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Machine learning aided atomic structure identification of interfacial ionic hydrates from atomic force microscopy images

Relevant to broad applied fields and natural processes, interfacial ionic hydrates has been widely studied by ultrahigh-resolution atomic force microscopy (AFM). However, the complex relationship between AFM signal and the investigated system makes it difficult to determine the atomic structure of such complex system from AFM images alone. Using machine learning, we achieved precise identification of the atomic structures of interfacial water/ionic hydrates based on AFM images, including the position of each atom and the orientation of water molecules. Furthermore, it was found that structure prediction of ionic hydrates can be achieved cost-effectively by transfer learning using neural network (NN) trained with easily available interfacial water data. Thus, this work provides an efficient and economical methodology which not only opens up avenues to determine atomic structures of more complex systems from AFM images, but may also help to interpret other science-wide studies involving sophisticated experimental results.


Introduction
Interfacial ionic hydrates are ubiquitous in nature and are closely related to a variety of essential issues in applied fields and natural processes, from electrocatalytic processes 1 2 3 4 , seawater desalination 5 6 7 8 , to biological ion channels 9 10 and chemical reactions 11 12 . The structural information of ionic hydrates at the atomic level is crucial for elucidating the various extraordinary physical and chemical properties of the ionic hydrate/solid interface. In recent years, qPlus-based noncontact AFM with COdecorated tip 13 , capable of directly imaging water nanoclusters with submolecular resolution 14 15 , has emerged as the most promising candidate for characterizing interfacial water network structure and dynamics at the atomic level 16 . However, in sharp contrast to the oxygen skeleton, which can be clearly reflected, identifying hydrogen atoms from AFM images is a challenge because they are barely visible 17 .
Therefore, accurate structure identification, by combining density functional theory (DFT)-based stability calculations and probe particle method-based AFM simulations 18 possible structural models with different OH orientations.
Recently, machine learning (ML) has been used in various scientific and technological studies 20 21 22 23 , such as structure indentification 24 25 26 , structure discovery 27 , and electrostatic discovery 28 related to microscopy imaging. Especially for AFM imaging, a convolution neural network (CNN) has been applied by Alldritt et al to resolve the configuration of organic molecules 29 . In their study, the feeding data for ML were the simulated AFM images generated based on DFT optimized structures from the preexisting databases. However, such an approach is not suitable for interfacial ionic hydration systems, since there is no ready database includes ionic hydrate structures, and it is costly and impractical to acquire such large amounts of structures based on DFT calculations. In addition, this ML method, originally designed to identify molecular skeletons, has difficulty identifying hydrogen atoms from AFM images because of its relatively weaker signal than those of other atoms (e.g., oxygen).
Therefore, it requires a cost-effective way to obtain input data, as well as a good structure representation and an effective NN architecture to distinguish H from other atoms.
Generally, the generation of input data consists of two key steps, structure acquisition and AFM image simulation. For structure acquisition, it requires sufficient phase space sampling of the target system to effectively introduce structural physics-induced biases into NN 21 . Obviously, the more accurate and richer the input structure, the higher the prediction accuracy. The DFT-based method has high accuracy, but cannot sample enough structures for training due to the great demands for computational resources.
As an alternative, the classical molecular dynamic (MD) simulations can provide many plausible structures economically and quickly 30 . At the same time, its lack of calculated energy accuracy has a minor impact on structure prediction and is therefore negligible in structure acquisition for ML.
In terms of AFM simulations, the calculations of the potential surface distribution of the system used for AFM simulation must be accurate enough to agree well with the experimental results. Without the need for DFT calculations to obtain the system electrostatic potential, the classical point charge model incorporating Lennard-Jones (L-J) interactions 18 19 can be used to cost-effectively perform AFM simulations of interfacial water. However, when ions are added, this point charge method no longer accurately provides the potential surface for the ionic hydrate system, so DFT calculations become crucial. Fortunately, transfer learning 31 can be used to transfer knowledge from interfacial water systems to the interfacial ionic hydrate systems because their hydrogen bond (H-bond) networks share similar characteristics. Such usage can nicely reduce the need for interfacial ionic hydrate data, making the training of NN for ionic hydrates more economical.
Therefore, taking Na + hydrates, one of the most abundant alkali metal ions in natural, as an example, we designed an ML method with transfer learning to economically determine the structure of interfacial ionic hydrates from the AFM images. A NN was first trained on a large number of AFM images of interfacial water structures simulated via classical MD, and then retrained via transfer learning on AFM images of Na + hydrates simulated based on DFT-computed electrostatic potentials. Strikingly, using only thousands of simulated data of Na + hydrates, the prediction accuracy of the retrained NN can reach 95% for both sodium and oxygen, and 85% even for hydrogen.
From the designed structure representations predicted by NN, one can easily identify the positions of each atom and the orientations of water molecules. The great accuracy and efficiency of this prediction are far beyond that of trial-and-error processes of human experts, and have not been achieved by any ML method to date. Furthermore, this economical ML method is also a fairly general workflow for structure prediction from AFM images, and can be extended from interfacial ionic hydrate systems to other complex systems, such as the surface of bulk ice, and even to identify information from the results of other spectroscopic experiments 24 25 28 .

