Hierarchical Deep Learning Neural Network (HiDeNN): An artificial intelligence (AI) framework for computational science and engineering

Sourav Saha, Zhengtao Gan, Lin Cheng, Jiaying Gao, Orion L. Kafka, Xiaoyu Xie, Hengyang Li, Mahsa Tajdari, H. Alicia Kim, Wing Kam Liu*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

51 Scopus citations


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.

Original languageEnglish (US)
Article number113452
JournalComputer Methods in Applied Mechanics and Engineering
StatePublished - Jan 1 2021


  • Artificial intelligence
  • Data-driven discovery
  • Deep learning
  • Machine learning
  • Multiscale simulation
  • Reduced order model

ASJC Scopus subject areas

  • Computational Mechanics
  • Mechanics of Materials
  • Mechanical Engineering
  • Physics and Astronomy(all)
  • Computer Science Applications


Dive into the research topics of 'Hierarchical Deep Learning Neural Network (HiDeNN): An artificial intelligence (AI) framework for computational science and engineering'. Together they form a unique fingerprint.

Cite this