Inferring interaction potentials from particle trajectories

Interaction potentials provide rich information about systems of interacting and self-assembling particles. Measuring interaction potentials has repeatedly revealed novel physics, and extracting effective interactions in complex systems provides a path towards simulation and design in systems where the precise physics is unknown. However, measurements of interaction potentials in experiments are difficult and time-intensive. Moreover, previous methods of measuring interparticle potentials rely on highly constrained motion of small numbers of particles at equilibrium, placing limits on which interactions can be measured. We introduce a method for inferring interaction potentials directly from trajectory data. Beginning with a form for the equations of motion, we find the potential that maximizes the probability of observing a known trajectory. The method is valid both in and out of equilibrium, and is well-suited to large numbers of interacting particles. We demonstrate our method in both simulated and experimental colloidal systems.