Results
As illustrated in Fig. 1, the workflow consists of preliminary training and retraining for structure prediction for interfacial water (Fig. 1a) and interfacial Na + hydrates (Fig.   1b), respectively. During preliminary training, the NN, which is a standard 3D-Unet model 32 33 (see Method), is fed with sufficient interfacial water data to learn to resolve the structure information of H-bond networks from AFM images. Then, via transfer learning, the NN is retrained with a small amount of expensive interfacial Na + hydrates data to achieve efficient structure identification of Na + hydrates economically. In both cases, the implemented learning schemes include data preparation, data labeling, NN training and performance evaluation. Data preparation, including phase space exploration based on classical MD simulations, structure sampling, AFM images simulation and data processing, is the key to transfer learning and is described in more detail below. For the identification of hydrogen atoms, the designed structure representation (data label) and the corresponding evaluating criteria will also be stated later.

Data Preparation for Preliminary Training
A large number of simulated AFM images of well-sampled different structures from the interfacial water layer on the Au(111) substrate were used in the preliminary NN training to ensure the robustness of the NN. Considering the large density variation in different layers 34 , the structure sampling in the sampled phase space was performed by sliding a detection window of 2.5 × 2.5 × 0.3'( ! along the direction parallel and perpendicular to the substrate (Fig. 1a, the first panel). We note that the detection window is large enough to cover various interfacial water structures in the XY plane, and ensure that the AFM can only probe one layer along the Z direction. Up to 80,000 two-dimensional (2D) water structures of different temperatures and densities were selected for AFM simulations, of which 70,000 and 10,000 were randomly selected for training and for validation, respectively. For each structure, 10 images were randomly selected from a set of simulated AFM images with a tip-sample distance (defined in methods) of 1.14 nm to 1.34 nm (10 pm intervals), and stacked as the input data for NN training. Data augmentation including cutout, noise and pixel-shift was implemented before NN training to prevent overfitting (see SI section 3 for details).

The NN Output and Performance Assessment for Structure Prediction
An ideal output of structure prediction should include the chemical identity and positions of the atoms. Considering that NN cannot effectively predict individual values 29 , we designed an intuitive representation to encode molecular structures, namely the advanced vdW (a-vdW) spheres. In this representation, atoms are represented by van der Waals radius (σ) and dispersion energy (ϵ) of the L-J interaction, as well as the charge +. Thus, a colored atom map (Fig. 2, right two panels) can be obtained as the NN output (see SI section 4 for details), from which atomic identities and positions can be easily distinguished. We stress that this representation also contains some 3D structure information, because the atomic circles are stacked sequentially with the increasing height, so that the uppermost one of the overlapping atomic circles represents the highest atom.
The per-pixel mean square error (MSE) calculated between the reference image and the predicted image was used as the loss function of NN training to thoroughly evaluate the predictions for each structure. Moreover, considering that the goal of NN is object detection, we designed an algorithm to locate the positions of all atoms and further calculated the prediction accuracy of each atomic species for intuitively evaluating the NN performance (see SI section 13 for details). For each atomic species, the prediction accuracy was calculated based on all predictions for it in the whole dataset, rather than averaging its prediction accuracy of each structure. This is because the small number of atoms in a particular structure results in discontinuity of the prediction accuracy and further leads to inaccurate statistical results. The error bar for the prediction accuracy was calculated from the data at the top and bottom 20% of the MSE ranking to account for the uneven performance of the NN on different structure. In addition, in order to avoid overestimating the NN performance, the parameter set in the prediction accuracy calculation algorithm was adjusted and cross-checked by comparing the automatically and manually calculated prediction accuracy. The prediction accuracy of machine calculation with the final chosen parameter set is slightly lower than that of manual calculation, ensuring the reliability of the prediction accuracy of the machine calculation.

