Welcome to the website of UQLID (pronounced as "Euclid") Lab at Northern Arizona University.

People:

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Subhayan De, Ph.D.
Assistant Professor
Northern Arizona University

CV (Nov. 2021).




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Maryam Maghazeh
Graduate Research Assistant


Maryam joined NAU in Spring 2023. Prior to joining NAU, she completed her Bachelor's and Master's degrees from the Iranian University of Science and Technology in 2018 and 2021, respectively, during which she worked on computational fluid dynamics. Her research at NAU focuses on topology optimization of fluid-structure interaction problems.

Research Projects:

The main research goal of UQLID Lab is to establish new probabilistic data-driven paradigms to efficiently develop and validate models using machine learning tools that can be used for the design of multi-scale multi-functional structural systems and materials.
Figure: Research activities at UQLID Lab.
Recently, machine learning (ML)-assisted models, such as neural networks, capable of describing some of the complex physical phenomena with good accuracy and reasonable computational cost are increasingly used in engineering applications. For exercises that involve many realizations of the engineering systems (e.g., uncertainty quantification, design under uncertainty), these ML-assisted models can be exploited here to develop physics-based surrogate models that are easy to evaluate once trained but at the same time accurate.However, these networks require a large dataset to train. In this research thrust, efficient training of neural networks using smaller datasets for applications to engineering problems are explored.

Our contributions are:
  • Development of transfer learning strategies for uncertainty quantification of complex engineering systems (paper). [codes]
  • Training of neural networks using l1-regularization and bi-fidelity data (paper).
  • Uncertainty quantification of locally nonlinear dynamical systems using neural networks (paper).
  • Prediction of Ultrasonic Guided Wave Propagation in Solid-fluid and their Interface under Uncertainty using Machine Learning (paper).
  • Application of the proposed strategies to multi-physics engineering prblems.
Figure: Schematic of the bi-fidelity weighted transfer learning.
Figure: Schematic of different regularization strategies. Standard l1 and weighted l1-regularizations are used in this paper to train neural networks.
Figure: The use of neural networks for uncertainty quantification of locally nonlinear dynamical systems.
The robust design of engineering systems requires the inclusion of uncertainties in the optimization process. The aim of this research thrust is to develop efficient design methodology and algorithms that can reduce the computational cost of robust and reliability-based optimization while considering uncertainty across multiple scales.

Topology Optimization under Uncertainty (TOuU)

In topology optimization (TO), we try to think about optimally distributing materials inside the structure to satisfy some performance criteria. However, in the presence of uncertainty, achieving a meaningful optimized design is computationally burdensome as the number of optimization variables is large in TO. In our recent works, we showed that the topology optimization under uncertainty for engineering design could be efficiently performed using multiple variants of the stochastic gradient descent algorithms (including two novel bi-fidelity algorithms), famously employed in the training of neural networks, but tailored for TO applications.
Our contributions are:
  • Development of a stochastic gradient approach for TOuU (paper). [codes]
  • Development of bi-fidelity stochastic gradient descent algorithms with proven linear convergence (paper).
  • Applications: Topology optimization under micro-scale uncertainty, reliability-based topology optimization (paper#1,paper#2).
    
Figure: A typical example used in topology optimization (Two-fold symmetry is used in the movie).

Figure: A bracket is designed to support a payload box under microstructural uncertainty.


Optimal Design of Passive Structural Control Devices

In the recent past, many types of structures have been equipped with control devices to achieve some performance criteria (such as drift or acceleration mitigation). We developed computationally efficient design procedure of passive control devices for complex structures using NVIE approach.
The proposed method has the following characteristics (paper):
  • Realizable computation time for large and complex structures.
  • Trade-off between accuracy and speedup exists.
  • Uncertainty in the existing structure can be incorporated.
  • Application to a benchmark cable-stayed bridge.
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Figure: Efficient optimal design of passive control devices for a cable-stayed bridge.


Probabilistic Model Validation Framework

We developed a computationally efficient model validation framework applicable to models from vast domains based on philosophy advanced by the famous statistician George P. Box: ``Essentially, all models are wrong, but some are useful.'' This framework integrates the principle of falsification into the model selection process within a Bayesian framework utilizing measurement datasets from physical experiments to mitigate the weaknesses of existing individual validation schemes.
Our contributions are:
  • Introduction of false discovery rate and likelihood-bound in model falsification (paper). [codes]
  • A probabilistic machine learning framework is proposed for efficient validation of models (paper).
  • Applications to structural, turbulence, and material modeling problems.
Figure: Proposed probabilistic model validation framework has been applied to a full-scale four-story building tested at Japan's E-Defense Lab.


Efficient Bayesian Model Selection

Bayesian model selection chooses, based on measured data, using Bayes’ theorem, suitable mathematical models from a set of possible models. In structural analysis, linear models are often used to facilitate design and analysis, though they do not always accurately reproduce actual structural responses. When the models also require the inclusion of nonlinearity to improve accuracy, the computation time required for response simulation increases significantly.
To address this issue, our contributions are (paper):
  • Development of a computationally efficient method using Nonlinear Volterra type Integral Equations (NVIE) to model selection problems.
  • Incorporating dynamic time history data for nonlinear models as the modal parameters changes with time in nonlinear models.
  • Using NVIE approach the speedup is upto three orders of magnitude compared to traditional nonlinear solvers.
  • The approach is demonstrated using a 100 DOF building structure subjected to earthquake excitation and a 1623 DOF three-dimensional building subjected to wind excitation.
Figure: A 100 DOF building with hysteretic isolation layer is used in this paper.

