TY - JOUR
T1 - Hierarchical Deep Learning Neural Network (HiDeNN)
T2 - An artificial intelligence (AI) framework for computational science and engineering
AU - Saha, Sourav
AU - Gan, Zhengtao
AU - Cheng, Lin
AU - Gao, Jiaying
AU - Kafka, Orion L.
AU - Xie, Xiaoyu
AU - Li, Hengyang
AU - Tajdari, Mahsa
AU - Kim, H. Alicia
AU - Liu, Wing Kam
N1 - Funding Information:
The authors would like to acknowledge the support of National Science Foundation ( NSF, USA ) grants CMMI-1762035 and CMMI-1934367 and AFOSR, USA grant FA9550-18-1-0381 . We thank Jennifer Bennett and her academic adviser Jian Cao for providing experimental data for Section 4.1 .
Publisher Copyright:
© 2020 Elsevier B.V.
PY - 2021/1/1
Y1 - 2021/1/1
N2 - In this work, a unified AI-framework named Hierarchical Deep Learning Neural Network (HiDeNN) is proposed to solve challenging computational science and engineering problems with little or no available physics as well as with extreme computational demand. The detailed construction and mathematical elements of HiDeNN are introduced and discussed to show the flexibility of the framework for diverse problems from disparate fields. Three example problems are solved to demonstrate the accuracy, efficiency, and versatility of the framework. The first example is designed to show that HiDeNN is capable of achieving better accuracy than conventional finite element method by learning the optimal nodal positions and capturing the stress concentration with a coarse mesh. The second example applies HiDeNN for multiscale analysis with sub-neural networks at each material point of macroscale. The final example demonstrates how HiDeNN can discover governing dimensionless parameters from experimental data so that a reduced set of input can be used to increase the learning efficiency. We further present a discussion and demonstration of the solution for advanced engineering problems that require state-of-the-art AI approaches and how a general and flexible system, such as HiDeNN-AI framework, can be applied to solve these problems.
AB - In this work, a unified AI-framework named Hierarchical Deep Learning Neural Network (HiDeNN) is proposed to solve challenging computational science and engineering problems with little or no available physics as well as with extreme computational demand. The detailed construction and mathematical elements of HiDeNN are introduced and discussed to show the flexibility of the framework for diverse problems from disparate fields. Three example problems are solved to demonstrate the accuracy, efficiency, and versatility of the framework. The first example is designed to show that HiDeNN is capable of achieving better accuracy than conventional finite element method by learning the optimal nodal positions and capturing the stress concentration with a coarse mesh. The second example applies HiDeNN for multiscale analysis with sub-neural networks at each material point of macroscale. The final example demonstrates how HiDeNN can discover governing dimensionless parameters from experimental data so that a reduced set of input can be used to increase the learning efficiency. We further present a discussion and demonstration of the solution for advanced engineering problems that require state-of-the-art AI approaches and how a general and flexible system, such as HiDeNN-AI framework, can be applied to solve these problems.
KW - Artificial intelligence
KW - Data-driven discovery
KW - Deep learning
KW - Machine learning
KW - Multiscale simulation
KW - Reduced order model
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U2 - 10.1016/j.cma.2020.113452
DO - 10.1016/j.cma.2020.113452
M3 - Article
AN - SCOPUS:85093694943
SN - 0374-2830
VL - 373
JO - Computer Methods in Applied Mechanics and Engineering
JF - Computer Methods in Applied Mechanics and Engineering
M1 - 113452
ER -