate features.

[0109] To comprehensively understand the predictive performance of ML on this dataset, a variety of machine learning algorithms are tested. The study specifically evaluated support vector regressor (SVR), least absolute shrinkage and selection operator (LASSO), ridge, stochastic gradient descent (SGD), Bayesian ridge, k-nearest neighbors (KNN), decision tree, random forest (RF), gradient boosting regressor (GBR), extreme gradient boosting (XGBoost), and multi-layer perceptron (MLP) regression algorithms, as implemented in the Python sklearn library. Machine learning model performance is evaluated using metrics of coefficient of determination ( R2), mean absolute error (MAE), and RMSE between predicted values on the test set and values from the dataset. For R2, the study considers a value greater than 0.8 to indicate good fit or predictive ability. Studies utilizing the MSS method indicate that the precision of this method is ~ O. leV. Therefore, machine learning predictions on AEillt, AEsol, and AFsolare considered sufficiently accurate if the MAE is less than 0.10 eV. The RMSE is generally larger than the MAE because the RMSE gives more weight to larger errors, making it more sensitive to data points with larger errors. This can lead to higher scores when certain data points fit poorly. The greater the difference between RMSE and MAE, the greater is the variance in the individual errors in the sample. Hence, the study aimed for the RMSE to be as close to the MAE as possible.

[0110] Evaluation of Machine Learning Predictions

[0111] Values of AE^tL, AES^L, and AFS^Lare compared to AE°T, AE°T, and ΔFsolMSStaken from an example dataset. Fivefold nested cross-validation (CV) is used to evaluate the models. This involves an outer loop to split the data into training and test sets for model evaluation and an inner loop that splits the data into training and validation sets forDocket Number: 103362-116WO1hyperparameter tuning. In the outer loop, 80% of the data (i.e., 72 adsorbates and their corresponding 360 configurations) are used as the training set, and the remaining 20% of the data are used for the testing set. This approach ensures that the model performance on the test set is evaluated on adsorbates not seen during training compared to a completely random split of data. This split is repeated five times, ensuring that each data point in the dataset is used as part of the training set four times and as part of the test set exactly once, as illustrated in FIG.8B. For each train-test split, the training set is further divided into five folds, each containing ~ 20% of the data (folds comprise 14 — 15 adsorbates each). In each iteration, four of these folds are used for training while the fifth fold is used for validation. During this phase, the model learns by iteratively updating the model weights (parameters) using the training folds to minimize the difference between the predicted and DFT / MSS energies / free energies. To optimize the model's hyperparameters (e.g., learning rate and regularization parameters), a grid search strategy is applied, where various hyperparameter combinations are evaluated on the training folds, and the best set is selected based on validation performance. With the optimal hyperparameters identified, the model is refit on the entire training set. After finalizing both the hyperparameters and model weights, the model's performance is evaluated on the reserved test set to ensure its generalizability. The final model score is the average of the test scores from all five splits. The details of the best-performing hyperparameters used for all algorithms can be found in the supplementary material, Table S6.

[0112] Results

[0113] Predictions of AEtTand AEff

[0114] The predictive performance for both the configuration and trajectory models, as well as the different ML algorithms is presented in FIGS. 9A-9B, which specifically shows R2, RMSE, and MAE for predicting ΔEintDFTand AE°fT. (The prediction results for AF.')'SSare not included in FIGS. 9A-9B since the range of AFsolin the dataset is notably smaller than that of AEintand AEsol, making it less straightforward to directly compare the RMSE and MAE values.) it can be observed from FIGS. 9A-9B that the prediction scores across different algorithms are quite similar. For example, the predictive capabilities of relatively simple linear algorithms such as ridge regression are comparable with those of more complex ensemble algorithms, such as RF and GBR. This suggests that the predictions are more dependent on the features and data quality than on the machine learning algorithm.Docket Number: 103362-116WO1

