Physical Learning on a Fluidic Network

Physical learning has been proposed as a learning procedure that avoids costly global computation. The tuning parameters (e.g. edge conductance) are updated using only local information such as pressure differences with neighboring nodes, while the global computation is performed implicitly by the governing physical laws (e.g. Kirchhoff's Law). This global feedback is exploited through an update rule that compares the local pressure drops to those in another network where the target-node pressures are nudged toward their desired values. We extend this framework from linear resistor networks to airflow networks operating in the turbulent regime with nonlinear valve characteristics. In simulations, we investigate the convergence behavior of physical learning on networks with a limited number of tunable edges and its ability to restore target pressures after edge damage. We further examine how network topology influences the simultaneous learning of multiple target-pressure configurations under different input-pressure combinations.