Optimization of the volume-to-point heat conduction problem with automatic differentiation based approach

Abstract

Heat conduction optimization problems, such as the volume-to-point problem, have always been core issues in industry and electronics cooling. Existing approaches either limit the solution space by using priori structures, or use manual operation rules to adjust the solutions gradually. And there does not exist a general way to deal with arbitrary objectives. The present study develops a novel method by using automatic differentiation technique. The heat conduction process is converted into a recurrent convolutional neural network equivalently, and the automatic differentiation technique is utilized to calculate the gradient of the final objective with respect to the thermal conductivity field directly. Based on these techniques, the thermal conductivity field is optimized directly to minimize the hot spot temperature. Cases with different heat sinks are introduced to test the proposed optimization method, respectively. Results demonstrate that the average temperature and hot spot temperature are both reduced remarkably after using the proposed method. Furthermore, compared with the previous iteration methods based on entropy generation minimization or entransy dissipation minimization, the proposed method produces similar results when minimizing the average temperature, and reduces the hot spot temperature rising by 17% ∼ 33% when minimizing the hot spot temperature. The optimization method based on automatic differentiation technique exhibits the potential capability of handling with various types of objectives.