Abstract
Optimization of experimental materials synthesis and characterization through active learning methods has been growing over the last decade, with examples ranging from measurements of diffraction on combinatorial alloys at synchrotrons, to searches through chemical space with automated synthesis robots for perovskites. In virtually all cases, the target property of interest for optimization is defined a priori with the ability to shift the trajectory of the optimization based on humanidentified findings during the experiment is lacking. Thus, to highlight the best of both human operators and AIdriven experiments, here we present the development of a human–AI collaborated experimental workflow, via a Bayesian optimized active recommender system (BOARS), to shape targets on the fly with human realtime feedback. Here, the human guidance overpowers AI at early iteration when prior knowledge (uncertainty) is minimal (higher), while the AI overpowers the human during later iterations to accelerate the process with the humanassessed goal. We showcase examples of this framework applied to preacquired piezoresponse force spectroscopy of a ferroelectric thin film, and in realtime on an atomic force microscope, with human assessment to find symmetric hysteresis loops. It is found that such features appear more affected by subsurface defects than the local domain structure. This work shows the utility of human–AI approaches for curiosity driven exploration of systems across experimental domains.
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Introduction
The achievable progress in the field of automated and autonomous experiments, and the idea of ‘selfdriving’ laboratories more generally, hinges on the ability of probabilistic machine learning models to be used to rapidly identify areas of the parameter space that have a high (modeled) likelihood of optimizing target properties of interest^{1,2,3,4,5}. Recent examples include explorations of chemical space^{6} in the synthesis of nanoparticles^{7} and thin films for photovoltaic applications^{8,9}. Additionally, numerous examples exist of autonomous microscopes that can be used to identify structure–property relationships in both electron^{4} and scanning probe spectroscopies^{10,11}, as well as scattering measurements at the beamline, for e.g., efficient capture of diffraction patterns for phase mapping or for strain imaging^{12,13,14,15}. Such work seeks to improve not only the efficiency at which the target property of interest can be found and/or maximized but also to improve our understanding of how composition and structure impact functionality, ideally unearthing them in realtime.
In nearly all cases of active learning within experiments, the target property of interest is defined a priori. This target can be a humandesigned behavior of interest, for example, some measured property, or feature of a spectrum that is captured such as area, peak position, peak ratio, etc. In these cases, the objective of the experiment is to efficiently probe the parameter space to maximize the selected target. Alternatively, an informationtheory approach can be used where the goal is instead to minimize the uncertainty of a developed surrogate model. In both cases, however, the human is generally kept out of the loop after the target is selected and a sampling policy is initiated. Indeed, a celebrated review of Bayesian optimization is titled ‘Taking Humans out of the Loop: A Review of Bayesian Optimization’^{16}. In traditional active learning methods for autonomous experiments such as Bayesian optimization, we need to preselect a target or goal and the BO guides the experiment autonomously to accelerate the learning towards the goal.
However, this may not always be ideal. During the course of the experiments (especially when the search space is minimally explored as in the early stage of autonomous experiments), we are likely to find completely different target structures which would be more interesting to explore. Thus, in some situations, experimentalists would prefer to observe a few of the spectra prior to target formulation, to obtain a sense of the potential importance of the regions that could be probed. A recent Nature article reports that leveraging human expertise within the optimization process can greatly improve recipes for materials processing^{17}. Additionally, with little prior knowledge, it may also be challenging to design a suitable scalarizer that captures the essence of the target. Moreover, it is possible that the human may prefer one target to seeing some spectra, and then observe something more interesting in subsequent points and decide that is more worthwhile exploring. The ability to shift the trajectory of the optimization based on humanidentified findings during the experiment is lacking in a fully AIdriven experiment. Thus, a method is needed to engender the best of both human operators as well as AIdriven experiments. We attempt to fill this void with the development of a humanguided AI system that steers microscope experiments based on realtime assessments, enabling types of experiments to be performed on the microscope that could likely be previously out of reach. In other words, human guidance overpowers AI at the early stage of optimization when prior knowledge is minimal and uncertainty is high, while the AI overpowers the human during the later stage to speed the overall process of learning with the humanassessed definite goal. This dynamic setting and changing of targets, which need to be inferred by the algorithm, is a problem that is well encountered in other fields such as social media and has been solved via recommendation engines, which are built from user voting (‘likes’) to populate the feeds with content agreeable with the user^{18,19,20}.
