Object-detecting deep learning method for analyzing multi-event electrochemical data

Abstract

Systems and methods for analyzing multi-event electrochemical data using object-detecting deep learning in accordance with embodiments of the invention are illustrated. One embodiment includes a method of detecting and classifying electrochemical mechanisms. The method includes obtaining at least one cyclic voltammogram from an electrochemistry system, and generating one or more datasets from the at least one cyclic voltammogram. The method further includes, evaluating the generated datasets using a machine learning model, determining whether redox events are present in a region of the at least one cyclic voltammogram, and when at least one redox event is determined to be present in a region of the at least one cyclic voltammogram, determining a probability of at least one electrochemical mechanism of the electrochemistry system based on the redox event.

Description

OBJECT-DETECTING DEEP LEARNING METHOD FOR ANALYZING MULTI-EVENTELECTROCHEMICAL DATACROSS-REFERENCE TO RELATED APPLICATIONS

[0001] The current application claims the benefit of and priority under 35 U.S.C. § 119(e) to U.S. Provisional Patent Application No. 63 / 605,355 entitled “Object-Detecting Deep Learning Method for Analyzing Multi-Event Electrochemical Data” filed December 1 , 2023. The disclosure of U.S. Provisional Patent Application No. 63 / 605,355 is hereby incorporated by reference in its entirety for all purposes.STATEMENT OF FEDERAL SUPPORT

[0002] This invention was made with government support under 2247426 awarded by the National Science Foundation. The government has certain rights in the invention.FIELD OF THE INVENTION

[0003] The present disclosure generally relates to methods for analyzing cyclic voltammograms and, more particularly, electrochemical mechanistic analysis of cyclic voltammograms using deep learning.BACKGROUND

[0004] Cyclic voltammetry is a common electrochemical characterization technique that can generate valuable mechanistic information for redox-active chemical systems. Cyclic voltammetry has been widely applied to electrochemical applications in sensing, energy-storage, and chemical transformations. However, the general protocol of initial mechanistic analysis after experiments has remained largely unchanged since its inception. Researchers manually inspect the shapes and variations of cyclic voltammograms under multiple different scan rates (v), sometimes with different reactant concentrations, and subsequently hypothesize a qualitative mechanism including interfacial charge transfers (E step) and / or solution reactions (C steps). Additional experiments and / or numerical simulations may be applied if extracting quantitative kinetic information is needed. Such manual inspection may requireextensive research training, potentially incurs human bias, and may not be compatible with automated testing needed for high-throughput screenings. SUMMARY OF THE INVENTION

[0005] Systems and methods for analyzing multi-event electrochemical data using object-detecting deep learning in accordance with embodiments of the invention are illustrated. One embodiment includes a method of detecting and classifying electrochemical mechanisms. The method includes obtaining at least one cyclic voltammogram from an electrochemistry system, and generating one or more datasets from the at least one cyclic voltammogram. The method further includes, evaluating the generated datasets using a machine learning model, determining whether redox events are present in a region of the at least one cyclic voltammogram, and when at least one redox event is determined to be present in a region of the at least one cyclic voltammogram, determining a probability of at least one electrochemical mechanism of the electrochemistry system based on the redox event.

[0006] In another embodiment, the dataset comprises numerical values of current, current density, scan rate, and any combinations thereof.

[0007] In a further embodiment, the electrochemical mechanism is selected from the group consisting of a charge transfer, an interfacial charge transfer, an electron transfer, a chemical reaction, a solution reaction, a diffusion reaction, a single-electron quasi- reversible homogenous electron transfer (E); a single-electron quasi-reversible homogenous oxidative electron transfer followed by a chemical reaction of the oxidant in the solution (ECa); a single-electron quasi-reversible oxidative electron transfer preceded by a chemical reaction of the reductant in the solution (ECb), an anodic variant of the classic CE mechanism that is the counterpart of (ECa); a single-electron heterogeneous electron transfer following the Tafel kinetics (T); a two-electron homogenous electron transfer, in which a single-electron transfer is followed by an irreversible chemical and a disproportionation steps (DISP1); a similar two-electron homogenous electron transfer, in which a single-electron transfer is followed by an irreversible chemical step and a thermodynamically less demanding single-electron transfer (ECE); an homogenous electrocatalysis, in which a single-electron transfer isfollowed by a chemical step that regenerates the redox-active catalyst (EC’); an interfacial single-electron transfer when the redox species follows the Butler-Volmer kinetic and is bound on the electrode surface (SR), and any combinations thereof.

[0008] In still another embodiment, at least one probability of an electrochemical mechanism of the electrochemistry system is determined to at least 95% accuracy.

[0009] In a still further embodiment, the method further includes determining a plurality of electrochemical mechanisms and ranking the plurality of electrochemical mechanisms of the electrochemistry system.

[0010] In yet another embodiment, the method further includes determining stoichiometric homogenous electrochemical mechanisms selected from the group consisting of: E, ECa, ECb, ECE, and DISP1.

[0011] In a yet further embodiment, the electrochemistry system is a portion of a system selected from the group consisting of: a catalyst, a fuel cell, a battery, a redox flow battery.

[0012] In another additional embodiment, the catalyst catalyzes a process selected from the group consisting of: a carbon dioxide reduction process, a carbon fixation process, a carbon sequestration process, a water electrolysis process, a hydrogen production process, and an energy storage process.

[0013] In a further additional embodiment, the machine learning model is a model having a Faster R-CNN architecture further comprising a ResNet-18 backbone and a feature pyramid network.

[0014] In another embodiment again, the region is identified by a region proposal network (RPN) using object detection.

[0015] One embodiment includes a method of training a machine model for detecting and classifying electrochemical mechanisms. The method includes generating at least one dataset for at least one electrochemical mechanism comprising a set of parameters based on a definition of the at least one electrochemical mechanism, providing the at least one dataset as input training data to a machine learning model, and training the machine learning model using the at least one dataset.

[0016] In still yet another embodiment, the at least one dataset is generated via simulation.

[0017] In a still yet further embodiment, the method further includes adding Gaussian-type noise to the at least one dataset.

[0018] In still another additional embodiment, the at least one dataset comprises numerical values of current, current density, scan rate, and any combinations thereof.In a still further additional embodiment, the set of parameters is selected from the group consisting of: numbers of scan rate, values of scan rate, electrode double layer capacitance, standard rate constant of interfacial charge transfer in a concentrationdependent Butler-Volmer equation following Nicholson’s formalism in the E step, equilibrium constants and forward / backward rate constants in the Crstep based on Saveant’s definitions, and any combinations thereof.

[0019] Additional embodiments and features are set forth in part in the description that follows, and in part will become apparent to those skilled in the art upon examination of the specification or may be learned by the practice of the invention. A further understanding of the nature and advantages of the present invention may be realized by reference to the remaining portions of the specification and the drawings, which forms a part of this disclosure.BRIEF DESCRIPTION OF THE DRAWINGS

[0020] The description and claims will be more fully understood with reference to the following figures and data graphs, which are presented as exemplary embodiments of the invention and should not be construed as a complete recitation of the scope of the invention.

[0021] Fig. 1 illustrates a process for detecting and classifying electrochemical mechanisms in accordance with an embodiment of the invention.

[0022] Fig. 2 illustrates a general deep learning (DL) architecture of Faster R-CNN utilized for detection and classification of redox events in accordance with an embodiment of the invention.

[0023] Fig. 3 illustrates a process for training a machine learning model for electrochemical mechanism detection in accordance with an embodiment of the invention.

[0024] Fig.4 illustrates a comparison of different approaches to the analysis of cyclic voltammograms, including the DL architecture based on Faster R-CNN in accordance with an embodiment of the invention.

[0025] Figs. 5A-B illustrate the classes of electrochemical mechanisms analyzed by various embodiments, and an exemplary illustration of simulated multi-redox cyclic voltammograms used as training set in accordance with many embodiments of the invention.