[0115] Statistics for predicting AEintusing the configuration model are represented by the blue bars shown in FIG. 9 A. The average R2across the 11 algorithms is 0.82, the average RMSE is 0.10 eV, and the average MAE is 0.08eV. AEsoican be predicted in two ways. First, the example implementation can use the values of AE^Jr (from the configuration model) to obtain AES^Lby averaging values of AE^ across the five configurations for each adsorbate. This is represented by the orange bars shown in FIG. 9B, The study found that the average R2for predicting AEsoiacross the 11 algorithms is 0.95, with the RMSE and MAE of 0.05 and 0.04 eV, respectively. Alternatively, AEso)can be directly predicted using the trajectory model shown in FIG. 9B. Using this method, the average R2across the II algorithms is 0.86, the average RMSE is 0.08 eV, and the average MAE is 0.06eV. AES^JLcan hence be more accurately predicted by averaging across the configuration model. This is due to the smaller number of data points in the trajectory7model, as each adsorbate has only one label for AEsolinstead of five for AEinl,

[0116] Parity plots of the prediction results from the configuration model using the GBR algorithm are shown in FIGS. I0A-10C. In particular, FIG. 10A shows AE^,vs ΔEintDFT; FIG. 10B shows AES^SLvs AE°SFT; and FIG. 10C shows AES”Land AE^0vs AE°FTI11these figures, shaded triangles represent the ML training set; the circles represent the ML test set; and alternatively shaded triangles represent data points calculated with MD. From FIG. 10A the RMSE on the AE^tLtest set is 0.096 eV and the MAE is 0.075 eV.Furthermore, higher accuracy is achieved in the range of AEilltfrom -0.7 to 0 eV since most adsorbates in the dataset have AEtFfvalues within this range. This finding is true across all ML algorithms. From FIG. 10B the RMSE on the AE^ test set is 0.038 eV and the MAE is 0.029 eV. The decrease in error in calculating AEsoiis due to cancellation of error from taking the average.

[0117] Since one w7ay to decrease the computational expense associated with calculating solvation thermodynamics of surface adsorbates is to eliminate the DFT step and instead use MD to predict energies of solvation, the study additionally compared the ML predictions from the example implementation against those calculated with MD in FIG. 10C. Here, each AEs^fTvalue is obtained by averaging five AE^tFTvalues and serves as the reference energy, while AE6^Dvalues are calculated using the classical potentials in MD, offering a simpler method. The study found that the RMSE for AES^|Dis 0.092 eV, which is higher than that for AE^1,(of 0.038 eV). Furthermore, a linear fit of the predicted valuesDocket Number: 103362-116WO1shows that AE^Lexhibits a slope of 0.92, which is closer to 1 compared to AE^0, which exhibits a slope of 0.76, A reason for this is that the classical force field and potential used in MD yields less-negative values of AEsolcompared to DFT, particularly for AEsolvalues more negative than -0.4 eV.

[0118] A parity plot of AE6^Lvs AE°Tusing the trajectory model is shown in FIGS. 11A-11B. From FIG. 11A, the RMSE on the test set is 0.073 eV and the MAE is 0.058 eV. These errors are larger than those for the configuration model given the smaller number of label values available for training in the trajectory model. A parity plot comparing ESPQ1Land AES^Dto AE°JTis presented in FIG. 11B. Similar to the configuration model, the MD results give larger errors than the ML predictions (with RMSE of 0.092 vs 0.073 eV). Furthermore, linear fits of the predicted values show that AE^ exhibits a larger slope (of O.84) than AE^0(of 0.76). Hence, ML outperforms MD for both the configuration and trajectory models in predicting AEsoi.

[0119] Predictions of

[0120] Parity plots between AF^Land ΔFsolMSSas well as AF’.^1L, AF^D, and AF^188using the MLP algorithm are shown in FIGS. 12A-12B. When comparingwith AF.1^53, the RMSE on the test set is 0.060 eV and the MAE is 0.043 eV (FIG. 12A). Although the prediction error for Atyolis smaller than that for AEsolusing the trajectory model, the R2score for AFsol(R2= 0.72) is lower than that for AEso!(R2= 0.90). This is because the range of the AFsollabel values is smaller than that of AEsol. From FIG. 12B, AFS^Dexhibits an RMSE of 0.092 eV, which is larger than AE.^,(of 0.060 eV ). Furthermore, the slope on E,Lis 0.71, which is closer to 1 than for AF^13(of 0.43 ). Hence, ML outperforms MD in predicting AFsol.