Structure prediction of Interfacial Water based on Preliminary Training
After preliminary training for 60 epochs using 70,000 data of interfacial water on Au(111) substrate, the loss converges to 0.0025. Structural predictions of high-density and low-density interfacial water by the preliminary trained NN are shown in Fig. 2a and b, indicating good predictions in both the atomic identity and position. Furthermore, the orientation of interfacial water molecules can also be well predicted by the different To gain insight into the NN performance and further analyze its insufficiency, we analyzed the best and worst 10% predictions in order of the network loss. It was found that the loss in nearly all predictions (more than 99%) are caused by the light-colored dots or shadows on the graph (see Fig. S5) which corresponds to low-confidence predictions, except for that in completely failed predictions (less than 1%). While these light-colored dots and shadows may hinder the accuracy improvements, the predicted structure is still a plausible atomic arrangement and thus can serve as a valuable reference.
To test the generalization ability of the NN preliminarily trained with interfacial water structures on Au(111), the structure prediction was carried out for interfacial water on Pt(111) which has a smaller lattice constant and is more hydrophilic than Au(111) 35 .
The test structures include 1000 interfacial water structures at different temperatures and distances from the Pt (111) surface, and their processing method is the same as that of the structures on Au(111) surface. The structure prediction tested on Pt (111) performs pretty well on both dense and dilute interfacial water ( Fig. 2c and d), with a slightly larger loss (0.0030) than that of Au(111) (0.0025). After testing, the prediction accuracies of oxygen atoms and hydrogen atoms are 94.8% and 86.9%, respectively, indicating the generalization ability of the NN and further laying the foundation for transfer learning.
In addition, further analyses of the structure predictions of Pt(111) found that the predicted hydrogen atom positions sometimes shift along the H-bonds compared to the reference (see Fig. S6, marked with arrows). Specifically, the hydrogen that should belong to water molecule A was predicted to belong to water molecule B, which is connected to A by hydrogen bonding. We speculate that, due to the weak hydrogen signal in the AFM images, the prediction of hydrogen positions is closer to structure inference based on the learned phase space than direct "object detection" that requires a strong signal (like oxygen). However, water molecules on hydrophobic Au(111) are more likely to be H-up than that on hydrophilic Pt(111), and thus the lack of the relevant structures in the preliminary training dataset caused the lower prediction accuracy of hydrogen on Pt(111). Indeed, the prediction mismatch of hydrogen (see Fig. S6) was almost completely reduced by retraining NN with the 5000 data of interfacial water structures on Pt(111). Thus, it can be found that data with physics-induced biases is essential and effective for NN to accurately predict one specific system.