Here we present the development of a method of an automated experiment that employs a humanintheloop experimental workflow, which we term the Bayesian optimized active recommender system (BOARS). We develop and apply it to the case of finding spectra encountered during piezoresponse force spectroscopy measurements, first trialing the method on preacquired data to gauge the effectiveness, and then implementing it in realtime on an operating instrument. The framework allows the human operator to vote for a certain number of spectra to construct a target and then proceeds to explore the search space optimally in view of retrieving spectra that bear a strong structural similarity to the target, and in the process, unearth key structure–property relationships present autonomously. In this manner, we bypass the need for a predefined target and add flexibility to a standard automated experiment, where rather than fixing a target prior to the start of the experiment, the human operator retains the ability to dynamically adjust the target via realtime result assessments. It is to be noted that the framework is purposefully developed to overcome the experimental scenarios when a definite goal to explore cannot be confirmed due to inadequate prior domain knowledge or the complexity of having several unknown key features of the system to explore when a predefined goal for a fully automated experiment is not possible. It is evident if the experimentalist prefers to set a definite goal and confirm it during the experiment, as it is when the material system is fairly known, then human collaboration with AI is not required (out of the scope of the proposed paper). In other words, the utility of the BOARS in the paper is when the above assumption is not true, as it is for several cases in the exploration and discovery of materials.
The overall framework has two major architectural components  an active recommender system (ARS) and Bayesian Optimization (BO) engine. The ARS is developed as a dynamic, humanaugmented computational framework where, given a location in the search area of the material samples, the microscope performs a spectroscopic measurement at the location in realtime. This spectrum provides knowledge about various key features (e.g., it can be energy loss, nucleation barriers, degree of crystallinity, etc.). The ARS system allows the user to upvote and downvote spectra according to the features of their own interest, and this method is free from any generalized objective functions. Previously, humanaugmented recommender systems have been developed in microscopy in accelerating meaningful discoveries in different fields of applications such as rapid validation of thousands of biological objects or specimen tracking results^{21}, and rapid material discovery of lithiumion conducting oxides through synthesis of unknown chemically relevant compositions^{22}.
The second part of the architecture is the BO engine, which guides the path to locate the regions of interest with maximum structural similarity to the humanupvoted spectra, through sequential updating with a computationally cheap surrogate model and enables an efficient tradeoff between exploration and exploitation of the unknown search area. Bayesian optimization (BO) or (multiobjective) BO^{16,23,24,25,26,27}, has been originally developed as a low computationally cost global optimization tool for design problems having expensive blackbox objective functions. BO has been extensively applied for rapid exploration of large material^{28,29,30,31,32,33,34,35} and chemical^{36,37} control parameters and/or functional properties space exploration to enable optimization towards desired device applications. Here, the BO replicates the expensive function evaluations with a cheap (scalable) surrogate model and then utilizes an adaptive sampling technique through maximizing an acquisition function to learn or update the knowledge of the parameter space towards finding the optimal region. Over the years, the development of BO has been extended for various complex problems. Biswas and Hoyle extended the application of BO over discontinuous design space by remodeling it into a domain knowledgedriven continuous space^{38}. BO has been extended in discrete space such as in consumer modeling problems where the responses are in terms of user preference discrete^{39,40,41,42}. Here, Thurstone^{40} and Mosteller^{41} transform the user preference discrete response function into continuous latent functions using the BinomialProbit model for binary choices, whereas Holmes^{42} uses a polychotomous regression model to be applicable for more than two discrete choices. For practical implementation of BO over highdimensional input space, some examples like Dhamala et al.^{43} Valleti et al.^{44} and Wang et al.^{45} attempted the approach of random embedding in a lowdimensional space; Grosnit et al.^{46} and Biswas et al.^{47} attempted the approach to project into a lowdimensional latent space with variational autoencoder; and Oh et al.^{48}, Wilson et al.^{49} and Ziatdinov et al.^{50} tackles with implementing special kernel functions.
A Gaussian Process Model (GPM)^{51} is generally integrated into BO as the surrogate model, which also provides the measure of uncertainty of the estimated expensive functions over the parameter space such that the uncertainty is minimal at explored regions and increases towards the unexplored regions. Alternatively, random forest regression has also been proposed as an expressive and flexible surrogate model in the context of sequential modelbased algorithm configuration^{52}. The detailed workflow of BO and mathematical representation of GPM is provided in Supplementary Method. Once a cheap surrogate model is fitted in a BO iteration with the sampled data, the next task is to find the next best locations for sampling through maximizing the acquisition function (AF). The latter defines the likelihood of finding the region of interest or better objective function values. Several acquisition functions, such as Probability of Improvement (PI), Expected Improvement (EI), Confidence Bound criteria (CB) have been developed with different tradeoffs between exploration and exploitations^{23,53,54,55}.
In all the stated BO applications where the target is required to be set prior to the optimization, in this paper, the proposed approach bypasses that requirement by introducing a humanintheloop architecture, thus adding flexibility to the automated experimental workflow. We additionally explore the effect of local structures encoded in image patches and different kernel functions on the performance of the optimization trajectory. Therefore, here the major contribution of the paper is the development of BOARS model. In the traditional setting, this flexibility of onthefly experimental steering is lacking with such a rigid defined target, which we have filled the gap with an active recommender system design. The other main contribution of this work is to implement the BOARS model for a test case of a microscope with a human in the loop voting for spectral target generation. We further explore the role of the kernel in the utility of our BOARS workflow.