[0121] TABLE I. Explanation of features most frequently selected and highly- ranked across different algorithms after feature selection. The atomic coordinates, partial charges, Lennard-Jones parameters, bond information, and atom type information used to calculate these features are obtained from the MD input and output files from the dataset.Docket Number: 103362-116WO1Docket Number: 103362-116WO1Docket Number: 103362-116WO1Docket Number: 103362-116WO1Docket Number: 103362-116WO1Docket Number: 103362-116WO1Docket Number: 103362-116WO1

[0122] Discussion

[0123] The study described herein shows that a machine learning model configured according to implementations of the present disclosure can effectively predict interaction energies ( AEint), solvation energies ( AEso!), and solvation free energies ( AFso!) for adsorbates on a Ptylll) surface under liquid water solvent. The results show that the ML predictions outperform those obtained from molecular dynamics (MD) simulations, particularly in terms of RMSE and MAE and mostly fall within the acceptable criterion of 0.10 eV. The R2values for predicting AFsolare lower than desired, likely due to the limited number of data points (only 90) available. Thus the predictive capability of the models could be improved with a larger dataset. However, ML-predicted values of AFsolare still significantly more accurate than the analogous values predicted with MD. Overall, ML is a suitable method for predicting the solvation energies, and the ML models developed in this work will facilitate estimating AEint, AEsol, and AFsolfor adsorbates on a Pty 111) surface. Moreover, the molecular descriptors and methodologies presented in this study can serve as a reference for predicting these values in other systems. The present disclosure contemplates that other implementations of the present disclosure include expanded datasets (e.g., including a broader range of reaction intermediates, incorporating multi-solvent systems, and different types of interfaces). The present disclosure further contemplates using larger and more complex simulation systems to allow for the calculation of a greater variety of descriptors, capturing a broader spectrum of molecular interactions.

[0124] ML models are often treated as "black boxes," making it difficult to interpret their decision-making processes. However, because most of the features used hereinDocket Number: 103362-116WO1are molecular descriptors that have not undergone dimensionality' reduction, the descriptors retain their inherent meanings, allowing a user to use feature importance to interpret the model's predictions and obtain each feature's impact. To identify the most important features, the study assessed feature importance using Shapley additive explanation (SHAP) analysis, which was chosen for its ability to fairly allocate contributions among features. SHAP values quantify the relative significance of each feature compared to others and illustrate how each feature impacts the final prediction as well as how the model depends on the interaction between features. The results of SHAP analysis for the configuration model predicting ΔEintDFTare presented in FIG. 13. SHAP analysis for AEs“1and ΔFsolMSSexhibited similar features and hence are not shown. Features with higher SHAP values indicate a more significant influence on the model output. From the SHAP analysis results, it is evident that the number of hydrogen bonds, pairwise van der Waals interactions, and water density are among the most critical features influencing the model predictions. These features relate directly to the interactions between the adsorbate and the surrounding water molecules, highlighting the importance of considering molecular interactions in predicting ΔEint. The study found similar results for adsorbates m Ti-FAU zeolites.

[0125] The number of water-adsorbate hydrogen bonds, per configuration and on average, are two of the most important features. To explore this further, the study analyzed the hydrogen bonding information and corresponding energy labels across the dataset, as shown in FIGS. 14A-14C. For the same adsorbate, different numbers of hydrogen bonds are formed with w'ater molecules in various configurations, resulting in varying levels of interaction energies with the w'ater solvent. FIG. 14A show s the correlation between the number of adsorbate-water hydrogen bonds for each configuration and the DFT-calculated ΔEint, which has an R2value of 0.56. FIGS. 14B and 14C respectively show’ the relationship between the average number of adsorbate-water hydrogen bonds across 501 frames in the MD trajectory and the adsorbate's ΔEsoland ΔFsolfor each adsorbate, with R2values of 0.79 and 0.67, respectively. The study observed that a higher number of hydrogen bonds correspond to more negative values of ΔEint, ΔEsol, and ΔFsol, w'hich becomes even more pronounced when analyzed across the entire MD trajectory.

[0126] Van der Waals interactions also scored highly, indicating the importance of solvent-adsorbate interactions. Van der Waals interactions and many of the other important features are derived from classical approximations rather than quantum mechanics-based methods, such as DFT, aligning with the goal of using computationallyDocket Number: 103362-116WO1efficient features that bypass additional quantum chemistry calculations. Despite their simplified nature, such features encode physically meaningful trends that, when combined with other features, enable the ML model to effectively capture key aspects of adsorbate-solvent interactions.