Structure prediction of Na + hydrates with Transfer Learning
For the interfacial Na + hydrates system, we used transfer learning to efficiently train NN by loading the parameters of the preliminarily trained NN. Na + ⋅nH2O (n=3,4) on NaCl(001) was chosen as the basic structure to explore the phase space of Na + hydrates system, whose structures were randomly located within the detection window. Unlike interfacial water, AFM simulations of the ionic hydrate structures were performed using electrostatic potentials obtained from DFT calculations. After training for 50 epochs with data based only on 1500 Na + hydrate structures, the loss converged to 0.0009 and the NN prediction performs very well (Fig. 3, the first and second row; Fig. S4). The predicted accuracies for sodium, oxygen and hydrogen calculated on 500 validation data are 96%, 95.4%, and 85%, respectively.
To test the transferability of the retrained NN via transfer learning, this NN was applied to predict the structure of more complex Na + hydrates with more than four water molecules. The predicted structure matches the actual structure remarkably well (Fig.   3, the third row; Fig. S4), and the prediction accuracies for sodium, oxygen and hydrogen atom based on the testing dataset of 1000 complex Na + hydrates, are 82.3%, 91.7%, and 72.9%, respectively. In addition, experimental AFM images of Na + ⋅4H2O were used for structure prediction to test the effectiveness of the NN. The corresponding predicted structures agree very well with the DFT-optimized geometry (Fig. 3, the fourth row), and its simulated AFM images are in perfect agreement with the experimental result (see Fig. S7). We note that the light red dots in the upper left corner of the Na + ⋅4H2O in the prediction can be discarded, as it is a low confidence prediction.
Therefore, it can be determined that NNs can provide valuable structure predictions even for complex Na + hydrate AFM images and experimental AFM images.
Generally speaking, the water molecules in Na + hydrate can be divided into those around Na + and those above Na + according to their positions relative to Na + . To further understand the prediction performance of NN on different water molecules, the prediction accuracy of these two types of water was also analyzed (Fig. S8) and significant differences were found between them. For water molecules around Na + , the prediction of oxygen and hydrogen are well. Conversely, atoms in water molecules above Na + are difficult to be predicted by NN. This poor prediction may be due to the fact that the actual height of such systems exceeds one layer and thus goes beyond the trained 2D representation, making NN parsing difficult.

Validity Assessment of the Transfer Learning
To evaluate the effectiveness of transfer learning, we used different training datasets (with different data volumes, , =200, 500, 1000 and 1500) to train NN with or without transfer learning. The prediction accuracy for these different training segments was calculated using the same validation dataset containing 500 Na + hydrate structures, and the best 100 and worst 100 data sorted by loss were calculated as the upper and lower bounds of the error bar (Fig. 4). When N ≥ 500, the NN trained with transfer learning has a higher prediction accuracy of all atomic species than that without transfer learning ( Fig. 4a and b, blue line). The prediction accuracy of the hydrogen based on the directly trained NN without transfer learning is almost zero (Fig. 4c, orange line), and only small patches of light gray near oxygen are presented (Fig. S9). However, with transfer learning of the preliminarily trained NN, the high prediction accuracy of hydrogen can be achieved with only a few thousand data.
Notably, when N< 500, the directly trained NN shows better performance in Na + prediction than that with transfer learning. We speculate that this phenomenon is due to two aspects. One is that the signal for Na + in the AFM image is the strongest, which is easy for a blank NN to learn. The other is that the retraining of preliminarily trained NN via transfer learning requires sufficient Na + hydrate data to get rid of previous local minima. Furthermore, this drawback of transfer learning soon disappears as N increases to 500, while the prediction accuracy of transfer learning does not increase much when N > 1000, suggesting that only a few hundred data is required to train an accurate NN in this case. Therefore, it can be concluded that the NN preliminarily trained with the interfacial water data can be transferred to the ionic hydrate system through transfer learning, so that it can be realized to train the NN with only a small amount of data to obtain the ability of high-precision prediction for more complex systems.

Discussion
In this work, we presented an economic method to identify the atomic structure of interfacial ionic hydrates from AFM images using transfer learning which solves the huge demand for high-cost DFT calculation in the data preparation. Through empirical potential-based MD simulations and AFM simulations based on simple point charges and L-J interactions, we first sacrificed a little precision to generate a large number of AFM images of interfacial water, and trained the NN of a 3D-unet with these data to capture the atomic structure of the H-bond network. Next, by retraining with only a few thousand hydrate structure data through transfer learning, the NN can achieve accurate structure prediction of all atoms in hydrates, outperforming the ability of human experts.
More important, after comparing the performance of NN training on hydrates structure with or without transfer learning, we verified the feasibility and validity of the transfer learning method in reducing computational resources demand. In addition, this method is transferable to different systems, as demonstrated by the good predictions for both interfacial water on different substrates (Au and Pt surface) and complex Na + hydrates with different water molecule numbers. Importantly, this work is a good start in high resolution atomic structures prediction based on AFM images. There is room for improvement, for instance, experimental errors such as noise distribution and tip drifting need to be handled more carefully to further improve the prediction accuracy. With the rapid application of physical laws and geometry symmetries informed NNs 21 36 in general drug de novo design 37 , biomolecular structure prediction 38 39 and molecule surface potential prediction 40 41 , we believe that our approach can determine 3D structures (e.g. ice) by introducing those NN architectures. Finally, it is worth noting that, our proposed ML method with transfer learning can also be extended from efficient structure prediction for AFM imaging to a broad range of applications for interpreting other experimental measurements 42 , such as STM 43 , SEM 25 and TEM 44 .

