Physical Learning Using Mechanical Spring Networks

Recent advances have unveiled materials and machines as promising platforms for implementing machine learning algorithms. An intriguing avenue lies in the emulation of neural networks using mechanical spring networks. Therein, the training process is a pivotal step. Nevertheless, the development of an efficient training process for spring networks is still in its infancy and faces significant challenges, including extensive computational demands and the approximated gradient information. In our work, we present a novel method harnessing adjoint variable methods to derive a mechanical analogue of backpropagation to facilitate highly efficient training of spring networks. We show that the exact gradient information can be directly extracted from the bonds of the spring network without heavy computation. We further showcase the successful training of a spring network for various machine learning tasks, achieving high accuracy in both classification and regression tasks.