Page 30 - IJAMD-2-1

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

Figure 1. Schematic of the workflow of constructing the dataset using DFT calculations, converting the structures into machine-learnable descriptors,
constructing the ML model using KAN, and measurements of material properties either directly or by constructing ML interatomic force fields for
MD simulations.
Abbreviations: DFT: Density functional theory; ML: Machine learning; KAN: Kolmogorov-Arnold Network; MD: Molecular dynamics.

require thousands of structures to capture diverse atomic constant Number, Pressure, and Temperature (NPT)
environments and interactions, single-element systems ensemble, followed by gradual heating from 300 to 3000
can achieve good accuracy with several hundred carefully K. The temperature was controlled using a Nosé-Hoover
selected configurations that comprehensively sample the thermostat with a damping parameter of 1.0, and the
relevant phase space. pressure was maintained at 0 bar using a Parrinello-
Rahman barostat during the NPT phase. Neighbor lists
MD simulations were performed using the open-
source Large-scale Atomic/Molecular Massively Parallel were updated every timestep with a cutoff distance of 0.3 Å
and a bin-based approach.
Simulator (LAMMPS) software package to calculate elastic
constants and melting point. The system was constructed 2.2. Training data generation
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using periodic boundary conditions with an hcp lattice Developing robust ML models for material science heavily
structure in a 10 × 10 × 10 unit cell configuration. relies on training data that encompasses a wide variety
Interatomic interactions were described using our of atomic environments. To this end, we performed
tabulated KAN potential combined with a Lennard-Jones structure relaxation on all symmetrically distinct
potential in a hybrid/overlay scheme. To calculate the configurations within a 16-atom supercell of Ru arranged
elastic constants, the system was constructed with periodic in an hcp structure. Our objective was to meticulously
boundary conditions using a lattice parameter of 2.70 Å, explore the potential energy surface by optimizing these
which was adopted from crystallographic data for Ru’s configurations to their lowest energy states, ensuring
hcp structure and documented in the crystallographic the atomic positions and lattice parameters closely
database maintained by Springer Materials. We then matched experimental and theoretical benchmarks. This
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performed energy minimization of this initial structure optimization would ensure that the material’s behavior
with a convergence criterion of 10 eV/Å for forces and under varying temperatures and pressures was captured
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10 eV for energy, followed by anisotropic box relaxation. accurately. We focused on three primary structural types
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The elastic constants were then calculated through strain- in our study:
stress relationships: C , C , and C were determined (i) Undistorted ground state structure: This represents
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by applying uniaxial strain, for example, by applying a the element’s most stable configuration, free from
strain along the x-axis and measuring the resulting stress external strains or forces.
response in the x-, y-, and z-directions. C was determined (ii) Distorted structures: By applying strains ranging
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through shear deformation in the xy-plane using a triclinic from −10% to +10% in six distinct modes – uniaxial
box transformation. All calculations were performed under tension, uniaxial compression, biaxial tension, biaxial
quasi-static conditions, with system relaxation achieved compression, shear, and torsional strain – to the bulk
through energy minimization after each deformation step. conventional cell, we generated atomic structures to
The melting point was determined using a heating method, analyze the material’s behavior under mechanical
where the system was first equilibrated at 300 K using a stress. 39

Volume 2 Issue 1 (2025) 24 doi: 10.36922/ijamd.8291