Physics-Informed Neural Network-Based Computational Modeling and Analysis of Lipid Bilayer Membranes

This paper presents a physics-informed neural network (PINN) framework for predicting the moment-induced bending behavior of a rectangular lipid membrane.Membrane deformation is modeled using the linearized Helfrich shape equation, which describes the equilibrium response of a lipid bilayer subjected to prescribed edge moments.In the proposed approach, the neural network approximates the transverse membrane deflection without requiring labeled numerical or experimental data.The governing fourth-order partial differential equation and edge moment boundary conditions are incorporated into the training loss, enabling the model to learn solutions that remain consistent with the underlying membrane mechanics.A boundary-constrained trial function is employed to satisfy the zero-deflection condition along the membrane edges, whereas automatic differentiation is used to evaluate the higher-order spatial derivatives required in the governing equation.The predicted deflection fields were validated against the available analytical solution for different applied edge moments.The results agreed closely between the PINN and analytical solutions in terms of maximum deflection and deformation profile.The model accurately captured the symmetric bending response of the rectangular membrane and reproduced the expected increase in deflection with increasing moment intensity.These findings demonstrate that a simple PINN formulation can serve as an effective mesh-free computational tool for solving high-order membrane mechanics problems and can provide a useful alternative to conventional numerical methods for analyzing lipid membrane deformation.