Investigation of Analysis and Gradient-Based Design Optimization Using Neural Networks
Investigation of Analysis and Gradient-Based Design Optimization Using Neural Networks
复制标题
使用神经网络进行分析和基于梯度的设计优化的研究
DOI：
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发表时间：
2020
期刊：
影响因子：
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通讯作者：
P. Beran
中科院分区：
文献类型：
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作者：
K. Fuchi;Eric M. Wolf;D. Makhija;Nathan A. Wukie;Christopher R. Schrock;P. Beran
自适应系统的设计优化需要一个鲁棒的分析方法，可以适应各种变化的设计和边界条件。在这项工作中，物理信息神经网络（PINN）被用来近似解决微分方程在一系列的问题参数值。这种无网格方法只需要在分析域内和沿着边界的采样点处进行残差估计，并且训练过程不需要通过传统的求解方法来求解任何参考问题。训练后的模型可用于预测解场、进行参数空间分析和设计优化。使用自动微分，设计目标及其导数可以作为基于梯度的设计优化的后处理来计算。该方法被证明在一个一维热传导问题所管辖的稳态热方程。使用PINN模型的设计优化说明在一个问题，找到一个材料的过渡位置，以尽量减少在指定位置的温度。不包括问题参数作为输入的PINN模型可以训练到0.05%的误差内。将问题参数作为输入的PINN模型更难训练，特别是当输入到输出关系复杂时。
Design optimization of adaptive systems requires a robust analysis method that can accommodate various changes in design and boundary conditions. In this work, physics-informed neural networks (PINNs) are used to approximate solutions to differential equations across a range of problem parameter values. This mesh-free method simply requires residual evaluation at sampling points within the analysis domain and along boundaries, and the training process does not require any reference problem to be solved through conventional solution methods. The trained model can be used to predict the solution field, conduct parameter space analysis and design optimization. Using automatic differentiation, the design objective and their derivatives can be computed as a post process for a gradient-based design optimization. The method is demonstrated in a 1D heat transfer problem governed by the steady-state heat equation. Use of the PINN model for design optimization is illustrated in a problem of finding a material transition location to minimize temperature at a specified location. The PINN model that does not include problem parameters as input can be trained to within 0.05% error. PINN models that involve problem parameters as inputs are more difficult to train, especially when the input-to-output relationship is complex.