Physics-informed neural networks for topological metamaterial design and mechanical applications

Abstract

With the advancement of metamaterials, topological metamaterials have shown great potential in acoustics, optics, and mechanical engineering due to their unique physical properties. However, traditional design methods often rely on experience and trial-and-error approaches, making it difficult to fully capture complex physical phenomena and achieve specific design objectives. Therefore, advanced computational tools are essential to improve design efficiency and accuracy. In this study, we propose a physics-informed deep learning model on the design of topological metamaterials, enabling low-frequency, broadband performance and flexible manipulation of waveguides in topological gradient metamaterials. First, we design a phononic crystal based on the local resonance principle, and establish a physical equivalent model to quantitatively evaluate the resonance frequency of the local resonator at the wave vector K in the band structure. Next, we develop a physics-informed neural networks (PINN) model using an inverse design model and a pre-trained model, incorporating eigenfrequencies generated by the physical equivalent model into the loss function. The inverse design model can directly generate the design parameters after training, while the pre-trained model can facilitate the mapping from the design parameters to the dispersion relations. Moreover, using the proposed PINN model, we design the metamaterial to meet low-frequency and broadband objectives. Under the broadband design, the complete bandgap of the model expands by about six times compared to the initial sample. Under the low-frequency design, the minimum bandgap frequency reaches approximately 226 Hz. Finally, we explore the application of the designed topological gradient metamaterial in energy localization and waveguide control. In summary, this study addresses the limitations of traditional design methods in the inverse design of topological metamaterials, facilitating their implementation in vibration control, energy capture, and information transmission.