Training overdamped dynamics

TL;DR

This paper introduces a framework for controlling overdamped dynamics in many-particle systems by using local update rules inspired by physical learning, enabling the tuning of material responses and behaviors.

Contribution

It develops a novel approach to manipulate overdamped dynamics through local rules derived from the Rayleighian formulation, applicable to dissipative systems.

Findings

Demonstrated tuning of viscous Poisson's ratio in a disordered Maxwell material.

Showed local modifications can control rate-dependent elastic responses.

Validated the approach through simulations of targeted material behaviors.

Abstract

In regimes where inertia is negligible, the temporal evolution is governed by overdamped dynamics. This limit is particularly relevant in soft-matter contexts, such as polymers, colloidal suspensions, and processes occurring at the cellular scale. Being able to manipulate the dynamics of such many-particle systems would enable control over rate-dependent elastic responses, time-dependent material properties, relaxation processes, and perhaps the hydrodynamics of suspensions. In this work, we develop a framework for manipulating overdamped dynamics through local, physically motivated update rules. Our approach is inspired by ideas from physical learning and directed aging, in which microscopic parameters adapt autonomously to endow a material with a desired function. Using the Rayleighian formulation, whose minimization reproduces the overdamped equations of motion, we derive approximate directed-aging and equilibrium-propagation rules tailored to dissipative systems. To demonstrate these ideas, we study a disordered Maxwell material that behaves elastically at short times but flows at long times. By locally modifying the viscous damping, we show that one can tune the viscous Poisson's ratio and shape local mechanical responses. These results illustrate how materials can be trained to exhibit targeted rate-dependent elastic and viscous behaviors.