Persistent Homology Analysis of Learned Tasks in Physical Learning Systems

Recent work has shown that physical systems such as mechanical, flow and electrical networks

can be trained to perform complex tasks. For tasks such as the delivery of specified pressure

drops across pairs of specified output nodes in response to a specified pressure drop at a

specified pair of input nodes, it has been shown that the learned response can be adduced from its

topological signature. Here we expand the persistent homology analysis to more complex tasks

such as the delivery of specified pressures to specified output nodes in response to specified

pressures at a set of input nodes, as well as linear regression and classification.