Accurate identification of basins of attraction in jammed and glassy systems

The mapping of liquid configurations to their inherent structures has been a critical component of

many studies of jammed and glassy systems. This mapping was previously established using

optimization algorithms neglecting the characteristics of the steepest descent ODE. We show that

directly solving for the trajectory using an implicit variable-order variable-step ODE solver (CVODE),

provides a nearly exact mapping for systems with more than 1000 particles. This allows us to

show that generic (and broadly adopted) optimizers never converge to the true basin of attraction

beyond a characteristic system size. We also present an approach that restricts the use of ODE

solvers only to the non-convex regions of the energy landscape, thus achieving significantly

improved performance with nearly no loss in accuracy. Finally, we explore the implications of

this incorrect mapping in the analysis of the structural relaxations of glassy systems.