[0127] Descriptors related to the electronic properties of the adsorbate, such as the Coulomb potential energy and adsorbate dipole as well as several principal components of the adsorbate fingerprint, also emerged as important features in the feature importance analysis. This suggests that the electronic properties and charge distribution of the adsorbate play important roles in determining its interaction with the solvent. In addition, the spatial distribution of water molecules around the adsorbate also scores highly.

[0128] These features relate directly to the interactions between the adsorbate and the surrounding water molecules. For instance, high SHAP values for hydrogen bonding and van der Waals energies indicate strong contributions of intermolecul ar interactions (and specifically hydrogen bonding) on the energies and free energies of solvation. These properties were also found to be important to solvation by Rendon-Calle et al. The importance of descriptors such as dipole contributions and spatial solvent distributions further point to intermolecular interactions as contributing significantly to solvation. These findings align with physical expectations. In summary', feature importance analysis reveals that a combination of different types of features collectively contribute to the model's predictive performance, underscoring the importance of incorporating a diverse set of descriptors that capture various aspects of the molecular system in machine learning models,

[0129] While machine learning provides an efficient framework for predicting solvation properties, other methods, such as many-body expansions, could also be applied to study solvation effects. Many-body expansions are less prone to overfitting compared to data-driven approaches. Furthermore, they are based on physics-based information and hence provide molecular-level insights, such as how specific arrangements of atoms and molecules influence the free energies of interfacial species. However, such approaches often face computational challenges when applied to highly disordered systems, as their complexity' increases rapidly with the number of interacting species.

[0130] Aqueous phase heterogeneous catalysis is relevant to a variety' of industrially important processes, such as biomass conversion, Fischer-Tropsch synthesis, and electrocatalysis for fuel ceils and water splitting. Hence, calculating the free energies of adsorbates involved in these chemistries is imperative for modeling catalyst performance. Therefore, it is essential to develop a methodology' that offers high efficiency and accuracy inDocket Number: 103362-116WO1calculating solvation thermodynamic properties in liquid phase. Computational approaches are key to comprehending solvent impacts on adsorbed species, and multiple strategies in molecular modeling, including molecular mechanics (MM), molecular dynamics (MD), and density functional theory' (DFT), have been applied.

[0131] Solvation can be modeled using two primary' approaches: explicit and implicit water representations. The explicit approach treats water as distinct H2O molecules, whereas the implicit approach models it as a continuous, structureless medium. Some methods with implicit solvation models have been proposed to model reactions at solid-liquid interfaces. Despite their computational efficiency, multiple authors have found that implicit solvation models cannot be generally applied for a number of reasons, including the inability to capture strong interactions or chemical binding between adsorbates and solvents, the tendency to oversolvate cavities between the adsorbate and solvent where actual solvent molecules cannot fit, and the failure to account for bond breaking and forming at the interface. Calculating the solvation free energies of adsorbates at the solid-liquid interface using explicit methods is challenging because both the many configurations of liquid solvent molecules and the energy accuracy due to bond breaking and forming need to be considered. In general, the energies of adsorbed species must be calculated with quantum mechanics (QM). What is more is that the free energies are affected by the thermal motions of solvent molecules, thereby requiring finite-temperature methods such as MM and / or MD. To address this, several groups have developed multi-scale methods that employ combinations of QM and MM and / or MD. While promising for their abilities to quantify solvation thermodynamics, these methods are computationally demanding, for example, requiring large-scale DFT analysis. Therefore, there is a significant interest in finding a suitable surrogate for DFT to improve computational efficiency.

[0132] In recent years, machine learning (ML) has emerged as a powerful tool in computational chemistry', offering the potential to significantly enhance the understanding of chemical systems and processes by enabling rapid prediction and analysis of various properties and phenomena. Some ML applications in catalysis are, for example, solving regression problems such as prediction of adsorption energies, reaction rates, electronic structures, and quantum chemical descriptors, as well as tasks such as searching for similar chemical structures in chemical databases and local structure identification. In exploring solvation effects, several studies have employed ML methods to predict solvation thermodynamic properties, particularly solvation enthalpies and solvation free energies. For example, Riniker presented a fingerprint termed Molecular Dynamics Fingerprints (MDFP)Docket Number: 103362-116WO1derived from MD simulations and applied ML to predict the solvation free energies of organic molecules across five different solvents. Lim and Jung developed an ML-based approach for predicting solvation free energies, encoding structural features of both solvent and solute, while providing key insights into which substructures significantly influence solvation processes. However, these studies focus on homogeneous systems, often relying on publicly available datasets such as Minnesota Solvation Database (MNSOL) and FreeSolv. In contrast, there are very few studies that use ML. to predict solvation energies in heterogeneous systems due to the lack of datasets and the challenges in obtaining accurate results at reasonable computational expense. Hence, ML has significant potential to transform the field of computational catalysis by providing an efficient way to compute solvation thermodynamics at interfaces.