Figure 1 shows the overall highlevel structure of the BOARS system with the detailed flowchart of the algorithm provided in Supplementary Fig. 1. The workflow can be stated as follows: Given a material sample, we run the microscope to scan a highresolution image, which is the parameter space for the exploration. Next, we segment the image space into several image patches of set window size, \(w\). We define these local image patches as the input for Bayesian optimization. Next, we initialize BO and capture spectra from microscope measurements at a few randomly generated locations. Next, we introduce the steps for humanoperation which is the major contribution of this work. Given a spectrum, the user (human) visualizes the spectra and provide subjective vote on its quality. The workflow for the computation of the human visual assessment based on the fly target structure generation and thereafter the humanguided objective function can be described as follows. As we start the experiment by visualizing the first characterized spectrum (\({\rm{i}}=1),\) consider the case where the user either skipped the voting or downvoted it: the target is still not defined, as \({{\bf{T}}}_{i=1}=\varnothing\). If the user votes after visualizing the second spectrum (\({\rm{i}}=2\)), a target is defined as \({{\bf{T}}}_{i=2}={{\bf{S}}}_{i=2}\) where \({{\bf{S}}}_{i}\) is the \({{i}}{{\rm{th}}}\) spectrum. Let us assume the user again downvoted the third spectrum (\({\rm{i}}=3\)), then \({{\bf{T}}}_{i=3}={{\bf{T}}}_{2}={{\bf{S}}}_{2}\). If the next spectrum is upvoted (\({\rm{i}}=4)\), the target is accordingly updated as per Eq. (1) below. Once the voting is complete for the first few randomly selected j spectra, a humanguided objective function is calculated as per Eq. (2).
where \({{\bf{T}}}_{i}\) is the target after \({{i}}{{\rm{th}}}\) spectra assessment given the user upvoted the spectra, \({p}_{i}\) is the user preference (0–1 with 1 being highest) of adding features of new spectra to the current target, \({v}_{i}\) is the user vote of the \({{i}}{{\rm{th}}}\) spectra, \({Y}_{i}\) is the objective function value for the \({{i}}{{\rm{th}}}\) spectra, \({{\bf{T}}}_{j}\) is the target after voting all the \({\rm{j}}\) spectra, \(R\) is the reward on voting.
The objective function is the voting augmented structural similarity index function where \(\psi\) is the structural similarity function, computed from the function structural_similarity in skimage.metrics Python library^{56}. Then, given the dataset with input local image patches and output objective function value, we run the BO—fitted with a Gaussian process model, and maximizing the acquisition function derived from the GP estimations. The acquisition function suggests the next best location to capture spectra. Next, microscopic measurement is carried out to retrieve the spectrum at the stated location and similar human assessment is carried out on the new spectrum. Given whether the user upvoted or downvoted the new spectrum, the target is either updated following Eq. (1) or remains the same, and the objective function is calculated iteratively following Eq. (2). This iterative GP training with new data, undertaking microscope measurements at new locations, and the introduced humanintheloop process to evaluate the spectra, update the target and calculate the objective function continues until the user is satisfied with the current target, which can be provided in a ‘Yes/No’ popup message after every iteration. Then, the remaining iterations are carried out until BO convergence without any further human interaction, with the objective function value modified to Eq. (3).
where \({Y}_{j+k}\) is the objective function for \({{k}}{{\rm{th}}}\) iteration of BO, after randomly sampling \({j}\) spectra. As seen, we removed the humanvoting part as now the target \({\bf{T}}\) is fixed and the task is to identify the spectra maximizing the structural similarity with the target. Thus, in the proposed design, within the loop of BO, here we define and refine the target (spectral structure) through human assessment, and simultaneously optimize either the humanaugmented objective function or the fully automated objective function, following Eqs. (2) or (3) respectively, given the state of decisionmaking in updating the target. The detailed mathematical algorithm of the methodology is provided later in the “Methods” section for additional information.
Results and discussion
We first begin by testing the BOARS system on preacquired data (i.e., data where the ground truth is known, and not on the active microscope) to determine the applicability of the method and to note the effects of hyperparameters. To this aim, we explored data from two PbTiO_{3} (PTO) thin film samples. The samples are both 200 nmthick PbTiO_{3} thin films grown on (110) SrTiO_{3} via pulsed laser deposition, with ‘designer’ grain boundaries fabricated by a process outlined in ref. ^{57}. In this instance, our measurements are not in the vicinity of the grain boundary; however, the domain structure of the PTO sample is dependent on the strain imparted by the thickness of the underlying substrate, and this leads to different domain structures for the part of the sample rotated with respect to the underlying (110) STO, as the underlying substrate is a rotated (110) STO membrane of limited (~10 nm) thickness. As such, both samples imaged display different domain patterns enabling us to test the BOARS on samples with different domain features. For this paper, we refer to PTO sample 1 as the sample where the domains imaged are on the original (110) oriented STO crystal (thickness 500 µm), and PTO sample 2 as the sample where we image the region of the sample where the sample is rotated (~2°) with respect to the substrate and has a much lower thickness of the STO (and thus likely to be much less strained).
Case study: BOARS analysis on existing PTO data
To demonstrate the method, and before implementing it on the realtime microscope, we began with a full ground truth dataset where we measured the spectral data for all the grid locations (2500 grid points on a 50 × 50 grid).
