Recently, the development of deep learning has accomplished unbelievable success in many fields, especially scientific computational fields. And almost all problems and physical phenomena can be described by partial differential equations. In this work, we proposed two potential high-order geometric flows. Motivation physical-information neural networks traditional level set method (LSM), have ...

Abstract We present an extension of the projection method proposed by Challis et al. (Int J Solids Struct 45(14–15):4130–4146, 2008) for constrained level set-based topology optimisation that harnesses Hilbertian velocity extension-regularisation framework. Our chooses a normal set function as linear combination (1) orthogonal operator applied to extended objective shape sensitivity and (2) wei...

Abstract The ability to efficiently solve topology optimization problems is of great importance for many practical applications. Hence, there a demand efficient solution algorithms. In this paper, we propose novel quasi-Newton methods solving PDE-constrained problems. Our approach based on and extends the popular algorithm Amstutz Andrä (J Comput Phys 216: 573–588, 2006). To do so, introduce ne...