冲击动力学反问题及其反演方法综述

随着计算机技术的快速发展，深度学习在工程领域的应用越来越广泛。在实际应用中，用于训练的数据集往往具有“小样本”、“高维度”、“稀疏”等特征，这导致传统深度学习模型的适用范围十分有限。该文建立了一种基于迁移学习增强的物理信息神经网络模型，用于解决数据稀疏的力学正、反问题。结合迁移学习策略，利用源模型中已有知识来加强目标任务中的学习，从而提高学习的效率，实现不需要大量数据就能得到较好预测性能的目标。该方法在薄板(两端简支+两端固支)的数据集上训练源模型，基于深度迁移学习从源模型上提取神经网络特征；利用目标任务中稀疏数据集实现源模型的微调，进而对不同边界的薄板响应预测(正问题)和边界识别(反问题)的目标任务进行验证。研究结果表明，该方法在小样本的目标任务上具有良好的精度和泛化能力。相比数据驱动的深度学习模型，物理信息神经网络模型可以有效避免数据生成带来的成本和网格独立性等问题。

Survey on inverse problem and its inversion methods of impact dynamics

Deep learning has become increasingly popular in the engineering profession as computer technology has advanced. However, the data set used for training frequently has the characteristics of a small sample set, of a high dimension and sparse in practical application, limiting the application breadth of standard deep learning models. In this study, a transfer learning enhanced physics-informed neural network is developed to solve the forward and inverse mechanics problems with the sparse data set. The physics-informed model, when used in conjunction with the transfer learning method, improves learning efficiency and maintains predictability in the target task by using existing information from the source model without requiring a large amount of data. The method starts by using a data set to train the source model of a thin plate (simple support at both ends and fixed support at both ends). The features of neural network are retrieved from the source model based on deep transfer learning. The source model is fine-tuned by using the sparse data set in the target task. The target task of response prediction (forward problem) and boundary recognition (inverse problem) in the thin plates with different boundaries are verified. The results show that the method has high accuracy and generalization ability for the target task with a small sample set. Compared with the single data-driven deep learning method, the physics-informed deep transfer learning has the advantage of avoiding the cost and grid independence caused by data generation.