Hierarchical Deep-learning Neural Networks Artificial Intelligence (HiDeNN-AI)

This seminar introduces the participants to mechanistic computational intelligence tools that can combine training/learning, calibrating, and solving (partial differential equations with unknown parameters) through deep learning-based computations for large-scale scientific and engineering (S&E) problems. The lecture covers the synergy between the interpolation and deep learning theories to increase the accuracy (Hierarchical Deep-learning Neural Network (HiDeNN)); extending the capability of HiDeNN using Convolution (C-HiDeNN); introduction of Tensor Decomposition (TD) to C-HiDeNN for learning and calibration of high dimensional data; and applications of C-HiDeNN in S&E. The advanced topics include kernel-based interpretation of deep neural networks and connection between interpolation and convolution-based methods.