[0026] Fig. 6A illustrates explanations to the true positives, false positives, and false negative in the custom DL model for both redox detection and mechanism classification, along with the definitions of metrics for performance evaluation in accordance with an embodiment of the invention.

[0027] Fig. 6B illustrates a comparison between test set voltammogram and the DL model’s performance.

[0028] Figs. 7A-K illustrates various voltammograms and performances by the custom DL model in detection and classification of redox events.

[0029] Fig. 8 illustrates a block diagram of a computing device for detecting electrochemical mechanisms in accordance with an embodiment. DETAILED DESCRIPTION

[0030] Cyclic voltammetry is a fundamental electrochemical technique. The correlation between current (i) and applied potential (E) as a function of multiple, n- numbered scan rates (v), represented as {v, i(E)}n, is necessary for a descriptive identification of z-numbered reaction mechanisms, in which each includes the combinations of electrochemical (Estep) and possibly chemical (Cstep) reaction steps. Such a mechanistic identification is a prerequisite for downstream quantitative analyses, hence the extraction of rate constants within reaction steps. Despite voltammetry being a foundational analysis technique, there is no consistent heuristic of visual inspection for voltammograms’ use in mechanism assignment. The manual visual inspection of the scan rate’s influence on voltammogram behavior remains the primary means of mechanism assignment. Reliance on manual inspection precludes any application inhigh-throughput systems, limits its utility for both experts and non-experts and renders analysis intractable when cyclic voltammograms increase in complexity and noise.

[0031] Recent advances in machine learning and artificial intelligence offer a different perspective on the voltammogram inspection and mechanism assignment. Machine-learning techniques have been applied to the mechanistic classification of single-redox voltammograms, as well as the numerical fitting of voltammogram data under a pre-determined mechanistic assignment. (See, e.g., Kennedy, G. F., et al., Anal. Chem. 2019, 91 (19), 12220-12227; Gundry, L., et al., J. Electroanal. Chem. 2023, 942; Chen, H., et al., J Phys Chem Lett 2022, 13 (2), 536-543; Chen, H., et al, J. Electroanal. Chem. 2022, 925; Chen, H., et al., Anal. Chem. 2023, 95 (34), 12826- 12834; the disclosures of which are incorporated by reference.) Recent work reported a deep-learning (DL) model based on the architecture of ResNet (Residual Neural Network) that automatically analyzed cyclic voltammograms, assuming the presence of one redox event, and designates the probable mechanism among five common ones in homogenous molecular electrochemistry. (See, e.g., Hoar, B. B., et al., ACS Measurement Science Au 2022, 2 (6), 595-604; the disclosure of which is incorporated by reference.) The ResNet algorithm yields a probability distribution for five mechanisms, represented as a vector y (n = 1 to 5) in which yirefers to the mechanistic propensity of ith mechanism. Such a probability-driven analysis provides a more satisfying accommodation given the finite amount of available electrochemical data and the finite instrumentational measurement resolutions.

[0032] However, the current machine learning models require a priori information, namely that the number of redox event z is presumably known (for example, z = 1), which renders the DL models not entirely on par with manual inspection. In a typical manual inspection of voltammograms without any a priori information, researchers first identify and locate any redox events in the voltammogram, i.e., a task of object detection, then determine the mechanism type for each redox event, i.e., a task of classification. While reported algorithms are capable of mechanistic classification for single-redox events in voltammograms, a DL algorithm, tasked with both objection detection and classification, remains to be developed for the automated analysis of cyclic voltammetry.

[0033] Systems and methods described herein enable automatic detection and classification of electrochemical mechanisms based on voltammograms. Several embodiments implement custom-designed DL architectures based on Faster R-CNN (Regional Convolutional Neural Network) for object detection and mechanism classification for multi-redox cyclic voltammograms with minimal a priori information. DL architectures in accordance with various embodiments are trained by simulated multi- redox voltammograms of up to 6 scan rates and up to 4 redox events ({v, i(E)}n, n = 1 to 6; z = 1 to 4), categorized in 8 different reaction mechanisms spanning homogenous, heterogeneous, and surface electrochemistry. In several embodiments, a variety of electrochemical mechanisms of the electrochemical processes measured by cyclic voltammograms can be characterized, categorized, and ranked. In a number of embodiments, probabilities for various electrochemical mechanisms can be generated as the analysis results. The automated analysis in accordance with some embodiments can be applied to simulated and / or experimental scenarios and achieve an accuracy of at least 95%. In many embodiments, deep learning-based analysis of cyclic voltammograms can analyze cyclic voltammogram curves without knowing if a redox event is present. Deep learning-based processes in accordance with various embodiments can provide qualitative, semi-quantitative, and / or quantitative results to deconvolute complex electrochemical systems.

[0034] Many embodiments provide classification and ranking of various electrochemical mechanisms for an electrochemistry system, which can be helpful for analyzing competing pathways and understanding the underlying electrochemical mechanisms of a complex system. Many embodiments provide automatic electrochemical analysis based on deep learning that can be used to analyze homogenous and / or heterogeneous electrochemical mechanisms and stoichiometric and / or catalytic transformations. Automated and accurate analysis of electrochemical processes using deep learning-based models can be applied to various electrochemical systems, including (but not limited to) catalysts and batteries. Automatic analysis can have the advantage of analyzing complex reaction schemes that may be beyond the capacity of manual analysis, such as square diagrams with the possibility of concerted pathways in proton-coupled electron transfer systems. Quick turnover of theelectrochemical mechanism analysis results can be used for high throughput screening of catalyst candidates. Being able to accurately characterize the electrochemical mechanisms of the reactions can be useful in identifying competing pathways of complex electrochemical processes and discovering catalyst degradation and / or catalyst turnover. Catalysts can be used in various processes, including (but not limited to) carbon dioxide reduction, carbon fixation, carbon sequestration, water electrolysis, hydrogen production, and energy storage. Catalysts can also be applied in redox flow batteries. The model can be applicable to analyze complex electrochemical systems when competing mechanisms are intertwined together. Being more sensitive and capable of detecting subtle elusive features, the electrochemical analysis in accordance with several embodiments may semi-quantitatively analyze competing pathways and observe the gradual transition from one mechanism to another. The automatic analysis processes can be integrated into software and / or hardware platforms for performing autonomous close-loop experiments.

[0035] DL-based analysis processes in accordance with many embodiments use datasets including (but not limited to) current at an applied potential and scan rate as inputs without knowing if a redox event is present. Several embodiments first detect a plurality of regions as regions of interest and determine if a redox event is present in the region. If a redox event is determined, some embodiments analyze the underlying electrochemical mechanisms based on each of the redox events and output a ranking of probabilities for each electrochemical mechanism. Many embodiments can automatically detect an arbitrary number of redox events. In some embodiments, when there is no redox event, the output would be null. In various embodiments, a plurality of redox events can be present in one cyclic voltammogram. The DL-based models analyze each redox region and output a ranking of the underlying electrochemical mechanisms. In a number of embodiments, electrochemical mechanisms including (but not limited to) the single-electron quasi-reversible homogenous electron transfer (E); the single-electron quasi-reversible homogenous oxidative electron transfer followed by a chemical reaction of the oxidant in the solution (ECa); the single-electron quasi- reversible oxidative electron transfer preceded by a chemical reaction of the reductant in the solution (ECb), the anodic variant of the classic CE mechanism that is thecounterpart of (ECa); the single-electron heterogeneous electron transfer following the Tafel kinetics (T); the two-electron homogenous electron transfer, in which a single- electron transfer is followed by an irreversible chemical and a disproportionation steps (DISP1); a similar two-electron homogenous electron transfer, in which a single-electron transfer is followed by an irreversible chemical step and a thermodynamically less demanding single-electron transfer (ECE); the homogenous electrocatalysis, in which a single-electron transfer is followed by a chemical step that regenerates the redox-active catalyst (EC’); the interfacial single-electron transfer when the redox species follows the Butler-Volmer kinetic and is bound on the electrode surface (SR), and any combinations thereof can be characterized and ranked using the automatic analysis. In a number of embodiments, the model can generate qualitative and quantitative characterization of electrochemical mechanisms associated with the reactions as output. Redox Event Detection

[0036] Systems and methods in accordance with several embodiments detect and classify redox events with only minimal priori information on the redox events. A process for detecting and classifying electrochemical mechanisms in accordance with an embodiment of the invention is illustrated in FIG. 1. Process 100 obtains (110) cyclic voltammograms from an electrochemistry system. In cyclic voltammetry, forward and backward potential sweep produces a plot known as a cyclic voltammogram. In cyclic voltammetry, the electrode potential ramps linearly versus time in cyclical phases. The rate of voltage change over time during each of these phases is known as the scan rate (V / s). The potential is measured between the working electrode and the reference electrode, while the current is measured between the working electrode and the counter electrode. Current (i) can be plotted versus applied potential (E) in the voltammograms. Cyclic voltammograms can be generated experimentally and / or via simulation. Cyclic voltammograms can have different scan rates and different current readouts.

