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Li et al. J Mater Inf 2024;4:4 I http://dx.doi.org/10.20517/jmi.2023.41 Page 7 of 14

(4)
( ) = +

where and are the weights and biases of the output layer, respectively.

The residual function can be defined as:

( ) = ( 2, ( 1, + 1, ) + 2, ) (5)

where 1, and 2, are the weights of two convolutional layers, 1, and 2, are their biases, represents the
convolution operation, and is the ReLU activation function.

Our framework possesses two key features to ensure the robustness and high performance of the model in
adsorption tasks. Firstly, we adopt the mean absolute error as the loss function and train the network with
the Adam optimization algorithm, ensuring the robustness and adaptability of the model. This choice not
only adapts to adsorption tasks with different complex structures but also ensures that the model performs
exceptionally well in various data scenarios. Secondly, we use the ResNet-34 model as our backbone network.
ResNet-34 consists of 33 convolutional layers, providing depth and capability to the model, enabling it to be
applied to larger databases, thereby enhancing the model accuracy and robustness. ResNet-34 is a widely used
DL framework with proven outstanding performance in numerous fields. Our choice also provides robust
support for adsorption tasks. Overall, by constructing a convolutional network based on LEI-framework, we
integrate the high-importance features of the three nearest neighbor atoms surrounding the adsorbate and
learn the relationships between elements of each layer. Then, we learn from the data of a large dataset based
on the convolutional network. Introducing ResNet reduces the learning difficulty of the model and enhances
its generalizability.

Regression result evaluation
To train the model, several regression outcome evaluation methods are employed. The true and predicted
values in the experiment are denoted as:

True value:

ˆ = { ˆ 1 ˆ 2 · · · , ˆ } (6)
Predicted value:
= { 1 , 2 , · · · , } (7)

Performance metrics for all methods used in this article include Median Absolute Error (MDAE), Mean
Absolute Error (MAE), Root Mean Squared Error (RMSE), and Mean Absolute Relative Percent Difference
(MARPD). The median absolute error is particularly interesting because it is robust to outliers, with its unit
being eV. The median absolute error estimated over samples is defined as:

MDAE( , ˆ ) = (| 1 − ˆ 1 |, · · · | − ˆ |) (8)

MARPD is used because it provides normalized measures of accuracy that may be more interpretable for those
unfamiliar with adsorption energy measurements in eV, as determined by

1 Õ − ˆ
MARPD = · 100% (9)
| | + | ˆ |
=1