Fourier Feature Embedded Physics-Informed Neural Network-Based Topology Optimization (Ff-Pinnto) Framework for Geometrically Nonlinear Structures

Abstract

This study presents a Fourier feature-embedded physics-informed neural network framework for topology optimization  (FF-PINNTO) of geometrically nonlinear structures. The framework leverages the mesh-free nature of physics-informed neural networks to model nonlinear partial differential equations, addressing instabilities in traditional methods. It integrates the deep energy method and a neural reparameterization scheme, replacing finite element analysis and sensitivity analysis operations. The deep energy method solves the hyperelasticity problem by minimizing potential energy within the neural network, while sensitivity analysis is performed via automatic differentiation. Unlike conventional methods, the framework achieves stable solutions without energy interpolation or relaxation techniques. Fourier feature embedding and periodic activation functions accelerate physics-informed neural network training, enabling more efficient computations than the traditional numerical methods. Benchmark problems validate the efficiency and accuracy of the framework, demonstrating its potential as a robust alternative for nonlinear topology optimization.

Keywords: topology optimization, Physics-informed neural network, Machine Learning, Deep energy method, Nonlinearity