Training thermodynamic computers by gradient descent

Significance As modern computing becomes limited by energy consumption, there is growing interest in physical computing paradigms that can operate closer to fundamental thermodynamic limits. Thermodynamic computing is an emerging field in which computation is done by the natural time evolution of a physical system in contact with a thermal bath, rather than by explicit simulation on a digital computer. Nonlinear thermodynamic computers can in principle perform nonlinear computations similar to those performed by classical neural networks, but with much less energy consumption. The contribution of the present paper is to show how a thermodynamic computer can be trained to perform such a task using gradient descent, thereby opening the door to the training of thermodynamic computers for large-scale problems.