[0037] In many embodiments, one or more datasets are generated (120) based on the obtained cyclic voltammograms and are used as input datasets. Input datasets from cyclic voltammograms can include (but are not limited to) current, current density, and / or scan rate, as will be discussed with respect to various embodiments furtherbelow. Many embodiments implement two-dimensional matrixes employed to store electrochemical information for the analysis. Additionally, data cleaning and / or normalization can be used to reduce and / or remove noise in the cyclic voltammograms before deriving datasets as will be discussed in greater detail further below.

[0038] Process 100 evaluates (130) the generated datasets using deep-learning- based approaches. Many embodiments implement deep learning-based processes using (but not limited to) residual neural networks (ResNet) to analyze cyclic voltammograms. The model can generate qualitative and quantitative characterization of electrochemical mechanisms associated with the reactions.

[0039] Process 100 determines (140) in a region if redox events are present. In various embodiments, systems and methods determine the voltage windows containing redox events. Custom Faster R-CNN architectures may be used to perform object detection on cyclic voltammograms to identify the voltage windows where redox events may be present.

[0040] Within the region where redox events are present, process 100 determines (150) electrochemical mechanisms of the electrochemistry system. Various electrochemical mechanisms can be characterized and / or ranked via automatic analysis. The neural network can yield a vector with each component representing the probability and / or fraction towards various electrochemical mechanisms. The classification process can be completed by designating the electrochemical mechanisms of the largest component in a vector as the most probable and / or most prominent one for the electrochemical system. Non-zero probabilities and / or fractions for mechanisms other than the most probable / prom inent one may suggest either a competing reaction or a gradual transition from one mechanism to another. Process 100 outputs (160) the probabilities of each electrochemical mechanism.

[0041] While specific processes for detecting and classifying electrochemical mechanisms are described above, any of a variety of processes can be utilized to detect and classify electrochemical mechanisms as appropriate to the requirements of specific applications. In certain embodiments, steps may be executed or performed in any order or sequence not limited to the order and sequence shown and described. In a number of embodiments, some of the above steps may be executed or performedsubstantially simultaneously where appropriate or in parallel to reduce latency and processing times. In some embodiments, one or more of the above steps may be omitted. Faster R-CNN Architecture

[0042] The presence of multiple electrochemical mechanisms within a single cyclic voltammogram can make it less ideal to use solely, image classification algorithms such as ResNet. On the other hand, convolutional layer-based algorithms, specifically object detection algorithms, can be considered as a mature technology for the elucidation of electrochemical mechanisms contributing to a convoluted {v, i(E)}noutput. Faster R- CNN architecture may be better for this purpose due to its online region proposal network (RPN), which enables end-to-end training on detection and classification tasks. Additionally, the deployment of feature pyramid networks in Faster R-CNN architectures can promote multi-scale detections. Further, the Faster R-CNN architecture’s alignment algorithm of regions of interest (RoI), generated from RPN, can generally provide high fidelity between known and predicted event bounds – in our case, the voltage windows containing redox events. As voltammetry data {v, i(E)}nare intrinsically sets of one- dimensional (1D) vectors instead of two-dimensional images, several embodiments develop custom-designed models of 1-D Faster R-CNN architecture to locate the potential window for a variety of ranges such as from 0 to 4 redox events (z ≤ 4) and designate the probable mechanism in a probabilistic manner.

[0043] In many embodiments, systems and methods utilize custom implementations of DL Faster R–CNN architectures with RPN and 1D RoI align algorithm to obtain a highly effective mechanism enumeration from complex voltammogram data. Various embodiments deploy ResNet for the classification in each RoI among the aforementioned 8 mechanisms and the null class (φ) that indicates the voltammogram background without any designated redox events. Instead of calculating the value of Intersection over Union (IoU,[0,1]) between 2D RoI and the ground truth during the training process, in several embodiments, IoU was calculated between the 1D RoI and the ground truth, namely the pre-assigned voltage window of a redox event in the E axis, to assess the quality of proposed RoI from RPN.

[0044] A general architecture of Faster R-CNN utilized for detection and classification of redox events in accordance with an embodiment of the invention is illustrated in Fig.2. The developed architecture can discern multi-redox voltammograms and enumerates the voltage window of each detected redox event z represented as normalized voltage values Elowand Ehigh, the corresponding mechanistic propensity distribution yztowards the trained 8 redox mechanisms plus φ class, and the assignment of most probable mechanism for each redox event. Training of DL Architectures

[0045] Several embodiments provide synthetic datasets for training of the deep learning models. Synthetic training datasets can cover various electrochemical scenarios with better uniformity in data quality and higher accuracy. A process for training a machine learning model for electrochemical mechanism detection in accordance with an embodiment of the invention is illustrated in Fig. 3. Process 300 generates (310) a plurality of datasets of electrochemical mechanism parameters using a computer system. Examples of electrochemical mechanism parameters can include (but are not limited to) current, current density, and / or scan rate. Parameters can be collected from a plurality of experimental measurements and / or from simulated datasets. Gaussian-type noise can be added to the training dataset to mimic various reaction conditions. Synthetic training datasets can cover various electrochemical scenarios with higher uniformity in data quality and accuracy. Cyclic voltammograms based on the targeted mechanisms can be numerically simulated as the training sets for deep neural networks.

[0046] Systems and methods in accordance with many embodiments train (320) a machine learning model using the generated datasets. Deep learning-based processes such as (but not limited to) residual neural networks (ResNet) can be implemented as the machine learning model. Cyclic voltammograms based on a plurality of the targeted mechanisms can be numerically simulated as the training sets for deep neural networks. A training dataset can be generated for each electrochemical mechanism. Numerical conditions, including (but not limited to) numerical models of partial differential equations (PDEs), boundary conditions, and initial conditions, can beconstructed based on the definitions of various mechanisms. Parameters of the numerical models include (but not limited to), the numbers and values of scan rate, electrodes’ double layer capacitance, standard rate constant of interfacial charge transfer in the concentration-dependent Butler-Volmer equation following Nicholson’s formalism in the Erstep, and the equilibrium constants and forward / backward rate constants in the Cr step based on Savéant’s definitions, can be incorporated into the simulations and carefully constrained with practical and fundamental considerations. Some embodiments include Gaussian-type noise due to background and instrumentation in the experimental voltammograms. Gaussian noise of varying degrees of standard deviation relative to the maximal current densities can be added to the simulated voltammograms to better reflect the realistic electrochemical data but also increases the algorithm’s tolerance towards noises in automatic mechanism categorization.

[0047] Process 300 generates (330) the machine learning model when training criteria are satisfied. Process 300 determines (340) electrochemical mechanisms in cyclic voltammograms. Several embodiments implement simulated multi-redox voltammograms of various scan rates and redox events to train the DL models. In some embodiments, the training data sets include multi-redox voltammograms up to 6 scan rates and up to 4 redox events ({v, i(E)}n, n = 1 to 6; z = 1 to 4), categorized in 8 different reaction mechanisms spanning homogenous, heterogeneous, and surface electrochemistry.

