A general differentiable layout optimization framework for heat transfer problems

In the present work, we intend to demonstrate how to efficiently perform heat source layout design in a gradient-based way to maximally enhance the performance of heat transfer systems. To this end, a general and differentiable heat source layout optimization framework based on parameterized level set functions is proposed to optimize a thermal objective. Heaviside projection is utilized to realize an analytical description of the heat source intensity function, thus engaging a differentiable finite element analysis (FEA) implementation. The automatic differentiation technique is incorporated into this framework for sensitivity analysis, which can avoid tedious manual derivation work. Furthermore, gradient oscillations caused by improper finite element discretization are observed within components moving boundaries, thus possibly resulting in optimization failures. To remedy this problem, an adaptive multiresolution FEA method is proposed to enhance the awareness of component boundaries and eliminate this instability without introducing an extra FEA cost. Several numerical experiments are presented to illustrate positive effects of the adaptive multiresolution strategy and demonstrate the effectiveness of the proposed general and differentiable approach in heat conduction problems. To the best of our knowledge, it is the first time to realize such a framework for heat transfer systems with arbitrary-shaped heat sources. It is very promising to extend this framework to other physical field problems, or combine this framework with a deep learning-based surrogate in a unified way and implement a more efficient low-cost layout design in future research.