Precise dynamical steady states in disordered materials

Manipulating the microstructure of disordered materials allows for designing precise microscopic responses, yielding materials with exotic properties.  While most work has focused on the quasistatic regime, at finite driving rates mechanics are governed by Newton's equations. The goal of this work is to study the feasibility of creating disordered materials with exotic properties in the dynamic regime.

We employ backpropagation through time and gradient descent to design spatially specific steady states. We find that with small alterations to the structure, a broad range of steady states can be achieved, operating both at small and large amplitudes. We study the effect of varying the damping, which interpolates between the underdamped regime and the overdamped regime, as well as the amplitude, frequency, and phase.

We show that the success of training depends strongly on the amplitude and damping. Most importantly, inertia in Newton’s equations implies there is a relaxation time to reach a steady state. To account for these relaxation rates the gradient of the loss function must be computed with respect to changes at a past time, known as the memory span. The required memory span grows sharply with decreasing damping, near the chaotic regime, and surprisingly also at small amplitudes.

Our work demonstrates that within physical bounds, a broad array of exotic behaviors in the dynamic regime can be obtained allowing for a richer range of possible applications.