Understanding the complex physics of particle-based systems at the nanoscale and mesoscale increasingly relies on simulation methods, empowered by exponential advances in computing speed. A major impediment to progress lies in reliably obtaining the interaction potential functions that control system behavior – which are key inputs for any simulation approach – and which are often difficult or impossible to obtain directly using traditional experimental methods.
Here, we present a straightforward methodology for generating pair potential functions from large multi-particle trajectory datasets, with no operational constraints regarding their state of equilibration, degree of damping, or presence of hydrodynamic interactions. In essence, particle trajectories are used to compute numerical estimates of positional derivatives, i.e., velocities and/or accelerations, which are then used to infer forces as a function of inter-particle separation. The approach described here shares some important aspects with, and differs in key ways from, the force-matching (FM) technique originally proposed by Ercolessi and Adams  for the parametrization of empirical potentials using ab initio data, and later generalized into a powerful coarse-graining framework by Voth and coworkers . Essentially, both the present approach and the numerous FM variants seek to fit a pairwise force field using information obtained from some reference system. However, while the FM technique uses forces computed from configurations obtained from simulations performed with a reference (known) force-field to fit a simpler one, the present approach numerically estimates forces from trajectories of particles that are subject to some unknown interparticle interaction force-field. Moreover, we consider the possibility that the particle trajectories used to approximate forces maybe additionally be impacted by thermal fluctuations, measurement uncertainty and hydrodynamic effects. Using simulated datasets, we demonstrate that the method is highly robust against trajectory perturbations from Brownian motion and common errors introduced by particle tracking algorithms.
1. F. Ercolessi and J. B. Adams, "Interatomic potentials from first-principles calculations: the force-matching method," EPL (Europhysics Letters) 26, 583 (1994).
2. S. Izvekov and G. A. Voth, "Multiscale coarse graining of liquid-state systems," The Journal of Chemical Physics 123, 134105 (2005).