arXiv subjects

Mohammadreza Fakhraei

Publications and source records attributed to Mohammadreza Fakhraei.

3 recordsLinked to original sources

arXiv2026

Approximation of anisotropic pairwise interactions for charged objects using multivariate polynomials and a multipole expansion

We formulate a physics-informed data-driven method for modeling anisotropic pairwise interactions in the presence of long-ranged electrostatics. The method separates the total interaction into a long-ranged electrostatic interaction that is approximated using a multipole expansion truncated at the dipole level and a short-ranged residual interaction that is approximated using multivariate Chebyshev polynomials fit to measurements from a limited number of configurations. We assess the approach on a sequence of aromatic molecules (benzene, benzonitrile, and phenoxide), finding that it produces satisfactory results using a modest cutoff distance for the short-ranged interaction. This method has applications for modeling complex interactions for, and conducting dynamic simulations of, synthetic and biological materials with charge.

cond-mat.soft↗

arXiv2025

Approximation of forces and torques from anisotropic pairwise interactions using multivariate polynomials

The dynamics of anisotropic particles are dictated by forces and torques that can be challenging to mathematically represent in computer simulations. Several data-driven approaches have been developed to approximate these interactions, but they often rely on having large amounts of training data that may be practically difficult to generate. Here, we extend a framework we recently developed for approximating anisotropic pair potentials to the approximation of pairwise forces and torques. The framework uses multivariate polynomials and physics-motivated coordinate transformations to produce accurate approximations using limited amounts of data. We first derive expressions relating the force and torque to partial derivatives of the potential energy with respect to the transformed coordinates used to represent the particle configuration. We then explore several options for approximating the forces and torques, and we critically assess their accuracy using model two- and three-dimensional shape-anisotropic nanoparticles as test cases. We find that interpolation of the pairwise potential energy produces the best result when it is known, but force and torque matching (regression) is a viable strategy when only the force and torque is available.

cond-mat.soft↗

arXiv2025

Approximation of anisotropic pair potentials using multivariate interpolation

The interaction between two particles with shape or interaction anisotropy can be modeled using a pairwise potential energy function that depends on their relative position and orientation; however, this function is often challenging to mathematically formulate. Data-driven approaches for approximating anisotropic pair potentials have gained significant interest due to their flexibility and generality but often require large sets of training data, potentially limiting their feasibility when training data is computationally demanding to collect. Here, we investigate the use of multivariate polynomial interpolation to approximate anisotropic pair potentials from a limited set of prescribed particle configurations. We consider both standard Chebyshev polynomial interpolation as well as mixed-basis polynomial interpolation that uses trigonometric polynomials for coordinates along which the pair potential is known to be periodic. We exploit mathematical reasoning and physical knowledge to refine the interpolation domain and to design our interpolants. We test our approach on two-dimensional and three-dimensional model anisotropic nanoparticles, finding satisfactory approximations can be constructed in all cases.

cond-mat.soft↗