Experience suggests that uncertainties often play an important role in quantifying the performance of complex systems. Therefore, uncertainty needs to be treated as a core element in the modeling, simulation, and optimization of complex systems. In this talk, I will first present a review of the novel UQ techniques I developed to conduct stochastic simulations for very large-scale complex systems. First, I will present how to employ deep neural network to build a Processing-Microstructure-Mechanical Properties Relationship. In particular, we will use a fibre-reinforced polymer composite material as an example on predicting stress field based on material?s microstructure and loading condition. In addition, a robust data-driven discovery of physical laws with confidence will be introduced. Discovering governing physical laws from noisy data is a grand challenge in many science and engineering research areas. I will present a new Bayesian approach to data-driven discovery of ODEs and PDEs. The new approach will be demonstrated through a wide range of problems, including Navier-Stokes equations. In addition, solving PDEs and predicting material fracture in a fundamentally different way will be discussed. I will present a new paradigm in solving linear and nonlinear PDEs on varied domains without the use of the classical numerical discretization. Instead, we infer the solution of PDEs using a convolutional neural network with quantified uncertainty. The proposed neural network can predict the solution and its uncertainty simultaneously on-the-fly. Finally, I will introduce a new convolutional neural network named Peri-Net we developed to predict and analyze fracture patterns on a disk in real time. I will present and validate the results using the molecular dynamic collision simulations.

Guang Lin received his M.S. and Ph.D. degrees in applied mathematics from Brown University. He was a Senior Research Scientist at Pacific Northwest National Laboratory from 2008 to 2014. He is currently Director of Data Science Consulting Service, Dean?s Fellow at College of Science, University Scholar, an Associate Professor at the Department of Mathematics, school of Mechanical Engineering, Department of Statistics (Courtesy), Department of Earth, Atmospheric, and Planetary Sciences (Courtesy) at Purdue University. He received NSF faculty early career development award (NSF, 2016), Mid-Career Sigma Xi Award, University Faculty Scholar award (Purdue, 2019), Mathematical Biosciences Institute Early Career Award (MBI, 2015), Ronald L. Brodzinski Award for Early Career Exception Achievement, Department of Energy Pacific Northwest National Laboratory Early Career Award (PNNL, 2012), and Department of Energy Advanced Scientific Computing Research Leadership Computing Challenge award (DOE, 2010). He has had in-depth involvement in developing big data analysis, deep learning and uncertainty quantification tools for a large variety of domains including energy and environment. His research interests include diverse topics in computational science both on algorithms and applications, uncertainty quantification, large-scale data analysis, and multiscale modeling in a large variety of domains. Dr. Lin is currently Associate Editor of Society for Industrial and Applied Mathematics Multiscale Modeling and Simulations.

Birck Nanotechnology Center

Researchers should cite this work as follows:

• Guang Lin (2020), "Uncertainty Quantification and Scientific Machine Learning for Complex Engineering Systems," https://nanohub.org/resources/32565.

  BibTex | EndNote

1. Bayesian
2. Bayesian statistics
3. convolutional neural networks (CNN)
4. data-driven materials discovery
5. deep learning
6. electron cryo-microscopy
7. generalized polynomial chaos (gPC) method
8. machine learning
9. material failure
10. materials properties
11. Navier-Stokes
12. NCN Group - Uncertainty Quantification
13. neural networks
14. PDEs
15. polymers
16. uncertainty quantification (UQ)