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SC16-002 Mechanistic Data Science for STEM Education and Applications

Instructors: Drs. Wing Kam Liu (Northwestern University), Zhengtao Gan (Northwestern University), Mark Fleming (Fusion Engineering), Victor Oancea (Dassault Systemes), Jing Bi (Dassault Systemes)

Mechanistic data science combines mathematical scientific principles with available data.  Mathematical scientific principles provide the fundamental understanding of the world and allow predictions which drive new discoveries and enable future technologies. Unfortunately, the development of new scientific principles often trails the pace of new inventions.  The ability to combine known scientific principles with newly collected data will be a boon for new inventions. In this short course,  three types of scientific/engineering problems will be discussed:

Type 1 problems have abundant data but undeveloped or unavailable scientific principles.  These are often called purely data-driven problems. 

Type 2 problems have limited data and limited scientific knowledge, and both the data and the scientific principles are needed to provide a complete solution. 

Type 3 problems have known mathematical science principles with uncertain parameters. These can be computationally burdensome to solve. 

This short course first introduces Mechanistic Data Science (MDS) as a structured methodology for combining data science tools with mathematical scientific principles (i.e., “mechanistic” principles) to solve intractable problems.  Traditional data science methodologies require copious quantities of data to show a reliable pattern, but the amount of required data can be greatly reduced by considering the mathematical science principles. MDS is the backbone of a mechanistic artificial intelligence (AI) framework.  The MDS-AI framework will leverage MDS with machine learning methods like active deep learning and hierarchical neural network(s) to process the input data, extract mechanistic features from it, reduce dimensions, learn hidden relationships through regression and classification, and provide a knowledge database.  The resulting reduced order form can be utilized for design and optimization of new scientific and engineering systems. The short course will cover: 1) Multimodal data generation and collection, 2) extraction of mechanistic features and knowledge-driven dimension reduction, 3) reduced order surrogate models and deep learning for regression and classification, 4) the formulation of system and design for optimization, and 5) the application of an MDS-AI Software system to address pressing global issues such as additive manufacturing, metallic and polymer matrix composites material systems, and biomedical imaging in medical sciences. 


  1. Wing Kam Liu, Zhengtao Gan, Mark A. Fleming, “Mechanistic Data Science for STEM Education and Applications”, Springer, to be published in July 2021.
  2. S. Saha, Z. Gan, L. Cheng, J. Gao, O. L. Kafka, X. Xie, H. Li, M. Tajdari, A. H. Kim, and W. K. Liu, "Hierarchical Deep Neural Network (HiDeNN): An artificial intelligence (AI) framework for Computational Science and Engineering,” Comput. Methods Appl. Mech. Engrg. 373 (2021) 113452.
  3. M. Tajdari, A. Pawar, H. Li, F. Tajdari, A. Maqsood, E. Cleary, S. Saha. Y.J. Zhang, J. F. Sarwark, W. K. Liu, “Image-based Modeling for Adolescent Idiopathic Scoliosis: Mechanistic Machine Learning Analysis and Prediction,” Comput. Methods Appl. Mech. Engrg. 374 (2021) 113590
  4. Hengyang Li, Orion L. Kafka, Jiaying Gao, Cheng Yu, Yinghao Nie, Lei Zhang, Mahsa Tajdari, Shan Tang, Xu Guo, Gang Li, Shaoqiang Tang, Gengdong Cheng, Wing Kam Liu, “Clustering discretization methods for generation of material performance databases in machine learning and design optimization,” Computational Mechanics, (2019) 64:281–305





8:00 – 8:30 AM

Registration and Sign in

8:30 – 9:30 AM

Wing Kam Liu

Mark Fleming

Introduction to Mechanistic Data Science for STEM Education and Applications (chapters 1 and 7 of the MDS book and references)

9:30 – 10:30 AM

Wing Kam Liu

Mark Fleming

Multimodal generation and collection and mechanistic feature extraction based on short time Fourier transform, wavelets and multiresolution analysis, focusing on concepts and interpretations of features extractions (chapter 2 of the MDS book and references)

10:30 – 10:45 AM

Virtual Coffee Break

10:45 – 11:45 AM

Zhengtao Gan

Knowledge-driven dimension reduction and surrogate reduced order models: SVD, PCA, and PGD (chapter 5 of the MDS book (references on HiDeNN-PGD)

11:45 – 12:45 PM

Virtual Lunch

12:45 – 1:45 PM

Zhengtao Gan

Wing Kam Liu

Deep learning for regression and classification with applications: COVID-19 classification and musical instrument sound conversion (chapter 6 of the MDS book and references)

1:45 – 2:45 PM

Zhengtao Gan

Wing Kam Liu

Exploration of two new ideas

  1. DimensionNet: A Deep Learning Network for Discovering Dimensionless Numbers (references)
  2. Self-consistent Clustering Analysis (SCA), a mechanistic data-driven model for computational mechanics of materials

2:45 – 3:00 PM

Virtual Coffee Break

3:00 – 4:00 PM

 Mark Fleming

Wing Kam Liu

System and design:

Chapter 7 of the MDS book

Mechanistic data-driven prediction of as-built mechanical properties in metal additive manufacturing (references)

4:00 – 5:00 PM

Jing BI

Victor Oancea

Data driven approaches for cross domain industrial applications: design exploration, manufacturing and health sciences: model surrogate, order reduction, rule extraction, model calibration and correction