The ability of a feed-forward neural network to learn and classify different states of polymer configurations is systematically explored. Performing numerical experiments, we find that a simple network model can, after adequate training, recognize multiple structures, including gaslike coil, liquidlike globular, and crystalline anti-Mackay and Mackay structures. The network can be trained to identify the transition points between various states, which compare well with those identified by independent specific-heat calculations. Our study demonstrates that neural networks provide an unconventional tool to study the phase transitions in polymeric systems.

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A feed-forward neural network has a remarkable property which allows the network itself to be a universal approximator for any functions. Here we present a universal, machine-learning based solver for multi-variable partial differential equations. The algorithm approximates the target functions by neural networks and adjusts the network parameters to approach the desirable solutions. The idea can be easily adopted for dealing with multi-variable, coupled integrodifferential equations, such as those in the self-consistent field theory for predicting polymer microphase-separated structures.

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