Page 29 - IJAMD-2-1

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

flexible, allowing for facile adjustment of parameters and potentials (Figure 1). Compared to other established neural
refinement of datasets to improve accuracy and predictive network architectures including CalHousNet Feedforward
performance. This flexibility allows ML models to Neural Network (CalHousNet), Accurate Neural Network
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adapt to new data and evolve continuously, providing a Engine for Molecular Energies (ANI), Continuous-filter
dynamic and scalable approach for studying a wide range Convolutional Neural Network (SchNet), and traditional
of materials and their complex behaviors. In addition, graph neural networks (GNNs), our approach simplifies
ML models enable faster updates as more data becomes data preprocessing and significantly reduces training
available, streamlining the process of material discovery time. When benchmarked against experimental data,
and optimization. our model demonstrates superior accuracy in predicting
mechanical properties using molecular statics simulations,
Among these ML models, the recently introduced highlighting the precision of KAN. Furthermore, we
Kolmogorov-Arnold Network (KAN), inspired by the successfully generated an interatomic potential capable of
Kolmogorov-Arnold Representation theorem, provides a accurately capturing key physical phenomena using MD
new way to model complex systems. Unlike multilayer simulations, including phase transitions and the melting
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perceptrons (MLPs) with fixed activation functions on point of Ru. This development not only underscores the
nodes, KAN has a learnable activation function on the advantages of KAN in computational materials science
edge, parameterized as a spline function. This seemingly but also lays the groundwork for incorporating additional
simple change enables KAN to outperform MLP in terms elements into the framework. This advancement enables
of accuracy and interpretability. In data fitting and partial the development of multi-element interatomic potentials,
differential equation solving tasks, KAN has demonstrated potentially facilitating accurate simulations of more
faster neural scaling laws than MLP, achieving comparable or complex high-entropy material systems.
better accuracy with a smaller network. The architectural
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advantage of KAN makes it particularly suited for materials 2. Methods
science applications. Its ability to process complex, non- 2.1. Molecular models and simulations
linear relationships makes it ideal for tackling quantum
phenomena, like Anderson localization, where disorder First-principles calculations were performed within DFT
in a system leads to the localization of electronic wave through the Quantum Open-Source Package for Research
functions. KANs excel in extracting mobility edges in in Electronic Structure, Simulation, and Optimization
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various tight-binding models, such as the Mosaic model (Quantum ESPRESSO) package, 31,32 using the Perdew–
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and the Aubry-André model, where previous methods Burke–Ernzerhof 33 exchange-correlation functional
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may struggle. Material properties often follow complex, and projector-augmented plane wave potentials. We
non-linear relationships that cannot be well-captured by optimized the wavefunction and charge density parameters
standard activation functions, making KAN’s learnable to cutoffs of 52.123 and 353.301 Ry, respectively, and used
activation functions especially valuable in this domain. a 4 × 4 × 4 Monkhorst-Pack grid for k-point sampling.
The model’s ability to discover and represent underlying With this scheme, the total energy and force converged
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physical patterns without requiring explicit physical at 10 Ry and 10 Ry/Bohr, respectively. Through these
constraints in the training process represents a significant calculations, we generated 699 data points to relate the
advancement in materials informatics. By allowing users changes in the volume and energy of the element Ru under
to incorporate prior knowledge and assumptions, KAN various stress conditions, facilitating detailed analysis
can collaborate with human intuition to simplify complex of its structural properties. From the DFT calculations,
expressions while maintaining high accuracy. This makes we obtained the initial crystal structure parameters,
KAN a powerful tool for predicting physical properties in including lattice constants (a, b, c), angles (α, β, γ), unit
materials and provides a robust framework for handling cell volume, and atomic positions in both fractional (a, b,
c) and Cartesian (x, y, z) coordinates. The DFT calculations
disorders and defects in computational material studies. further provided the corresponding total energies, stress
Therefore, integrating KAN into the materials informatics
workflow can enhance our understanding of complex tensors, and atomic forces. This combined dataset was
material phenomena, accelerate the discovery of new then processed and structured into a comprehensive
dataset using the pymatgen (Python Materials Genomics)
materials with desired properties, and provide results that package. This dataset size is comparable to typical single-
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are easier to interpret than traditional neural networks.
element training sets in literature; for instance, previous
Our study addresses the lack of ML models specifically studies have demonstrated that accurate potentials can
tailored for Ru and introduces the novel application of KAN be developed with 461 and 284 structures for Ni and
to predict material properties and construct ML interatomic Mo, respectively. While multi-element systems typically
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Volume 2 Issue 1 (2025) 23 doi: 10.36922/ijamd.8291