Deep Learning Acceleration Optimization of Stress Boundary Value Problem Solvers

The solution to boundary value problems is of great significance in industrial software applications. In this paper, we propose a novel deep learning method for simulating stress field distributions in simply supported beams, aiming to serve as a solver for stress boundary value problems. Our regression network, Stress-EA, utilizes the convolution encoder module and additive attention to accurately estimate the stress in the beam. By comparing the Stress-EA prediction results with the stress values calculated using ABAQUS, we achieve a mean absolute error (MAE) of less than 0.06. This indicates a high level of consistency between the stress values obtained from the two approaches. Moreover, the prediction time of Stress-EA is significantly shorter, taking only 0.0011s, compared to the calculation time of ABAQUS, which is 16.91s. This demonstrates the high accuracy and low computational latency of our model. Furthermore, our model exhibits smaller model parameters, requires less computation, and has a shorter prediction time compared to training results obtained using classic and advanced networks. To accelerate training, we utilize data parallel methods, achieving up to 1.89 speedup on a dual-GPU platform without compromising accuracy. This advancement enhances the computing efficiency for large-scale industrial software applications.