[0048] While specific processes for training a machine learning model for electrochemical mechanism detection are described above, any of a variety of processes can be utilized to train a machine learning model for electrochemical mechanism detection as appropriate to the requirements of specific applications. In certain embodiments, steps may be executed or performed in any order or sequence not limited to the order and sequence shown and described. In a number of embodiments, some of the above steps may be executed or performed substantially simultaneously where appropriate or in parallel to reduce latency and processing times. In some embodiments, one or more of the above steps may be omitted.Model Evaluation

[0049] A comparison of different approaches to the analysis of cyclic voltammograms, including the DL architecture based on Faster R-CNN in accordance with an embodiment of the invention, is illustrated in Fig. 4. DL architectures based on Faster R-CNN in accordance with several embodiments classify each RoI among the designated 8 electrochemical mechanisms. Figs. 5A-B illustrates the classes of electrochemical mechanisms analyzed by various embodiments and an exemplary illustration of simulated multi-redox cyclic voltammograms used as training sets in accordance with many embodiments of the invention. Each data point in the training set contains a set of multi-redox cyclic voltammograms with n scan rates and z redox events ({v, i(E)}n, n = 1 to 6; z = 1 to 4).

[0050] After random-sampling 3,000 parameter combinations for each mechanism type at up to 6 different scan rates (n = 1 to 6), various embodiments combine no more than four individual mechanisms of parameter combinations into each simulated multi- redox voltammogram (z = 1 to 4), with randomized redox sequences, voltage spacings among every redox event, and redox concentrations that dictate the current density i of measured redox features. Voltammograms in training sets may assume that each redox event is independent of the other. In various embodiments, the training set includes well-separated redox peaks, and the current densities of redox peaks are of the same order of magnitude as all redox events. In many embodiments, a certain extent of Gaussian noise, with a dimensionless standard deviation σtrain= σtest= 0.01 unless otherwise noted, may be applied to the normalized current density i.

[0051] Explanations of the true positives, false positives, and false negatives in the custom DL model for both redox detection and mechanism classification, along with the definitions of metrics for performance evaluation in accordance with an embodiment of the invention are illustrated in Fig. 6A. There are two separate yet related evaluation matrices for the evaluation of a DL model for both object detection and classification. Metric 1 relates to the effectiveness of the RPN to detect events independent of their mechanism, i.e. predictability in object detection alone, and metric 2 relates to the overall inference performance, which is the combination of object detection (matching of predicted voltage windows with the ground truth in the training data) and classification(matching with the true mechanism in the training data) of the RoIs provided by the RPN. In the evaluation of objection detection alone, a few prediction types were possible through the course of region proposal and object detection. RoIs predicted by the RPN could ultimately align with the ground truth of redox bounds (object detection true positive, tp1; IoU ≥ 0.75) or not (object detection false positive, fp1), and regions where known true redox bounds were not detected were assigned as false negatives (fn). In the evaluation of metric 2, overall inference performance, a true positive (fp2) is logged when the ground truth mechanism i is confidently denoted as the most probable mechanistic propensity in yzvector (yz,i≥ 0.7) with good overlap with the redox’s voltage bounds (IoU ≥ 0.75); while false positives are defined as incorrect final classification (fp2). There is no delineation between the false negatives (fn) between object detection (Metric I) and overall inference (Metric II). Hence, the fn sub-population contributes equally to the evaluation of object detection and overall inference matrices.

[0052] The developed DL model was evaluated for its performance after being trained and tested by about 80,000 simulated multi-redox voltammograms ({v, i(E)}n,n = 6; z = 1 to 4; σtrain = 0.01). Following the protocol of statistical analysis in imaging recognition and more generally, binary classification, the precision (P) and recall (R) of both matrices are calculated to evaluate the predictability and sensitivity, respectively, of the DL model, as demonstrated by the comparison between test set voltammogram and the DL model’s performance illustrated in Fig. 6B. Calculating the harmonic means of P and R in both matrices lead to the F1 scores, an overall measure of a model’s performance. As shown in Fig. 6B, the F1scores in Metric I and II reach 0.952 and 0.936, respectively, illustrating strong performance by the RPN and overall inference performance by the fully trained DL model. An overall F1score of 0.936 in Metric II indicates a balance of precision and recall with high magnitudes of both, which was further strengthened by an average IoU of 0.966, where unity constituted a perfect overlap of predicted bounds with ground truth voltage windows.

[0053] Class-by-class prediction accuracies were also evaluated based on the developed DL model. As the developed ResNet classifies RoI into not only the 8 designated electrochemical mechanisms but also the null class (φ), i.e. the background without any redox events, a confusion matrix that includes 8 mechanisms and the φevents with tp1, fn, and fp1events highlighted was established as illustrated in Fig. 6C. However, practically the DL’s functionality will not be affected by the presence of fp1cases with φ prediction, contributing to 39% of total fp1cases (“Unnecessary fp1” in Fig. 6C), when the DL algorithm unnecessarily yet correctly identifies a voltage window in the voltammogram that does not have any redox events and can be easily dropped in our model. In the context of mechanism classification, a revised confusion matrix can be plotted with a tp2accuracy of 97.2% among all tp1cases, presumably better reflecting the model’s utility in mechanistic analysis. The results suggest that DISP mechanism is the most confused one, evident from non-negligible probabilities of mis-assigning a DISP mechanism as ECa / ECb, or vice versa.

[0054] The utility of the developed DL model can be demonstrated with the analysis of both simulated voltammograms. Figs. 7A to 7D illustrated simulated voltammograms ({v, i(E)}n, n = 6, σ = 0.01) with the number of redox events z = 1, 2, 3, and 4, respectively, that was new to the DL model after the training process. The solid dark-red rectangles denote the redox events’ voltage windows (Elowand Ehighvalues) designated as the ground truth, while the dashed ones of bright-red color denote the RoIs generated from the custom DL model’s analysis. The close match between the designated ground truth and analyzed RoIs suggest satisfactory performance of objection detection with a IoU threshold value of 0.75. Moreover, each detected redox event is subject to mechanistic classification via the ResNet architecture. The most probable mechanism is labelled on the voltammograms along with the correspondingly propensities yi, while the DL model outputs the whole y vector of mechanistic propensities. The high yivalues for the correctly predicted mechanisms illustrate the model’s high analytic fidelity. Statistically, approximately 10,000 simulated voltammograms report the tp2accuracies of 98.2%, 97.8%, 97.2%, and 96.6% when z = 1, 2, 3, and 4, respectively. Such results indicate that despite slight decay, the tp2 accuracy is relatively insensitive against the number of redox events (z), and the developed DL model is robust against the increasing complexity in the voltammograms.

[0055] Figs. 7E-G illustrate experimental voltammograms of 1 mM Cobalt (II) tetraphenylporphyrin (CoIITPP) in accordance with an embodiment of the invention. Cobalt(II) teterphenylporphrin (CoIITPP) is known to undergo a quasi-reversible one-electron charge transfer (E step) between Co(II) and Co(I) redox states (~ −0.75 V vs. Saturated Calomel Electrode, SCE) in dimethylformamide (DMF). From experimental voltammograms (n = 6), such an E step can be correctly detected and classified by the DL model based on both RoI alignment and the corresponding y vector that includes mechanistic propensities of 8 mechanisms and background (φ). When chloroacetonitrile (ClCH2CN) was added to the solution, the electrogenerated Co(I) species reacted as ClCH2CN as a nucleophile, yielding Co(III)−CH2CN, rendering the Co(II) / Co(I) redox irreversible (ECbmechanism due to its cathodic nature). At a more cathodic potential (< −1.0 V vs. SCE), the yielded Co(III)−CH2CN species is reported to undergo multiple steps in a catalytic fashion, yielding voltammogram responses resembling either a T or EC’ mechanism.24At a small equivalent of ClCH2CN, illustrated in Fig.7F, the DL model correctly detects and classifies the catalytic process at more cathodic potentials (RoI1), while detecting the Co(II) / Co(I) and classifies it as a E mechanism (RoI2), albeit at a much lower propensity (yE= 60.4 % in Fig.7F against 79.1% in Fig. 7E), consistent with the decrease of irreversibility owing to the reaction between Co(I) and ClCH2CN.24At a larger equivalent of ClCH2CN (Fig. 7G), similar catalytic (RoI1) and Co(II) / Co(I) (RoI2) features are detected from the voltammograms, yet now the Co(II) / Co(I) redox is so irreversible that the most probable assignment is ECb(71.8%), indicative a more large extent of the reaction between Co(I) and ClCH2CN.

