Page 40 - IJAMD-2-1

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

1882 K; the proportion of the hcp phase also decreases networks and GNN, our KAN-based model demonstrated
from 100% initially to 0%. As displayed in Figure 7B, superior performance in terms of learning speed, accuracy,
before 1882 K, Ru exhibits an hcp crystal structure. and computational efficiency. While GNNs reported
The first significant peak appears at about 2.70 Å, comparable accuracy, they required more complex data
representing the distance between the nearest neighboring preparation and higher computational resources. KAN’s
atoms. The second and third peaks correspond to the ability to capture complex non-linear relationships
distances of the second and third nearest neighbor atoms, efficiently, without extensive preprocessing or high
respectively, between 4.3 – 4.4 and 5.1 – 5.4 Å. These peaks computational overhead, makes it particularly suitable for
reflect the short- and medium-range orders of the hcp computational materials science applications, particularly
crystal, and the characteristic peaks are clear and relatively in the exploration of RSAs. Our model’s predictions of
sharp. As observed in Figure 7C, around 1882 K, when the elastic constants, thermal expansion coefficient, Poisson’s
temperature rises, the crystal structure of hcp becomes ratio, bulk modulus, shear modulus, and Young’s modulus
unstable and gradually transforms, which is manifested by displayed excellent agreement with experimental
the obvious shift of the peak position of the characteristic reference data, with discrepancies within 6%. This high
peak in RDF. The second and third peaks gradually become level of accuracy validates the reliability of our KAN-
wider and begin to shift, which makes the characteristic based approach. Furthermore, the integration of KAN
peaks relatively more symmetrical and regular, reflecting models with MD simulations accurately captured Ru’s
the high symmetry of atomic stacking in the fcc structure. phase transitions, including the transition from hcp to fcc
This indicates that the regularity of atomic arrangement structure and melting point.
has changed during the transformation of hcp to fcc. This However, it is important to acknowledge the limitations
phase transition is consistent with the known behavior of of our approach. The slight deviation observed in the
Ru under heating and aligns with results from previous melting point prediction, while small, highlights the
studies. 55 inherent challenges in accurately modeling complex
Further heating led to a significant increase in potential material behaviors. This deviation may be attributed to
energy at around 2416 K, which we identified as the several factors, including quantum effects not accounted
melting point, marking the transition from the fcc solid for in classical MD simulations, incomplete representation
phase to the liquid phase. As displayed in Figure 7D, the of long-range electrostatic interactions, and thermal
characteristic peaks in the RDF become broader and and statistical fluctuations inherent in MD simulations.
smoother, reflecting that the long-range order of the In addition, while our model performs well for Ru, its
crystal structure completely disappears. There is only applicability to a wider range of elements and compounds
the first short-range order peak in the RDF, while the warrants further investigation. The model’s accuracy may
subsequent peaks gradually disappear, which is different vary for materials with significantly different electronic
from the crystal structure of the solid. The melting point structures or bonding characteristics. Although more
observed during the simulation is strikingly close to the efficient than some alternatives, the KAN approach
experimentally known true melting point of Ru, affirming still requires substantial computational resources for
the potential’s accuracy. The energy continued to rise training and large-scale simulations, which may limit its
56
beyond this temperature, consistent with the behavior of applicability in certain research settings.
melting materials. Although a slight deviation is observed, Despite these limitations, the success of KAN in
this can be attributed to inherent limitations of the characterizing Ru properties has significant implications
simulation model, such as quantum effects, long-range for the broader field of computational materials science. By
57
electrostatic interactions, and thermal and statistical providing a method that balances high-fidelity predictions
58
fluctuations, rather than a deficiency in KAN’s potential. with practical computational demands, this approach
59
could accelerate the discovery and design of novel RSAs
4. Conclusion and other advanced materials. KAN’s ability to generate
This study demonstrates the efficacy of the KAN model in accurate interatomic potentials for MD simulations
predicting the mechanical and thermodynamic properties further enhances its utility in predicting complex material
of Ru with high accuracy and computational efficiency. behaviors under various conditions. Looking ahead, the
The KAN model not only achieves comparable accuracy KAN framework demonstrates promise for extension
to prior literature but also offers significant advantages to other elements and more complex alloy systems. For
in terms of reduced computational requirements and transferring this model to other materials, the approach
descriptor complexity. Compared to traditional neural differs depending on the system’s complexity. For single

Volume 2 Issue 1 (2025) 34 doi: 10.36922/ijamd.8291