Applications of the physics-informed neural network in computational mechanics

  • Bai, Jinshuai (Tsingshua University)
  • Feng, Xi-Qiao (Tsingshua University)
  • Gu, YuanTong (Tsingshua University)

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In the study of mechanical problems, numerical simulation methods play a crucial role. Their core lies in employing diverse numerical techniques to accurately and efficiently approximate solutions to partial differential control equations based on continuum mechanics, such as equilibrium equations and momentum conservation equations. In recent years, with the rapid development of deep learning technologies, their application in solving partial differential equations has gradually emerged, making deep learning-based computational mechanics methods a hot topic in academia. This report will focus on our research group's latest findings in applying physics-informed neural network (PINN) techniques to the field of computational mechanics. Our research covers various aspects, including linear elasticity, nonlinear elasticity, multibody dynamics, topology optimization, torsional instability, contact problems, and fluid dynamics. Through numerical experiments, we have verified the reliability and stability of this new method in solving nonlinear mechanical problems. This not only provides new ideas for solving mechanical problems but also demonstrates the immense potential and broad prospects of PINN in the field of computational mechanics. We firmly believe that, with continuous technological advancements and in-depth research, PINN will play an increasingly important role in computational mechanics and even in broader scientific fields.