A local learning rule for training precise stress patterns

We develop a simple local learning rule that allows us to encode desired stress patterns in a disordered network of springs. Our goal is to control the stresses on a subset of the bonds, which we call targets. The remaining bonds are the learning degrees of freedom and each is assumed to be a spring and dashpot in series. By applying training stresses to the targets we cause the system to evolve until ultimately, in force balance, the system acquires the desired stresses. We show that the system is able to learn random stress patterns to computer precision. Training is successful for a large number of bonds, approaching the theoretical limit dictated by the Maxwell-Calladine theorem. We conclude by demonstrating that our training rule is robust and applicable to dashpots with a yielding stress. Our work is another example of ordinary matter whose properties can be precisely controlled through training rather than by design.