Fakhraei Mohammadreza, Kieslich Chris A, Howard Michael P
Department of Chemical Engineering, Auburn University, Auburn, Alabama 36849, United States.
Wallace H. Coulter Department of Biomedical Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332, United States.
J Phys Chem B. 2025 Jul 10;129(27):6985-6996. doi: 10.1021/acs.jpcb.5c01451. Epub 2025 Jun 27.
The interaction between two particles with shape or interaction anisotropy can be modeled by 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 are 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 and 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 that satisfactory approximations can be constructed in all cases.
两个具有形状或相互作用各向异性的粒子之间的相互作用可以通过使用一个依赖于它们相对位置和取向的成对势能函数来建模；然而，这个函数在数学上往往难以公式化。用于近似各向异性对势的数据驱动方法因其灵活性和通用性而备受关注，但通常需要大量的训练数据，当训练数据收集起来计算量很大时，这可能会限制其可行性。在这里，我们研究使用多元多项式插值从有限的一组规定粒子构型中近似各向异性对势。我们考虑标准的切比雪夫多项式插值和混合基多项式插值，后者对已知对势具有周期性的坐标使用三角多项式。我们利用数学推理和物理知识来细化插值域并设计我们的插值函数。我们在二维和三维模型各向异性纳米颗粒上测试了我们的方法，发现在所有情况下都可以构建出令人满意的近似。