[0056] The custom DL model can be deployed to analyze the redox and catalysis of nitroxyl derivatives in aqueous solutions, but now with only a single voltammogram curve (n = 1) instead of the default value of 6. This is intended to test whether the DL model, while trained by {v, i(E)}n(n = 6), is applicable towards electrochemical datasets with a smaller number of scan rates. 3D input tensor can be populated with 6 identical voltammograms and scan rates and feed the tensor into the DL model for analysis. As illustrated by the voltammograms of 1 mM 1-methyl-2-azaadamantane-N-oxyl (1-Me- AZADO) in Figs. 7H-K, quasi-reversible redoxes of 1-methyl-2-azaadamantane-N-oxyl (1-Me-AZADO) (Fig. 7H) and 4-methoxy-2,2,6,6-tetramethylpiperidine-1-oxyl (4-MeO- TEMPO) (Fig. 7I) are both successfully detected and classified as E mechanisms. When substrate benzyl alcohol (PhCH2OH) is added to the solution of 1-Me-AZADO, two-electron electrocatalytic oxidation of PhCH2OH via the EC’ mechanism emerges(Fig. 7J). Such voltametric response is corrected detected and identified (RoI2), yet a false positive (fp2) is also yielded with a 79.0% of φ propensity (RoI1). When PhCH2OH are added to the mixture of 1-Me-AZADO and 4-MeO-TEMPO, both 1-Me-AZADO and 4-MeO-TEMPO serve as EC’ electrocatalysts in parallel, albeit at different catalytic onset potentials (Fig. 7K). The resultant voltammogram display a two-step staircase shape, which was not close to any of the scenarios by which the DL model was trained. Surprisingly, the DL model correctly detects and classifies the general trend of the EC’ mechanism (RoI4), amid one fp1(RoI1) and two fp2(RoI2and RoI3) cases with high φ propensities (> 75%) (Fig.7K). It is interesting that both fp2cases correctly detect redox events beyond the background and the second most likely mechanism are both EC’ (6.13% and 16.3%, respectively). These results suggest that systems and methods may still be used for voltammograms with fewer scan rates (n < 6), yet prone to false-positive outputs. Practically, the issue of false-positives can be addressed in post-analysis by removing any detections whose φ propensity is larger than a threshold (say, 60% based on Fig.7J and 7K).

[0057] FIG. 8 illustrates a block diagram of a computing device for detecting electrochemical mechanisms in accordance with an embodiment. The electrochemical mechanism detection device 800 includes a processor 805, memory 820, and a data interface 815. In the illustrated embodiment, memory 820 can include an electrochemical machine learning application 825 and cyclic voltammograms data 830. The electrochemical machine learning application 825 can be machine-readable instructions that can configure the processor 805 to execute the instructions, thereby creating machine learning models using cyclic voltammograms data such as according to processes discussed further below. In several embodiments, cyclic voltammograms data and / or output data from the electrochemical ML application 825 can be input and / or output by data interface 815. Data interface 815 can be any of a variety of interfaces, such as, but not limited to, removeable memory or a network interface.

[0058] Although a specific example of a computing device for detecting electrochemical mechanisms is illustrated in this figure, any of a variety of computing devices can be utilized to perform processes for detecting electrochemical mechanismssimilar to those described herein as appropriate to the requirements of specific applications in accordance with embodiments of the invention. EXEMPLARY EMBODIMENTS

[0059] 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 to make and use the present invention, and are not intended to limit the scope of what the inventors regard as their invention nor are they intended to represent that the experiments below are all or the only experiments performed. Efforts have been made to ensure accuracy with respect to numbers used (e.g., amounts, temperature, etc.) but some experimental errors and deviations should be accounted for. Example 1: Finite-element simulation of cyclic voltammograms

[0060] Finite-element simulations of cyclic voltammograms are conducted using COMSOL Multiphysics v5.5. The modules of Electrochemistry and Chemical Reaction Engineering are used for a one-dimensional model under the supporting electrolyte assumption with a time-dependent solver specialized for cyclic voltammetry, using an adaptive mesh with a maximal mesh size of 41 μm and a growth rate of 1.3. COMSOL simulations were iterated using COMSOL LiveLinkTMwhich implements MATLAB R2020b. Random samples of variables are realized by Python 3 scripts and fed to COMSOL via MATLAB for the simulations of at least five consecutive cycles in cyclic voltammetry. Additional sanitization is implemented after COMSOL simulation to ensure the simulated cyclic voltammograms not only satisfy the corresponding mechanism but also are electrochemically accessible. A total of about 80,000 valid simulated cases, each containing cyclic voltammograms up to 6 different v values, are conducted. Example 2: Establishment of machine-learning algorithm

[0061] In many embodiments, simulated and experimental data was sanitized and translated in to the two-dimensional matrix {v, i(E)}nbefore the implementation of machine learning. For each data point that includes either simulated or experimental cyclic voltammograms at n number of v values ({v, i(E)}n), the current densities i involtammograms were normalized as inormalizedagainst the largest i among all voltammograms in {v, i(E)}n, with inormalizedin the forward scan designated as positive value. The electrochemical potentials E were shifted so that adjusted electrochemical potential Eadjusted= 0 V for the data point of the most negative voltage in the voltammogram (Eadjusted≥ 0). As shown in the next paragraph, the interpolation and / or imputation of the i-E characteristics were conducted so that the tensor input of the machine-learning model does not explicitly contain the information of E.

[0062] Pytorch machine-learning frameworks in accordance with various embodiments are used to implement the designed neural network architecture. Because different starting potentials of voltammograms create additional variations for the first cycle of the voltammograms in both simulated and experimental scenarios, algorithms trained by the second cycles of voltammograms may be used. Graphs were generated using the MatPlotLib library and the PyPlot module. Training data were input with stochastically added noise, the dimensionless standard deviation as σtrain, after the raw / pre-noise data were normalized to have a global absolute current of 1, increasing the robustness of the model to the noise encountered in real experimental data.

