Page 36 - IJAMD-2-1

International Journal of AI for
Materials and Design
ML molecular modeling of Ru: A KAN approach

0.31 across training, validation, and test sets, respectively, properties such as elastic constants, thermal expansion
alongside stable MSE metrics (0.79, 0.50, and 0.49). While coefficients, Poisson’s ratio, bulk modulus, shear modulus,
the GNN demonstrated marginally superior numerical and Young’s modulus, each essential for understanding the
performance (MAE: 0.15, 0.13, and 0.22), it demands material’s mechanical behavior.
substantially more complex data preprocessing and feature To facilitate direct comparison in their natural units,
engineering, significantly limiting its practical applicability. we performed denormalization of the model predictions
In contrast, KAN’s straightforward implementation and on the test dataset. Figure 5 presents the distribution of
minimal preprocessing requirements make it particularly prediction errors in their original units, with energy errors
valuable for real-world applications where computational presented in Ry (Figure 5A) and force errors in Ry/au
efficiency and ease of deployment are crucial.
(Figure 5B). After denormalization, the box plots reveal
As featured in Figures S3-S7, the training dynamics of that KAN maintains excellent prediction accuracy with
KAN display remarkable learning efficiency and stability. median energy errors around 0.1 Ry, while most predictions
During the initial 30 epochs, KAN exhibits rapid learning fall within a narrow range of 0.05 – 0.2 Ry, demonstrating
characterized by a sharp decline in MAE, indicating swift robust performance. For force predictions, the median
comprehension of the underlying data patterns. The error is approximately 0.0003 Ry/au, with most predictions
learning curve demonstrates consistent convergence, with showing errors between 0.0001 – 0.0005 Ry/au. The
both training and validation errors stabilizing after 50 presence of a few outliers (i.e., points above the whiskers)
epochs, suggesting robust generalization capabilities. This in both plots indicates occasional challenging cases, but
stability in later epochs, coupled with the close alignment these represent a small fraction of the predictions. This
between training and validation performance, indicates analysis in physical units further validates KAN’s strong
that KAN effectively avoids overfitting while maintaining predictive capabilities, as it maintains high accuracy even
strong predictive power. when evaluated in the original, unnormalized scale of
Other benchmarked models displayed less competitive calculations.
performance-to-complexity ratios. SchNet demonstrated
moderate but inferior accuracy (MAE: 0.46, 0.38, and 3.1.2. Mechanical properties measurement
0.41) while requiring specialized graph-based data Various mechanical properties were measured, as follows:
structures. ANI exhibited the highest error metrics (i) Elastic constants calculation: Elastic constants,
(MAE consistently around 0.79), suggesting limitations including , , , and , were derived by
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in its feature extraction capabilities. CalHousNet’s applying the relevant strains to the crystal structure
performance (MAE: 0.34, 0.27, and 0.29) approached and measuring the resultant stress tensors with KAN.
KAN’s accuracy but lacked its efficient training dynamics The strain tensor ϵ is applied to the structure’s lattice:
and straightforward implementation. The consistent R’ = R(I + ϵ) (Ⅻ)
performance of KAN across diverse datasets, combined
with its minimal preprocessing requirements and stable where is the original lattice matrix, and is the
training behavior, establishes it as the most practical identity matrix. The relationship between stress () and
and efficient choice for large-scale molecular property strain () tensors is defined as:
prediction tasks. σ=Cϵ (ⅩⅢ)
In contrast, KAN provides a balanced approach, The stress () and strain () data were linearly regressed
achieving good performance with less complex data to determine the material constants () from the slope of
preparation and lower computational demands, as the stress-strain relationship.
demonstrated in Figure S8. Leveraging the principles of (ii) Thermal expansion coefficient: The thermal expansion
the Kolmogorov-Arnold representation theorem, KAN coefficient was determined by simulating temperature-
captures complex non-linear relationships efficiently, induced lattice expansions. The expansion was
without the need for extensive preprocessing or high modeled by scaling lattice vectors according to a
computational overhead. This efficient utilization of temperature-dependent factor (), and the resulting
resources combined with robust predictive capabilities volumetric changes were used to compute by fitting
grants KAN a significant advantage in computational these changes over a range of temperatures. The lattice
materials science, making it a preferred choice for vectors are scaled based on a temperature-dependent
researchers seeking to balance performance with practical
operational demands. By leveraging KAN’s predictive expansion factor ():
accuracy and using molecular statics, we compute R’ = R(1 + α∆T) (ⅩⅣ)

Volume 2 Issue 1 (2025) 30 doi: 10.36922/ijamd.8291