To study the performance, we first considered the BOARS architecture with a simple benchmarked surrogate model such as the Gaussian process model with a standard periodic kernel function. It is to be noted we tested with other inbuilt kernel functions like radial basis, and matern kernel, but periodic kernel provided superior exploration. The hyperparameter of the kernel function is optimized with Adam optimizer^{58} with learning rate = 0.1. We started with 10 initial samples, \(j=10\) and 200 BO iterations, \(M=200\), a total of 210 evaluations. In regard to incorporating the local image patches as an additional channel for structurespectra learning, we considered the image patch of window size, \(w=4\,{\rm {{px}}}.\) Thus, the dimension of each input, \({{\bf{X}}}_{1},\) is an array of 16 elements. For a comparative study, we upvoted spectra that appeared (by eye) to possess roughly symmetrical hysteresis loops in terms of amplitude, i.e., similar remanent piezoresponse for positive and negative bias. For both PTO samples, we utilized voting (target learning) of the first 10 spectra and then fixed the target for the remaining iterations. The detailed user voting of the spectra used to set the final target for both PTO samples is provided in Supplementary Figs. 2 and 3. The detailed analysis of the BOARS system with a standard surrogate model has been provided in Supplementary Figs. 4 and 5, for the first and second PTO samples, respectively.
The analysis shows the traditional kernel function could be unstable depending on the complexity of the parameter space and the degree of correlation between the prior knowledge (embedded in local structural image patches) and the posterior knowledge on structural similarity with the humanassessed target. This could be due to the inefficient learning of traditional kernel functions over high dimensional inputs^{59}. Our prior work^{60} has shown that in such instances, it may be advantageous to utilize deep kernels in a scheme termed deep kernel learning (dKL)^{49}. dKL is built on the framework on a fully connected neural network (NN) where the highdimensional input image patch is first embedded into low dimensional kernel space (in this case set as 2), and then a standard GP kernel operates, such that the parameters of GP and weights of NN are learned jointly. This dKL technique has been implemented for better exploration through active learning in experimental environments^{4,50,61,62,63}. Here, we utilized a DKL implementation from an opensource AtomAI software package^{60}.
The overall BOARS structure remains the same, but we simply replace the standard GP with a dKLbased approach. All other parameters were kept constant. The detailed user voting of the spectra to set the final target for both oxide samples is similar in Supplementary Figs. 2 and 3. Figures 2 and 3 are the detailed analysis of the estimated spectral similarity maps, after adaptive learning with BOARS system, for the first and second PTO samples, respectively. Firstly, it can be clearly seen comparing the scanned images of the PTO samples (Figs. 2a and 3a) with the respective structural similarity (ground truth) images (Figs. 2d and 3d) that these are not highly correlated, particularly for Fig. 3. That is, there is minimal correlation between the initial PFM scan and the structural similarity map. This is expected in cases where the features targeted in the spectral domain, here, symmetric remnant response, is not significantly dependent on the surface domain structure image and is likely to be more heavily determined more by subsurface defects that are not manifest in the image. The objective for the appropriate model, which the standard kernels fail to do in this case, would be to balance between prior (local domain correlation) knowledge from scanned images and the posterior objective function knowledge through sequential learning, such that it tends towards efficient estimation of the structural similarity map at the explored and unexplored regions (predicting the unknown ground truth with sparse adaptively selected samples).
Observing both Figs. 2 and 3, it can be seen that the dKL method serves to better capture the correlations between the local image patches and the objective function, ultimately in adaptive learning of the estimated GP spectral similarity maps (see Figs. 2e and 3e). We also observe an overall better tradeoff with regards to BO exploration and exploitation, with more scattered sampling to look for potential regions of interest, particularly in Fig. 3 when the local structure–spectral correlation is minimal, ultimately to provide a better structural similarity map. For example, unlike in Supplementary Fig. 4, the estimated uncertainty map Fig. 2f within the white region has relatively lower variance, with a comparatively significant reduction of variances throughout the image space. Additionally, as in Supplementary Fig. 5, BOARS with dKL (Fig. 3c) still explores more near the phase boundary (dark channels) of the scanned image due to the input of the image patches; however, unlike the BOARS with traditional kernel, the dKL also adjusts the knowledge through posterior exploration and yields a majority of regions with highvalued targets (light region), as we know from the ground truth, providing a significant reduction of uncertainty as well. Thus, with the comparative analysis, we see an overall stability and enhancement of BOARS system, with efficient learning of userdesired spectra with incorporating local image patches of the system and rapid discovery of the changes in the structural similarity map through experimental evaluations, provided that the kernel is intelligently learned from the sparse data as by dKL.
To support our interpretation and validate the models, we provide the squared error map between the ground truth and the GP estimated spectral map in Fig. 4 for all the discussed case studies and the relative mean squared errors (MSE) over the entire image space. For both the samples, we see an overall low MSE which shows a goodness of fit of the general BOARS architecture. For PTO sample 1, we see the MSEs are comparatively similar between the BOARS with periodic and dKL functions, with slightly better performance with dKL. However, as expected, we see a significant improvement (much lower MSE) in the performance of BOARS with dKL for PTO sample 2. Furthermore, we see similar MSE values under BOARS with dKL for both the case studies which gives better stability or insensitiveness to the complexity of the problem and the efficiency of the prior knowledge (given in the form of the image patch). To summarize, the purpose of testing our proposed BOARS model with samples 1 and 2 is to test on different domain structures. Again, the