Numerical methods for unraveling inter-particle potentials in colloidal suspensions: A comparative study for...

Area of Science:

• Soft matter physics
• Computational materials science
• Statistical mechanics

Background:

• Determining interparticle interaction potentials is crucial for understanding soft matter systems.
• Model-free numerical methods offer powerful tools for inferring potentials from structural or dynamic data.
• Existing methods have limitations regarding data requirements and applicability to non-equilibrium systems.

Purpose of the Study:

• To compare the performance and applicability of three distinct model-free numerical methods for potential inversion: iterative Boltzmann inversion (IBI), test-particle insertion (TPI), and ActiveNet (a machine-learning approach).
• To evaluate these methods using archetypal two-dimensional colloidal models and experimental microscopy data.
• To provide guidance for selecting appropriate inversion methodologies for diverse scientific applications.

Main Methods:

• Iterative Boltzmann Inversion (IBI): Utilizes the radial distribution function to reconstruct potentials.
• Test-Particle Insertion (TPI): Employs particle configurations (snapshots) to derive pair and higher-body potentials without simulations.
• ActiveNet (Machine Learning): Analyzes time-tracked particle trajectories to determine forces and potentials, capable of handling non-equilibrium conditions.

Main Results:

• IBI is suitable when only the radial distribution function is available.
• TPI can extract potentials from particle positions without requiring simulations.
• ActiveNet can unravel interactions from one-body forces and does not need equilibrium distributions, but requires time-tracked particles and outputs forces.

Conclusions:

• The choice of numerical method depends critically on the available data (radial distribution function, particle positions, or time-tracked trajectories) and system conditions (equilibrium vs. non-equilibrium).
• These findings offer a practical guide for researchers applying potential inversion techniques to experimental and simulation data.
• The study serves as a benchmark for future developments in computational methods for soft matter systems.