[0063] In many embodiments, data of normalized cyclic voltammograms are processed by python library OpenCV to a three dimensional tensor / matrix with a size of (6 × 3 × 1000) and internal labels {n, y, m} that were only used in the codes. Here, n has a dimension of six correlating to the number of simulated scan rates, m has a dimension of 1000 correlating to the 1000 potential values used during resizing (see above comments about Eadjusted), and y has a dimension of three corresponding to ifor, irevand vn, which are the forward (ifor) and reverse (irev) normalized current values for scan rate v, at potential m. When training models with some data point whose dimensions n < 6, the size of the tensor in accordance with several embodiments remains the same and copies of certain dimensions are used to fill empty dimensions so that the tensor size remains (6 × 3 × 1000) for all data points. The input tensor was evaluated using a kernel / filter of size (6 × 3 × 7). The kernel only views the data present in the tensor, and the filter is not changed with different values of n.Example 3: Experiments of electrochemical characterization

[0064] The tetraphenylporphyrin cobalt(II) (CoII(TPP)) (80%), tetra-n-butylammonium hexafluorophosphate (n-Bu4NPF6) (98%) and tetra-n-butylammonium perchlorate (n- Bu4NClO4) (98%) are purchased from TCI America; anhydrous diethyl ether is purchased from Fisher Scientific; ferrocenium (Fc+) hexafluorophosphate (98%) is purchased from Santa-Cruz Biotechnology; 1-bromobutane (n-BuBr) (99%), anhydrous N,N-dimethylformamide (DMF), anhydrous benzene, anhydrous acetonitrile, anhydrous tetrahydrofuran (THF), anhydrous dichloromethane, anhydrous pentane, dimanganese(0) decacarbonyl (98%), ethylenebis(diphenylphosphine) (99%), boric acid (99.5%), potassium chloride (99%), sodium hydroxide (99%) and 4-tert-butylcatechol (97%, HPLC) are purchased from Sigma-Aldrich. All the chemicals are used as received unless otherwise specified below. Bu4NPF6 and Bu4NClO4 salts are recrystallized from ethanol before use. CoII(TPP) is recrystallized from methylene chloride before use. n- BuBr is fractionally distilled over CaSO4under N2at atmospheric pressure. The second fraction is collected at 102 °C and is dried over molecular sieves before use. THF is dried over molecular sieves before use. 4-tert-butylcatechol is distilled under reduced pressure and is allowed to recrystallize under vacuum at room temperature as a white crystalline solid before use.

[0065] The Mn complex [trans-Mn(CO)2(DPPE)2]PF6 is synthesized. Dimanganese(0) decacarbonyl (0.2 g, 0.5 mmol) and DPPE (DPPE = ethylenebis(diphenylphosphine), 0.4 g, 1 mmol) are dissolved in 10 mL of benzene and the solution is refluxed under N2 for 4 hrs. The [trans-Mn(CO)2(DPPE)][Mn(CO)5] salt is formed and collected as a yellowish solid. A portion of this solid (0.11 g, 0.1 mmol) is dissolved in 3 mL acetonitrile and 1 equivalent ferrocenium hexafluorophosphate (0.033 g, 0.1 mmol) is added to this solution and the reaction mixture is stirred vigorously for 30 min. Layering diethyl ether over this reaction mixture afforded an orange-yellow solid, which upon further recrystallization with dichloromethane / pentane afforded an orange- yellow crystalline solid (0.06 g, 59%).31P NMR (CDCl3): δ 77.9 ppm (s) and −144.3 ppm (m).

[0066] Experiments of cyclic voltammetry are performed at room temperature using a CH Instruments 630D potentiostat. Solutions in organic solvents are performed underan Ar atmosphere in a glovebox (Vigor SG1200 / 750TS), while aqueous experiments are performed under N2 atmosphere. iR corrections are conducted with positive feedback compensations for the ohmic drop. Ag / Ag+pseudo-reference electrode is calibrated against Fc+ / Fc redox after electrochemical measurements. Example 4: General considerations for the model of cyclic voltammetry

[0067] A time-dependent one-dimensional model is established under the supporting electrolyte assumption for the COMSOL-based finite-element simulation of cyclic voltammograms. The model numerically simulates the oxidative electrochemical systems, in which before cyclic voltammetry only the reduced species (R) are present in the solution. Only the oxidative electrochemical processes may be needed in the training model thanks to the process of data pre-treatment and sanitization. Below are the boundary and initial conditions in specific mechanistic scenarios. The ranges in variable’s values and the sampling method (linearly or logarithmically) are discussed and summarized in Table 1. As shown below, the range in variable’s values could be interdependent. Such interdependence and random sampling are implemented by python 3 scripts. Example 4.1: Partial differential equationsHere denotes the mechanism-specific function that describes any possible C step in the solution. denotes the absence of any homogenous C steps.

[0068] The diffusion coefficients sampled logarithmically, are assumed to besame for all the molecular redox species in the solution. The hypothesis of constant D values is reasonable for two reasons: (1) The assumed reversible and quasi-reversible E step suggest a small reorganization energy λ and the resultant a small change of the molecular structure. (2) The value of D is relatively insensitive to the changes of chemical identities since the scaling relationship between D and molecular weight is relatively weak based on the Stokes-Einstein relationship.

[0069] The initial concentration of the reduced species CR,iis linearly sampled from 0.1 mM to 100 mM with additional constrains listed below. Example 4.2: Boundary and initial conditions

[0070] Diffusion layer assumption is implemented in the simulation. A finite diffusion layer L is implemented so that x = 0 denotes the electrode and x = L denotes the boundary diffusion layer. In Nicholson’s formalism of cyclic voltammetry and presented below for single-electron transfer from O to R with the period of triangular voltage wave as λ, function describes the temporal concentration variation of O in the presenceof diffusion for each period of triangular voltage wave,in which is the standard rate constant of interfacial charge transfer and is the transfer coefficient.

[0071] The above expression suggests that the characteristic time constant of diffusional behavior is for Therefore, in our simulation, the thickness of thediffusion layer L is adaptively chosen so that the L is more than six times of the characteristic length scale of diffusion within the noted characteristic time constant when T = 298.15 K (same below).Here the scan rate v is evenly sampled both logarithmically and linearly between 0.01 to 2 V / s. Additional algorithms to sample n number of different v values in the same simulated electrochemical systems is extensively discussed below.

[0072] In addition to the Faradaic processes simulated below, capacitive double- layer charging events are also simulated with double-layer capacitance Cdlrandomly sampled linearly between 5 to 35 μF / cm2.Example 4.3: E mechanism

[0073] The thermodynamic potential of O / R redox EO / R= 0 V versus an arbitrary reference electrode. The cyclic voltammograms are simulated with a potential window in which the anodic bound Ewindow,a is linearly sampled between 0.5 and 1 V vs. NHE and the cathodic bound Ewindow,cis linearly sampled between −0.5 and −1 V vs. NHE. The starting potential of the cyclic voltammogram Estartis linearly sampled between −0.2 V vs. NHE and Ewindow,c. Such an arrangement of Estartensures that there is minimal transient current at the beginning of voltage sweep.

[0074] Concentration-dependent Butler-Volmer equation is employed to define the E step at the electrode interface.Here, and denotes the equilibrium concentration when andThe exchange current density i0is logarithmically sampled with the upper- bound and lower-bound

[0075] Following the Nicholson’s formalism in cyclic voltammetry, is dependent onthe standard rate constant of surface change transfer :

[0076] [10, 0.3] can be used following the Nicholson’s formalism, whichcorresponding to a peak separation = 62 ~ 120 mV in the cyclic voltammograms.The upper bound of values may be high enough that the resultant scenarios resemble the Nernstian scenario in cyclic voltammetry in which the interfacial charge transfer is fast enough to ensure a Nernstian equilibrium for the redox species in the immediate proximity near the electrode.

[0077] As to ensure detectable peaks in cyclic voltammograms, additional constraint about the minimal concentration of redox O / R (CR,i) are needed. The current densities of the redox peaks can be estimated based on Randle-Sevcik equation and ensure that the estimated current densities are at least about 5 times of the background current density from the capacitive double-layer charging / discharging.Example 4.4: ECamechanism

[0078] Most of the constraints in the ECamechanism are the same as the E mechanism with the following additional constraints.

[0079] The equilibrium constant of the C step is logarithmically sampledbetween 100.5~ 103.

[0080] The kinetic rate constant of C step in the forward direction is logarithmicallysampled within the following upper and lower bound so that

[0081] The above ranges ofand values capture all of the possible variations in the EC mechanism, before the small value of leads to situations that are indeedthe E mechanism and presented at the very upper part of that figure.

[0082] Because of the resultant potential shifts of redox peaks in the ECamechanism, the Estartis now linearly sampled between Ewindow,cand V vs. NHE.Example 4.5: ECb mechanism

[0083] Most of the constraints in the ECbmechanism are the same as the E mechanism with the following additional constraints.

[0084] The equilibrium constant of the C step is logarithmically sampledbetween 10−3~ 10−0.5.

