Recent breakthroughs in deep-learning algorithms enable dreams of artificial intelligence (AI) getting close to reality. AI-based technologies are now being developed rapidly, including service and industrial robots, autonomous and self-driving vehicles. This work proposes Two-Way Deepnets (TW-Deepnets) trained using the physics-law-based models such as finite element method (FEM), smoothed FEM (S-FEM), and meshfree models, for real-time computations of both forward and inverse mechanics problems of materials and structures. First, unique features of physics-law-based models and data-based models are analyzed in theory. The training characteristics of deepnets for forward problems governed by physics-laws are then investigated, when an FEM (or S-FEM) model is used as the trainer. The training convergence rates of such an FEM-AI model are examined in relation to the property of the system matrix of the FEM model for deepnets. Next, a study on the training characteristics of deepnets for inverse problems, when the forward FEM-trained AI Deepnets are used as the trainer to train an AI model for inverse analyses. Next, a discussion is conducted on the roles of regularization techniques to overcome the ill-posedness of inverse problems in deepnet structures for noisy data. Finally, TW-Deepnets (FEM-AI and AI-AI models) are presented for real-time analyses of both forward and inverse problems of materials and structures with high-dimensional parameter space. The major finding of this study is as follows: (1) The understandings on the fundamental features of both data-based and physics-based methods is critical for creations of novel game-changing computational methods, which take advantages of both types of methods; (2) The good property of the system matrix of FEM allows effective training of FEM-AI deepnets for forward mechanics problems; (3) Our new technique to training inverse deepnets using FEM-AI deepnets as a surrogate model offers an innovative means, to effectively train deepnets for solving inverse mechanics problems; (4) The TW-Deepnets is capable of performing real-time analysis of both forward and inverse problems of materials and structures with high-dimensional parameter spaces; (5) Such TW-Deepnets can be easily utilized by the mass: a transformative new concept of AI-enabling democratization of complicated computational technology in modeling and simulation.
Quantics-TT Collocation Approximation of Parameter-Dependent and Stochastic Elliptic PDEs