[0133] Although the subject matter has been described in language specific to structural features and / or methodological acts, it is to be understood that the subject matter defined in the appended claims is not necessarily limited to the specific features or acts described above. Rather, the specific features and acts described above are disclosed as example forms of implementing the claims.

Claims

Docket Number: 103362-116WO1WHAT IS CLAIMED:

1. A computer-implemented method of training a machine learning model to predict a solvation property of an adsorbate, the method comprising:receiving an adsorbate dataset;generating a feature set from trajectories obtained by a plurality of molecular dynamics simulations;extracting, from the trajectories, a plurality of features; andtraining the machine learning model using the plurality of features, wherein the machine learning model is configured to predict the solvation property of the adsorbate.

2. The method of claim 1, wherein the feature set comprises one or more of adsorbate features, hydrogen bond features, or solvent features.

3. The method of claim 1 or claim 2, wherein the feature set comprises molecular descriptors, a molecular fingerprint, or both.

4. The method of claim 3, wherein the molecular fingerprint comprises an Ewald sum matrix fingerprint.

5. The method of any one of claims 1-4, further comprising concatenating at least a portion of the feature set into a feature matrix, wherein training the machine learning model uses the feature matrix.

6. The method of any one of claims 1-5, wherein training the machine learning model comprises performing recursive feature elimination to select a subset of informative features.

7. The method of claim 6, wherein training the machine learning model further comprises performing cross-validation to evaluate model performance and tune hyper-parameters.Docket Number: 103362-116WO18. The method of any one of claims 1-7, wherein the adsorbate dataset comprises a plurality of results from density functional theory simulations, a plurality of results from multi-scale sampling simulations, or both.

9. The method of any one of claims 1-8, wherein the adsorbate dataset comprises interaction energies, solvation energies, solvation free energies, or any combination thereof.

10. The method of any one of claims 1-9, wherein the solvation property comprises an interaction energy, a solvation energy, a solvation free energy, or any combination thereof.

11. The method of any one of claims 1-10, wherein the plurality of features includes at least one feature representing hydrogen bonding, van der Waals interactions, solvent density, or an electronic property of the adsorbate.

12. The method of any one of claims 1-11, wherein the machine learning model comprises a support vector regressor, a least absolute shrinkage and selection operator model, a ridge model, a stochastic gradient descent model, a Bayesian ridge model, a k-nearest neighbors model, a decision tree model, a random forest model, a gradient boosting regressor, an extreme gradient boosting model, or a multi-layer perceptron regression model.

13. A computer-implemented method of predicting a solvation property of an adsorbate, the method comprising:performing a molecular dynamics simulation of the adsorbate; generating, based on the molecular dynamics simulation, a plurality of features for the adsorbate;inputting the plurality of features into a trained machine learning model; and outputting, by the trained machine learning model, the solvation property of the adsorbate.

14. The method of claim 13, wherein the plurality of features comprises one or more of adsorbate features, hydrogen bond features, or solvent features.Docket Number: 103362-116WO115. The method of claim 13 or claim 14, wherein outputting the solvation property comprises predicting interaction energies for a plurality of molecular-dynamics configurations and averaging the predicted interaction energies to obtain a solvation energy.

16. The method of any one of claims 13-15, wherein the plurality of features comprises ensemble-average features derived from a plurality of molecular-dynamics configurations, and wherein the solvation property comprises a solvation energy or a solvation free energy.

17. The method of any one of claims 13-16, wherein the trained machine learning model was trained using an adsorbate dataset comprising results from density functional theory simulations, multi-scale sampling simulations, or both.

18. A system comprising:a molecular dynamics simulation module; anda machine learning module, wherein the machine learning module is configured to perform the method of any one of claims 1-17.

19. The system of claim 18, further comprising a density functional theory module configured to generate single-point density functional theory energy calculations for training the machine learning module.

20. A non-transitory computer-readable medium storing instructions that, when executed by one or more processors, cause the one or more processors to perform the method of any one of claims 1-17.

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