Neural Network Structure
The NN for structure prediction from AFM images was a standard 3D U-Net 32 model,  Table S1. MD simulations over a wide temperature range from 140K to 300K (40= a step) , were performed to sample various water phase spaces sufficiently. The simulation timestep is 1 fs and the total simulation time at a given (,, >, ?) is 5 '@ where the first 2 '@ is run for structure relaxation.
The MD simulations of Na + hydrates were performed using the AMBER16 software package 50 with polarizable force fields 51,52 . The effectiveness of this force field has been demonstrated in our previous publication 54 . The force field parameters are shown in  assuming an isotropic, uniform bulk particle distribution beyond the cut-off, was added to the van der Waals energy and pressure 50 .

Structure Sampling
We note that the detection window (Fig. 1a,  For acquiring sufficient interfacial water structure, the detection window is initially settled at the first water layer and then slides in the direction parallel and perpendicular to the substrate. In XY plane, the number of steps of the detection window is 2 and the stride is 0.5 '( for each step. While in Z direction, the number of steps and stride is 1 and 0.5 '(, respectively. To ensure the variety of the data, the water molecules within the distance δO * and δO + from the window boundary are neglected during each detection. The distance δO * and δO + are settled randomly, but can guarantee that at least one water molecule remains in the detection window. The configurations used for data acquisition is sampled from the MD simulations trajectories with a time interval of 10 C@.

DFT calculation
We calculate the electrostatic potential of Na + hydrate at Au (111) surface using DFT within the generalized gradient approximation of Perdew-Burke-Ernzerhof 54 (PBE-GGA), which has been shown to give good results for H2O hydrogen bonding 55 DFT calculations were performed using the Vienna ab initio simulation package (VASP) 56 Projector augmented wave pseudopotentials were used with a cut-off energy of 550 eV for the expansion of the electronic wave functions. Van der Waals corrections for dispersion forces were considered by using the optB86b-vdW functional 57 58 .

Simulations of AFM Images
The AFM images were simulated using a molecular mechanics model based on methods described in refs 18 and 19. We use the following parameters for the probe-  Table S3.

Data availability
The data that support the findings of this study are available from the corresponding author upon reasonable request.

Notes
The authors declare no competing financial interest.

Neural Network Structure
The Neural Network (NN) for structure prediction from atomic force microscopy (AFM) images was a standard 3D U-Net 1 model, a CNN widely used for biological and clinical image segmentation 2 . It consists of an encoder part for feature extracting, a decoder part for converting input (AFM images) to output (visual representation), and skip connections between the encoder and decoder parts, effectively preventing the feature loss of H-atom during the encoder process (Fig. S3). 10 of the gray scale AFM images at different tip-sample distances are stacked to a 3D image as the input to the network.
The size of the input data is 1 × 10 × 128 × 128 where each number represents the channel, depth, height and width respectively. The output of the network is a 3 channels 2D image of size 3 × 128 × 128 where each number represents the channel, height and width respectively. Each block in the encoder part contains two 3 × 3 × 3 convolutional layers, each layer is preceded by a Group Normalization (GN) layer and followed by a leaky rectified linear unit (L-ReLU). And a maxpooling is added at the end of each block. The first two maxpoolings are 1 × 2 × 2 in size to keep the AFM stack depth at 10, and the next two maxpoolings are 2 × 2 × 2 in size to reduce the data depth to 2. In the decoder part, each block consists of an interpolation upsampling of the size of maxpooling in the corresponding block in the encoder, followed by two 3 × 3 × 3 convolution layers, each of which is preceded by a GN layer and followed by a L-ReLU. Skip connections between layers with the same size in the encoder and decoder part provide the decoder with essential high-resolution features. After the decoder, there are two 3 × 3 × 3 convolution layers and two 3 × 3 convolution layers. The data was flattened before the 3 × 3 convolution. Except for the last layer using ReLU, other convolution layers use L-ReLU. The slope of the L-ReLU is 0.001.   To make the network more robust to experimental data and avoid overfitting, the input data is processed as follows.