purpose of doing so is to ensure the model works appropriately without underfitting or overfitting by checking how well it learns the unknown ground truth. For that case, we considered two samples: PTO sample 1—where we have seen the degree of correlation between the known input PFM amplitude image and the unknown ground truth image is relatively higher, and PTO sample 2—where the degree of correlation between the known input PFM amplitude image and the unknown ground truth image is minimal. We wanted to test how the kernel will perform in such two cases. It is evident to mention that the objective is not to find what kind of imaging techniques will provide more correlation with ground truth, but the goal is that given a structure image how well the BOARS model can perform to provide a better structure–property relationship (align to better representation of ground truth), irrespective of any degree of actual correlation between structure image and unknown ground truth (good or poor prior knowledge from structure image). In the actual experimental setting, there is no such guarantee the input structure image will always have a high correlation with the objective we are looking for and therefore the added focus on appropriate implementation of kernel function for deployment.
Case study: BOARS realtime implementation on atomic force microscopy (AFM)
Given that the model once developed needs to be implemented on an operational microscope where the cost of experiments is actually high and we do not know the ground truth, we need to ensure the proposed BOARS model (like any AIdriven model) aligns with the humanidentified targets and provide meaningful information. After investigations on preacquired data, it is clear that the implementation on the real microscope will require the use of deep kernel learning. As such we proceeded to apply the BOARS system with dkl kernel in realtime automated experiments on the microscope. Considering PTO sample 2, we considered the highresolution image (128 × 128) with an input image patch of window size, \(w=4\,{\rm {{px}}}.\) We started with 10 initial samples, \(j=10\) and 100 BO iterations.
Here also, we considered the goal to obtain a symmetrical loop, however, the voting sequences to set the target were different from our earlier analysis. This is done intentionally to understand the sensitivity of the result with different voting or targets but considering similar userdesired features (as common in a subjective assessment between two users but with similar goals). The purpose of analyzing the structureproperty relationship over aiming to autonomously learning the potential defectfree areas (good regions) in the material domain space due to imaging and the potential defected areas (bad regions) as represented by higher nonsymmetrical loops. Figure 5 shows the iterative learning of the spectral structural similarity map with the BOARS system. We can see the estimated spectral similarity map (see Fig. 7g) shows similar trends as to what we observed in Fig. 5, with a more refined map due to a higherresolution parameter space. As in Fig. 5, we see the domain walls in the scanned image are highlighted as the potentially interesting regions of userdesired spectra, and therefore the relative estimated structural similarity map has high values at the domain walls. However, as we also see from earlier analysis, the overall space is highly valued virtually throughout, and here also we see such a trend (the estimated map in Fig. 7g has very minimal dark regions). Regarding the computational cost, the total runtime of this AE analysis took less than 1 h, whereas the computational cost to run the experiment exhaustively for all grid points (in 128 by 128pixel image) can take about 15–24 h.
These results highlight two key points. One is that the degree of symmetry of the amplitude response to hysteresis loops in standard ferroelectrics like PbTiO_{3} can be more affected by features that are not correlated with the surface domain structure, such as subsurface defects that cannot be imaged by PFM and serve to suppress or enhance polarization. This opens the possibility to deliberately find spectral features that are not correlated with the original PFM image, and therefore, to identify notable subsurface defect regions (for example, as in ref. ^{64}). It should be noted that it is possible that subsurface defects may show signatures in either electrostatic force microscopy or Kelvin probe force microscopy measurements if they significantly affect the local surface potential^{65}. As such, one can imagine attempting to find spectra that are similar to those predicted from particular types of defects, enable the algorithm to find the locations in the sample where these spectra are located, and then use these as sites for further chemical and electronic characterization with other AFM and chemical imaging modalities. Secondly, the fact that the dKL method is able to learn the appropriate correlations between the local image patches and the local spectra is a key distinguishing feature. Standard kernels appear to struggle to ‘ignore’ the domain structure, whereas the learned kernel appears better at this task. This suggests that kernel choice is important not only for feature learning but for minimizing the impact of spurious correlations in active learning regimes.
Case study: Edge case scenarios of early human assessment of spectral structures
Finally, though the BOARS architecture is designed based on the assumption that the operator is a domain expert (i.e., assumed to make knowledgeable decisions and upgrade learning of suitable targets on the fly), we looked at two edge case scenarios where the assessment is not done with expert knowledge. We attempt to test the edge case scenarios to learn how the assessment can change the shape of the target and thereby change the ground truth map. We refer to these edge cases as EC1 and EC2. EC1 is defined as a random assessment of initially randomly generated 30 samples. EC2 is defined as assessing the quality of three highly different (hard to find in the image space) spectra as ‘good’.