[0085] The kinetic rate constant of C step in the forward directionis logarithmically sampled within the following upper and lower bound so that.

[0086] The above ranges of values capture all of the possible variationsin the CE mechanism, before the large value of leads to situations that are indeedthe E mechanism and presented at the very upper part of that figure.

[0087] Because of the resultant potential shifts of redox peaks in the CE mechanism, the anodic bound of electrochemical window Ewindow,a is now linearly sampled betweenV vs. NHE, and the Estartis now linearly sampled between Ewindow,cand V vs. NHE.Example 4.6: ECE mechanism

[0088] The E step between R1 and O1 follows the same definition of R and O in the E mechanism.

[0089] The kinetic rate constant k of the C step is logarithmically sampled with the following constraints so that

[0090] The selection of above k range covers almost all of the possible variations in the ECE mechanism.

[0091] The E step between R2 and O2 are defined with its thermodynamic redox potential linearly sampled between −0.7 and −0.1 V vs. NHE. Theelectrochemical kinetics of the Erstep is defined as a concentration dependent Butler- Volmer process illustrated in eq. (3). The standard rate constant of surface change transfer and the corresponding exchange current density is defined andsampled similarly as the i0in the E mechanism.When was chose as [10, 0.3], we have,

[0092] In order to accommodate the additional redox features, the Estartis now linearly sampled between Ewindow,cand −0.6 V vs. NHE. Example 4.7: DISP1 mechanism

[0093] The E step between R1 and O1 follows the same definition of R and O in the E mechanism.

[0094] The Estartand the kinetic rate constant k of the C step follow the same definition of k in the ECE mechanism.

[0095] The kinetic rate constant kDISP of the DISP step is logarithmically sampled with the following constraints.

[0096] The above definition of kDISP covers almost the full phase diagram since the corresponding defined below, is within the range of [10−2, 102].

[0097] The above definition indeed may also include scenarios that is similar, but not quite the same, to the DISP2 mechanism, when the DISP step is slow and rate-limiting (yet the limiting case of DISP2 mechanism requires a reversible pre-equilibrium for the C step between O1 and R2). Such slight ambiguity of simulated voltammograms in the training data will be addressed in future versions of the algorithm.Example 4.8: E’ mechanism

[0098] The E step between R and O follows the same definition of R and O in the E mechanism.

[0099] Here S and P denote the substrate and product of the EC’ electrocatalysis, respectively. The concentration of S in the initial electrolyte CS,iwas logarithmically sampled between 20CR,iand 18 M, which is the approximate H2O concentration of aqueous water. Such a range of CS,ivalues are chosen to ensure the simulated voltammograms represent the breadth of pure homogenous catalysis conditions as derived from Savéant’s definitions.

[0100] The kinetic rate constant for the irreversible C’ step is sampledlogarithmically with the following constraints.

[0101] The presence of electrocatalysis may also shift the potentials of redox features in a EC’ mechanism.This shift and the expected large current density cathodic of EO / Ralso lead to a revised sampling range of Estart[Ewindow,c, −0.6 + EO / R] V vs NHE.

[0102] The above discussion defines an oxidative electrocatalysis of EC’ mechanism, typically observed on the anodic end of experimental voltammograms. Our simulated single-redox voltammograms of EC’ mechanism are all oxidativeelectrocatalysis. When a multi-redox voltammogram is assembled (see Supplementary Note 4), EC’ mechanism will only be selected on either anodic or cathodic end of voltammogram. If a cathodic EC’ scenario is selected, the i(E) curve of a randomly sampled anodic electrocatalysis will first be inverted and then super-imposed with other selected mechanisms. Example 4.9: T mechanism

[0103] In the T mechanism, Tafel kinetic is deployed, in lieu of the Butler-Volmer kinetic shown in eq. 4, to represent heterogenous electrocatalysis and electrochemical solvent window,The definitions of i0and EO / Rhere follow the same definition in the E mechanism.

[0104] Similar to the case of EC’ mechanism, the concentration of redox-active substrate R, CR,i, may be logarithmically sampled between 20CR,i,minand 18 M, which is the approximate H2O concentration of aqueous water.

[0105] In order to simulate the common mechanisms of heterogeneous electrocatalysis, Tafel slopes ( ) were linearly sampled satisfying between 25 to 150 mv•dec–1, the common range of values in heterogeneous electrocatalysis. This allows us to determine the range of charge transfer coefficient used in eq. 17 following the below equation,

[0106] The range of exchange current densities i0that represent electrode materials were logrithmatically sampled with i0,upperand i0,loweras the upper and lower bound, respectively. The upper bound i0,upperis established to ensure the current densities i will be always controlled by electro-kinetics and will not plateau owing to mass transport limitations. This is designed to mimic the solvent window and common heterogenouselectrocatalysis such as water oxidation / reduction that practically there solvent is the reactant. The lower bound i0,loweris established to ensure there is sufficient electrochemical signal beyond the baseline double-layer charging current, with a threshold signal-to-noise ratio of 5.

[0107] Similar to the EC’ mechanism, here only an oxidative heterogenous electrochemical process is defined here. The protocol for a cathodic T mechanism is the same as described in the case of T mechanism. Example 4.10: SR mechanism

[0108] The SR mechanism describes the quasi-reversible electrochemical charge transfer for surface-bound redox couple Rsurfand Osurf, on the assumption that the mass transport of counter-ions to maintain charge neutrality is not rate-limiting. In addition the surface-functionalized redox-active molecules, the model is also relevant to pseudo- capacitors. A Butler-Volmer kinetic for the surface-bound redox reaction may be assumed, and the heterogeneity on materials’ surface renders a distribution of redox potentials for the Rsurf / Osurfpopulation.

[0109] EO / Rcan be defined as the mean redox potential of the Rsurf / Osurfcouple, whose population’s redox potential is evenly distributed between EO / R− ΔEO / Rand EO / R+ ΔEO / R. The above equation assumes transfer coefficient = 0.5.

[0110] The [Rsurf(E’)] and [Rsurf(E’)] in eq. 20 and 21 are the population density of redox O / R whose redox potential equals E’.

[0111] The sampling of EO / Rfollows the practice reported in E mechanism, while ΔEO / Ris sampled linearly between 0.003 V and 0.128 V, so that the dimensionless parameter [0.1, 5.0].

[0112] Csurf,imay be defined as the total surface concentration of the redox species on the electrode. Sampled logarithmically, Thelower bound is set so that the measured current density of surface redox will be roughly 10 times higher than the double layer charging when one assumes no redox potential dispersion and no hinderance in charge transfer kinetics. The upper bound can be set to reflect the amount of redox on a MnO2 pseudocapacitor of 1000-nm thickness with a specific capacitance of 1300 F / g as reported before.12

[0113] i0is sampled logarithmically between i0,upperand i0,loweras defined below. The ranges of exchange current densities were derived so that the dimensionless charge transfer coefficient for immobilized reactants, follows the numericalrange of [10−1, 101], a reasonable range based on the discussion of pseudo-capacitors.

[0114] Different from other mechanisms that require the use of COMSOL Multiphysics, the numerical simulation of the voltammograms of SR mechanism is based on MATLAB, thanks to the absence of mass transport in solution.Example 4.11: Additional considerations when sampling scan rate v

[0115] In the sampling of simulated cyclic voltammograms, variables intrinsic to the chemistry of the electrochemical systems are first sampled either linearly or logarithmically. Variables related to the electrochemical testing conditions, including Estart, Ewindow,a, Ewindow,c, and v are sampled subsequently. Particular attention is paid to the sampling of v since multiple chemistry-intrinsic variables are also dependent on the v values as shown in Table 1. Aiming to obtain up to 6 simulated cyclic voltammograms with different v values (n = 6), an iterative process of variable samplings is implemented in the python 3 scripts as shown below.

