Physics-informed neural energy-force network: a unified solver-free numerical simulation for structural optimization

In this study, a physics-informed neural energy-force network (PINEFN) framework is first proposed to directly solve the optimum design of truss structures that structural analysis is completely removed from the implementation of the global optimization. Herein, a loss function is constructed to guide the training network based on the complementary energy, constitutive equations, and weight of the structure. Now only neural network (NN) is used in our scheme to minimize the loss function wherein weights and biases of the network are considered as design variables. In this model, spatial coordinates of truss members are examined as input data, while corresponding cross-sectional areas and redundant forces unknown to the network are taken account of output. Accordingly, the predicted outputs obtained by feedforward are employed to establish the loss function relied on physics laws. And then, back-propagation and optimizer are applied to automatically calculate sensitivity and adjust parameters of the network, respectively. This whole process, which is the so-called training, is repeated until convergence. The optimum weight of the structure corresponding to the minimum loss function is indicated as soon as the training process ends without using any structural analyses. Several benchmark examples for sizing optimization of truss structures are examined to determine the reliability, efficiency, and applicability of the proposed model. Obtained outcomes indicated that it not only reduces the computational cost dramatically but also yields higher accuracy and faster convergence speed compared with recent literature.