Simulation Parameters
a) White Nosie. A random uniform noise with an amplitude in a range of [−δ*, δ*] is added to each image, where * !"# and * !$% is the maximum and minimum pixel value of an image, and . is the amplitude ratio. Here c=0.003 for interfacial water data.

Structure Representation
We design a new structure representation named advanced vdW (a-vdW) spheres as the neural network output/ data label. As shown in Fig. S4, it composed of three grayscale images representing atom type, positive charge and negative charge. They are the same size and are all the projection of the structure onto the 2 − 3 plane. Since the interfacial structure is restricted in a box with a height of only 0.356, its information in the 7 direction is negligible, and the projection of all the atoms is sufficient to represent the structure to some extent. In our representation, each atom is described as a sphere and projected onto the 2 − 3 plane in height order. If two atoms overlap, the higher atom cover the lower one. In atom-type images, the diameter 8 and grayscale 9 & of atoms are related to their LJ potential parameters σ and ϵ. Here, in order to differentiate different elements for easier identification, ϵ of each element is scaled and transformed, where ϵ !$% D58 ϵ !"# are the minimum and maximum ϵ values among all elements, respectively, and > & = 0.6 and > ) = 0.7 are the scale factors. All the LJ potential parameters are chosen from the OPLS Force Field 3 . For positive and negative charge images, the diameter of atom is defined as above, and the grayscale 9 ) is scaled by charge, where G is the charge of the atom and G !"# is the charge of the most charged atom in the structure.
If we consider these three images as three channels of a color image and combine them, we get a colormap where each atom has a different color. According to the definition of

Training Process
The loss function is mean square error (MSE) and the optimizer for gradient descent is

Figure S5 | Bad prediction of NN on interfacial water (Au surface) data. The representations
of structure a, which is atom type, negative charge, positive charge, and color plot, respectively (the upper panels, predicted by NN; the lower panels, reference representations).

Correction of the hydrogen atom shift by transfer learning
After training the NN using data of interfacial water on Au (111)

Prediction for experimental AFM images of Na + 4H2O
Before prediction, the experimental AFM images to be predicted should be preprocessed. They should be padded or cut to the same size as the detection space of the training data, so as to ensure that the size of the imaging of a specific molecule relative to the detection space remains unchanged. Here, the detection space of experimental AFM images to be predicted is 1.  The representations of Na hydrates, from left to right where one of the water molecules posited from around the ion to above the ion (the upper panels, predicted by NN; the lower panels, reference representations).

The prediction performance of NN with or without transfer learning
We compare the prediction performance of NN with or without transfer learning as the training dataset size varies. The same validation dataset is used regardless of how much training data there is and whether or not the NN training uses transfer learning techniques. As shown in fig. S11, we chose the structures on which the NN without transfer learning performs best according to MSE, however, the NN trained without transfer learning still cannot predict the position of hydrogen atoms and the water molecule orientation.

Object detection for each atom
Negative and positive charge maps are used for atom detection. For the detection of oxygen atoms and sodium ions, we take pixel grayscale and pixel number as the criteria for atom detection and identification. For each element, any pixel with grayscale 9 , we should consider the shape of the region as an important criterion. We define the shape factor of a region as follows: where V $ denotes the distance from the i-th pixel to the center of the region, and the sum is over all pixel at the edge of the region. A perfect circle has a shape factor of 1.
Once the T > T !"# where T !"# is a threshold, the shadow should be discarded. In addition, if two hydrogen atoms overlap in the label and we can only detect one region in the prediction, we count them as two TPs.
Finally, for each element, the prediction accuracy is calculated by eq. S7 based on all predictions for it in the target dataset. To avoid overestimating the performance of the NN, the parameter set in the prediction accuracy calculation algorithm was adjusted and cross-checked by manual calculated prediction accuracy of each atom species. We manually identified the atoms and calculate the prediction accuracy for each atom species among different dataset.
Calculated using the same datasets used in Fig. 4, we plot the error bars with the manually collected data (see fig. S12). The prediction accuracy of machine calculation of this parameter set is slightly lower than that of manual calculation, indicating that the prediction accuracy of the machine calculation is reliable.