Figures 6 and 7 show the detailed analysis for PTO samples 1 and 2, respectively. We refer to the target with expert assessment as shown in Figs. 2 and 3 as the actual target and the respective generated ground truth as the actual ground truth. That is, let us assume that the goal in this experiment was to find spectra close to that found by the domain expert in sample 2, but here, a different operator is chosen who has significantly less experience and decides to either randomly assign ratings, or chooses to upvote spectral features that are very rare in the dataset. We attempt to quantify how these would be different from the actual ground truth and explore how these edge cases will play out with this algorithm.
The results are shown in Fig. 6 for this type of analysis. First, we start with a reproduction of the target in Fig. 2a, which is shown in Fig. 6a. We compute the structural similarity score of every spectrum in the dataset, against this target, and the results are plotted in Fig. 6b. Next, we generate targets by strategy EC1, i.e., random voting of 30 samples. The resultant target is shown in Fig. 6c. It is evident that randomly voting for spectra tends to generate a target spectrum that is close to the mean in the dataset, as is expected from intuition (see the mean spectral response in Fig. 6c). The structural similarity map is shown in Supplementary Fig. 6. To gain an idea as to what areas are now focused on, we plot the difference between the structural similarity map for this target, subtracted from the structural similarity map from Fig. 6b. If this resultant difference map was close to zero, then it effectively means that the resultant BO would be almost identical. As can be seen, there are some differences in the structural similarity map, but many regions where there is little difference. This suggests that the original voting by the domain expert was not too far from a common ‘mean’ hysteresis loop, so the result of random voting is also not likely to result in very different behavior through the BO process.
At the other end of the spectrum, it is possible that the operator chooses to find and upvote spectra that are comparatively rare in the dataset, i.e. edge case 2. In EC2, the target is formed after upvoting 3 quite rare spectra, and the resultant target is shown in Fig. 6e. It can be seen in the associated difference map of the structural similarity in Fig. 6f, that there are not many overlapping regions (i.e., regions where the difference is close to 0).
This analysis suggests that providing a few incorrect assessments based on the level of expertise of the operator will be less likely to have an effect on the potential region of interest, which is learned autonomously with BO (sampling <5% over whole image space). However, if there are very few spectra that are rated, then this becomes more problematic as individual outliers can begin to shape the target in undesired ways.
Summary
In summary, we developed a dynamic, humanaugmented Bayesian optimized active recommender system (BOARS) for curiositydriven exploration of systems across experimental domains, where the target properties are not priorly known. The ARS system provides a framework for humanintheloop automated experiments and leverages user voting as well, and a BO architecture to provide an efficient adaptive exploration towards rapid spectral learning and maximize the structural similarity of the captured spectra. We explore the effect of different kernel functions towards providing a flexible framework in a balanced learning between prior structural knowledge of local scanned image patches and the captured spectra. This partially combined humanintheloop—AI workflow enables types of experiments to be performed on the microscope that have been previously out of reach.
Currently, the model has three ratings (one downvote option and two different upvote options). Also, the number of assessments required to shape the target is up to the operators, based on the tradeoff between the cost of assessment (time the operators need) and the satisfaction of the target shaping (which the operator aims to explore). In our case (shaping for symmetrical loop structure), we have considered 10 assessments for preacquired data and 10 for real analysis, before switching off the human input. From the BOARS architectural point of view, there is no constraint applied on the minimum number of downvoted assessed spectra and the need for at least one upvoted assessed spectra. In other words, as long as any spectra are upvoted and a target is generated, the operator can switch to the fully autonomous approach (see Step 6 in the “Methods” section). The model also performs based on the assumption that the decisionmaker, to shape the target spectral structure, is a domain expert and does not provide the visual assessment randomly.
It is evident to mention this assumption also holds for configuring any predefined targets in the fully autonomous BO approach as well. In other words, it is reasonable to assume the experimentalist or the microscope operator is aware of the physics to define the target in order to learn over the unknown image space, and a traditional BO drives the characterization autonomously based on the predefined targets. Our BOARS model fills the gap when the experimentalist does not have prior knowledge of what would be the best spectral structure (target) to learn for the material. In our use of the BOARS model, we found that shaping of the target is robust to a few incorrect assessments as the number of assessments progresses (say after 10–20), due to formulating on the weighted (preferencebased) average from all the assessed spectra. However, the BOARS model is limited to incorporating uncertainty propagation based on the differences in the assessment from multiple domain expert operators to attain a similar goal. Moreover, the limitation of this method occurs when different spectra are upvoted that have competing mechanisms, i.e., when usually trying to find one type of structure will be anticorrelated with finding another type of structure. This problem needs to be handled through multiobjective means, and such work will be considered in future scope.
Methods
Detail algorithm of Bayesian optimized active recommender system
Here, we provide the detailed algorithm of the BOARS system. Here we provided two objective functions formulation, based on whether the user input is satisfied or not with the current target. It is to be noted the algorithm is the major contribution, specifically the humanoperated process in steps 2 and 6, and therefore is the pivotal element to the paper. We described the workflow and mathematical approaches taken in steps 2 and 6 to define/update the targets and the objective functions and their connections with standard BO steps.

