  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.