[0116] Step 1: After the initial generation of random combinations of chemistry- related variables listed in Table 1, a medium scan rate vmediumis linearly sampled between 0.1 to 0.5 V / s, the range of v mostly commonly used in cyclic voltammetry. As shown below vmedium serves as a temporal variable in the selection of v values and is not numerically used in simulation. The current densities of the redox peak are roughly estimated based on the Randle-Sevcik equation.

[0117] Step 2. The maximal and minimal scan rate vmaxand vminare randomly selected based on the following constraints.

[0118] The above constraints ensure that vmax and vmin are within the ranges of 0.01 to 2 V / s, the peak separations in the Nicholson’s formalism will not deviate too much from the targeted values separation = 62 ~ 120 mV), the voltammograms atmaximal scan rates won’t lead to indistinguishable redox peaks due to capacitive double-layer charging / discharging, and there is significant differences, 100.6~ 4 fold difference in current densities, among the n number of simulated cyclic voltammograms.

[0119] Step 3. If go back to Step 1 again. Otherwise, proceedto Step 4.

[0120] Step 4. 4 more additional v values are linearly or logarithmically sampled between the vmax and vmin, leading to 6 values of v in total (n = 6). Example 5: The number of voltammograms n needed for mechanism determination

[0121] As discussed above, when n ≥ 2 the prediction accuracies of DL models trained by {v, i(E, σ)}n(n = 1 to 6, σ = 0.3) more or less remain equally satisfactory (> 95%). Such results suggest that within the tested set of simulated voltammograms, statistically on average there is diminishing returns of prediction accuracy when n > 2.

[0122] In Example 4, the procedures of selecting the maximal and minimal values of v in the training set of simulated voltammograms are reported. When n = 2, there may exist the following approximate relationship between the two v valuesand the medium value

[0123] Here the“ ” sign suggests that the above relationship is a statistically approximation given that are randomly sampled around the value of

[0124] Hence, the approximate range of can be defined as:

[0125] Equations (26a), (26b), and (26c) provide an approximate empirical range of values in order to satisfy the defined training data set of voltammogramsand hence offer good accuracy of mechanistic prediction based on our DL model. The above relationships indicate that values are dependent on the redoxspecies’ concentrationand diffusion coefficientthe electrodes’ double-layer capacitance and the exchange current densityhence the standard rate constant of interfacial charge transfer (based on equation (5). A combination of experimental parameters and redox’s intrinsic propertiesdetermines the values of d for effective discernment of electrochemicalmechanisms.

[0126] Although specific methods of analyzing multi-event electrochemical data using object detection are discussed above, many different methods of analyzing multievent electrochemical data using object detection can be implemented in accordance with many different embodiments of the invention. It is therefore to be understood that the present invention may be practiced in ways other than specifically described, without departing from the scope and spirit of the present invention. Thus, embodiments of the present invention should be considered in all respects as illustrative and not restrictive. Accordingly, the scope of the invention should be determined not by the embodiments illustrated, but by the appended claims and their equivalents.

Claims

WHAT IS CLAIMED IS:

1. A method of detecting and classifying electrochemical mechanisms, the method comprising: obtaining at least one cyclic voltammogram from an electrochemistry system; generating one or more datasets from the at least one cyclic voltammogram; evaluating the generated datasets using a machine learning model; determining whether redox events are present in a region of the at least one cyclic voltammogram; and when at least one redox event is determined to be present in a region of the at least one cyclic voltammogram, determining a probability of at least one electrochemical mechanism of the electrochemistry system based on the redox event.

2. The method of claim 1, wherein the dataset comprises numerical values of current, current density, scan rate, and any combinations thereof.

3. The method of claim 1, wherein the electrochemical mechanism is selected from the group consisting of a charge transfer, an interfacial charge transfer, an electron transfer, a chemical reaction, a solution reaction, a diffusion reaction, a single-electron quasi-reversible homogenous electron transfer (E); a single-electron quasi-reversible homogenous oxidative electron transfer followed by a chemical reaction of the oxidant in the solution (ECa); a single-electron quasi-reversible oxidative electron transfer preceded by a chemical reaction of the reductant in the solution (ECb), an anodic variant of the classic CE mechanism that is the counterpart of (ECa); a single-electron heterogeneous electron transfer following the Tafel kinetics (T); a two-electron homogenous electron transfer, in which a single-electron transfer is followed by an irreversible chemical and a disproportionation steps (DISP1); a similar two-electron homogenous electron transfer, in which a single-electron transfer is followed by an irreversible chemical step and a thermodynamically less demanding single-electron transfer (ECE); an homogenous electrocatalysis, in which a single-electron transfer is followed by a chemical step that regenerates the redox-active catalyst (EC’); aninterfacial single-electron transfer when the redox species follows the Butler-Volmer kinetic and is bound on the electrode surface (SR), and any combinations thereof.

4. The method of claim 1, wherein at least one probability of an electrochemical mechanism of the electrochemistry system is determined to at least 95% accuracy.

5. The method of claim 1, further comprising determining a plurality of electrochemical mechanisms and ranking the plurality of electrochemical mechanisms of the electrochemistry system.

6. The method of claim 1, further comprising determining stoichiometric homogenous electrochemical mechanisms selected from the group consisting of: E, ECa, ECb, ECE, and DISP1.

7. The method of claim 1, wherein the electrochemistry system is a portion of a system selected from the group consisting of: a catalyst, a fuel cell, a battery, a redox flow battery.

8. The method of claim 7, wherein the catalyst catalyzes a process selected from the group consisting of: a carbon dioxide reduction process, a carbon fixation process, a carbon sequestration process, a water electrolysis process, a hydrogen production process, and an energy storage process.

9. The method of claim 1, wherein the machine learning model is a model having a Faster R-CNN architecture further comprising a ResNet-18 backbone and a feature pyramid network.

10. The method of claim 1, wherein the region is identified by a region proposal network (RPN) using object detection.

11. A method of training a machine model for detecting and classifying electrochemical mechanisms, the method comprising: generating at least one dataset for at least one electrochemical mechanism comprising a set of parameters based on a definition of the at least one electrochemical mechanism; providing the at least one dataset as input training data to a machine learning model; and training the machine learning model using the at least one dataset.

12. The method of claim 11, wherein the at least one dataset is generated via simulation.

13. The method of claim 11, further comprising adding Gaussian-type noise to the at least one dataset.

14. The method of claim 11, wherein the at least one dataset comprises numerical values of current, current density, scan rate, and any combinations thereof.

15. The method of claim 11, wherein the electrochemical mechanism is selected from the group consisting of a charge transfer, an interfacial charge transfer, an electron transfer, a chemical reaction, a solution reaction, a diffusion reaction, a single-electron quasi-reversible homogenous electron transfer (E); a single-electron quasi-reversible homogenous oxidative electron transfer followed by a chemical reaction of the oxidant in the solution (ECa); a single-electron quasi-reversible oxidative electron transfer preceded by a chemical reaction of the reductant in the solution (ECb), an anodic variant of the classic CE mechanism that is the counterpart of (ECa); a single-electron heterogeneous electron transfer following the Tafel kinetics (T); a two-electron homogenous electron transfer, in which a single-electron transfer is followed by an irreversible chemical and a disproportionation steps (DISP1); a similar two-electron homogenous electron transfer, in which a single-electron transfer is followed by an irreversible chemical step and a thermodynamically less demanding single-electrontransfer (ECE); an homogenous electrocatalysis, in which a single-electron transfer is followed by a chemical step that regenerates the redox-active catalyst (EC’); an interfacial single-electron transfer when the redox species follows the Butler-Volmer kinetic and is bound on the electrode surface (SR), and any combinations thereof.

16. The method of claim 15, wherein the set of parameters is selected from the group consisting of: numbers of scan rate, values of scan rate, electrode double layer capacitance, standard rate constant of interfacial charge transfer in a concentrationdependent Butler-Volmer equation following Nicholson’s formalism in the E step, equilibrium constants and forward / backward rate constants in the Crstep based on Saveant’s definitions, and any combinations thereof.

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