Neural-network-based solver for vesicle shapes predicted by the Helfrich model

That a three-dimensional vesicle morphology can be modeled by an artificial neural network is proposed and demonstrated. In the phase-field representation, the Helfrich bending energy of a membrane is equivalently cast into field-based energy, which enables a more direct representation of a deformable, three-dimensional membrane surface. The core of our method is incorporating recent machine-learning techniques to perform the required energy minimization. The versatile ability of the method, to compute axisymmetric and nonsymmetric shapes, is discussed.