1.
Segmentation of local image patches as additional channel for structurespectra learning:

a.
Choose a material sample. Set the control parameters of the microscope.

b.
Run microscope. Scan a highresolution (e.g. 128 × 128 grid points) image of the sample.

c.
Segment the image into several square patches with window size, \(w\). The image patches are considered as input for BO, which provides the local physical information (eg. correlation) of the input location.

a.

2.
Initialization for BO: State maximum BO iteration, \(M\). Randomly select \(j\) samples (image patches), \({\bf{X}}\). We highlight this step as the contribution in this paper in introducing human operations in the proposed AE workflow.

a.
For sample \(i\) in \(j\), pass \({{\bf{X}}}_{i}\) into microscope. Run microscope and generate spectral data, \({{\bf{S}}}_{i}.\)

b.
Humanaugmented process: User votes \({{\bf{S}}}_{i}\) with voting options, \({v}_{i}\): Bad(0), Good(1) and Very Good(2). Next follow either (c) or (d).

c.
Generate target: If the user voted good/very good for first time, then target, \({{\bf{T}}}_{i}={{\bf{S}}}_{i}\). Normalize \({{\bf{T}}}_{i}\).

d.
Update target: If \({{\bf{T}}}_{i}\ne \varnothing\), user select preference, \({p}_{i}\) (0–1 with 1 being highest) of adding features of new spectral to the current target. Calculate \({{\bf{T}}}_{i}\) as per Eq. (4). Normalize \({{\bf{T}}}_{i}\).
$${{\bf{T}}}_{i}=\left(\left(1{p}_{i}\right)* \mathop{\sum }\limits_{{ii}=1}^{i1}{v}_{{ii}}* {{\bf{T}}}_{i1}\right)+({p}_{i}* {v}_{i}* {{\bf{S}}}_{i})/\left(\left(1{p}_{i}\right)* \mathop{\sum }\limits_{{ii}=1}^{i1}{v}_{{ii}}\right)+({p}_{i}* {v}_{i})$$(4) 
e.
Calculate humanaugmented objective function: For sample \(i\) in \(j,\) calculate the voting augmented structural similarity index function as per Eq. (5). \(\psi\) is the structural similarity function; \({{\bf{T}}}_{j}\) is the current target following step c, d, after user voted \(j\) samples; \(R\) is the reward parameter. \(\psi\) is computed from the function structural_similarity in skimage.metrics library.
$${Y}_{i}=\psi \left({{\bf{T}}}_{j},{{\bf{S}}}_{i}\right)+{v}_{i}* R$$(5) 
f.
Build dataset, \({{\bf{D}}}_{j}\,{\boldsymbol{=}}\,{\boldsymbol{\{}}{\bf{X}}{\boldsymbol{,}}{\bf{Y}}{\boldsymbol{\}}}\) with \({\bf{X}}\) is a matrix with shape \((j,w* w)\) and \({\bf{Y}}\) is an array with shape \((j)\)

a.
Start BO. Set \(k=1\). For \(k\le M\)

3.
Surrogate modeling: Develop or update GPM models, given the training data, as \({\boldsymbol{\triangle }}{\boldsymbol{(}}{{\bf{D}}}_{j+k1}{\boldsymbol{)}}\).

a.
Optimize the hyperparameters of kernel functions of the surrogate models.

4.
Posterior predictions: Given the surrogate model, compute posterior means and variances for the unexplored locations, \(\overline{\overline{{{\bf {X}}}_{{k}}}}\), over the parameter space as \({\boldsymbol{\pi }}\left(\right.{\bf{Y}}(\overline{\overline{{{\bf{X}}}_{k}}}){\Delta}\) and \({\boldsymbol{\sigma}}^{{\bf{2}}}\left(\right.{\bf{Y}}(\overline{\overline{{{\bf{X}}}_{k}}}){\Delta}\), respectively.

5.
Acquisition function: Compute and maximize acquisition function, \(\mathop{\max }\nolimits_{X}U(.{{\triangle }})\) to select next best location, \({{\bf{X}}}_{j+k}\) for evaluations.

6.
Expensive Blackbox evaluations:
We highlight this step as the contribution in this paper in introducing the human operations in the proposed AE workflow.

a.
User interaction for target update: User gets a prompt message if the user is satisfied with the current target. User has option to choose, Yes or No. Mathematically, we can represent as \({\upsilon }_{k}=\left\{\begin{array}{c}0\,({No})\\ 1\,({Yes})\end{array}\right.\)

b.
Humanaugmented process: Given \({\upsilon }_{k}=0\), follow steps 2(b)–(e) for sample patch \({{\boldsymbol{X}}}_{{\boldsymbol{j}}{\boldsymbol{+}}{\boldsymbol{k}}}\). Equations (4) and (5) can be simply modified to Eqs. (6) and (7) respectively.

a.

a.
Automated process: This step is included to speed up the search process to avoid redundant user interaction in case the user is satisfied with learning of the target spectral and therefore the goal changes to learn the spectral similarity map towards achieving the converged target. Therefore, Given \({\upsilon }_{k}=1\), \({{\bf{T}}}_{j+k}\,{\boldsymbol{=}}\,{\bf{T}}\,{\boldsymbol{=}}\,{{\bf{T}}}_{j+k1}\). Calculate the structural similarity index function as per Eq. (8). It is to be noted that we recalculate the objective function once the user switches from a humanaugmented to an automated process since the function changes. However, since we already have stored the previous spectral data for the explored image patches, the recalculation cost is negligible. Also, the architecture is currently set up where the switch from humanaugmented to automated process is irreversible to avoid prompting the user repeatedly in Step 6(a).

7.
Augmentation: Augment data, \({{\bf{D}}}_{j+k}=[{{\bf{D}}}_{j+k1};\{{{\bf{X}}}_{j+k},{Y}_{j+k}\}\).
Data availability
The analysis reported here is summarized in Colab Notebook for the purpose of tutorial and application to other data and can be found in https://github.com/arpanbiswas52/varTBO.
Code availability
The code is summarized in Colab Notebook for the purposeof tutorial and application to other data and can be found in https://github.com/arpanbiswas52/varTBO.
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Acknowledgements
The experiments, autonomous workflows, and deep kernel learning were supported by the Center for Nanophase Materials Sciences (CNMS), which is a US Department of Energy, Office of Science User Facility at Oak Ridge National Laboratory. Algorithmic development was supported by the US Department of Energy, Office of Science, Office of Basic Energy Sciences, MLExchange Project, award number 107514; and supported by the center for 3D Ferroelectric Microelectronics (3DFeM), an Energy Frontier Research Center funded by the U.S. Department of Energy (DOE), Office of Science, Basic Energy Sciences under Award Number DESC0021118. J.C.Y. and Y.C.L. acknowledge support from the National Science and Technology Council (NSTC), Taiwan, under grant no. NSTC1112628M006005.
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A.B. designed the algorithm, wrote the codes for implementation and analysis, analyzed data and wrote the paper. N.C. wrote codes for the spectral voting system. Y.L. assisted with experimental setup and code integration. Y.C.L. and J.C.Y. grew the samples used. S.J. wrote the acquisition software for pythoncontrolled spectral acquisition. S.V.K. assisted with analysis of results and paper writing. M.A.Z. assisted with code development in the dKL framework. R.K.V. supervised the project, conceived of the idea, performed AFM experiments, and cowrote the paper. All authors commented on the manuscript.
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Biswas, A., Liu, Y., Creange, N. et al. A dynamic Bayesian optimized active recommender system for curiositydriven partially Humanintheloop automated experiments. npj Comput Mater 10, 29 (2024). https://doi.org/10.1038/s41524023011915
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DOI: https://doi.org/10.1038/s41524023011915