Figure: A 1623 DOF (right) building with three tuned-mass dampers on its roof is used in paper.



Publications:

Google Scholar
ResearchGate

Journals
  1. De, S., Maute, K. and, Doostan A. "Topology Optimization under Microscale Uncertainty using Stochastic Gradients", Structural and Multidisciplinary Optimization (in review).
  2. Maute, K. and De, S. "Shape and Material Optimization of Problems with Dynamically Evolving Interfaces", Structural and Multidisciplinary Optimization (in review).
  3. De, S., and Doostan A. "Neural Network Training Using l1 Regularization and Bi-fidelity Data", Journal of Computational Physics (in press).
  4. De, S., Maute, K. and, Doostan A. "Reliability-based Topology Optimization under Uncertainty using Stochastic Gradients", Structural and Multidisciplinary Optimization (2021).
  5. De, S., Ebna Hai, B.S.M., Doostan A. and, Bause, M. "Ultrasonic guided wave-based structural health monitoring under uncertainty using machine learning", Journal of Engineering Mechanics, (2022).
  6. De, S. "Uncertainty Quantification of Locally Nonlinear Dynamic Systems using Neural Networks", Journal of Computing in Civil Engineering, (2021).
  7. De, S., Britton, J., Reynolds, M. and, Doostan A. "On Transfer Learning of Neural Networks using Bi-fidelity Data for Uncertainty Propagation", International Journal for Uncertainty Quantification (2020).
  8. De, S., Maute, K. and, Doostan A. “Bi-fidelity Stochastic Gradient Descent for Structural Optimization under Uncertainty", Computational Mechanics (2020).
  9. De, S., Hampton, J., Maute, K. and, Doostan A. "Topology Optimization under Uncertainty using a Stochastic Gradient-based Approach", Structural and Multidisciplinary Optimization (2020).
  10. De, S., Brewick, P.T., Johnson, E.A. and, Wojtkiewicz S.F. "A Probabilistic Hybrid Framework for Model Validation of Dynamic Systems", Mechanical Systems and Signal Processing (2019).
  11. De, S., Brewick, P.T., Johnson, E.A. and, Wojtkiewicz S.F. "Investigation of Model Falsification using Error and Likelihood Bounds with Application to a Structural System", Journal of Engineering Mechanics (Editor's choice) (2018).
  12. De, S., Johnson, E.A., Wojtkiewicz S.F. and, Brewick, P.T. "Computationally-Efficient Bayesian Model Selection for Locally Nonlinear Structural Dynamical Systems", Journal of Engineering Mechanics (Editor's choice) (2018).
  13. De, S., Wojtkiewicz S.F. and, Johnson, E.A. "Computationally Efficient Optimal Design of Passive Control Devices for a Benchmark Cable-Stayed Bridge", Structural Control and Health Monitoring (2017).
Conferences
  1. De, S., Kamalzare, M., Johnson, E.A. and , Wojtkiewicz S.F., "Efficient Optimal Design of Passive Structural Control Devices for Complex Structures", ASCE Engineering Mechanics Institute Conference, August 2014 . McMaster University, ON, Canada.
  2. De, S., Kamalzare, M., Johnson, E.A. and , Wojtkiewicz S.F., "Computationally-Efficient Bayesian Model Selection for Structural Systems with Local Nonlinearities", ASCE Engineering Mechanics Institute Conference, August 2014, McMaster University, ON, Canada.
  3. De, S., Johnson, E.A. and , Wojtkiewicz S.F., "Efficient Optimal Design-Under-Uncertainty of Passive Structural Control Devices", 12th International Conference on Applications of Statistics and Probability in Civil Engineering, ICASP12, July 2015, Vancouver, BC, Canada.
  4. De, S., Johnson, E.A. and , Wojtkiewicz S.F., "Fast Bayesian Model Selection with Application to Large Locally-Nonlinear Dynamic Systems ", 6th International Conference on Advances in Experimental Structural Engineering, 11th International Workshop on Advanced Smart Materials and Smart Structures Technology, August 1-2, 2015, University of Illinois, Urbana-Champaign, USA.
  5. De, S., Johnson, E.A. and , Wojtkiewicz S.F., Brewick, P.B., "Efficient Bayesian Model Selection for Locally Nonlinear Systems incorporating Dynamic Measurements", 10th International Workshop on Structural Health Monitoring (IWSHM), September 2015, Stanford University, CA, USA.
  6. De, S., Brewick, P.T., Johnson, E.A. and, Wojtkiewicz S.F. "Exploration of Error Rate Criteria to Decide Bounds for Model Falsification'', ASCE Engineering Mechanics Institute Conference, May, 2016, Vanderbilt University, Nashville, TN, USA.
  7. De, S., Brewick, P.T., Johnson, E.A., Wojtkiewicz S.F. and, Bermejo-Moreno I. "Error and Likelihood Bounds for Falsification of Dynamical Models'', IMAC XXXV Conference, 2017, Hyatt Regency Orange County, CA, USA.
  8. De, S., Johnson, E.A. and, Wojtkiewicz S.F. "Efficient Uncertainty Quantification for Locally Nonlinear Dynamical Systems'', ASCE Engineering Mechanics Institute Conference, 2017, University of California, San Diego, CA, USA.
  9. De, S., Brewick, P.T., Johnson, E.A. and, Wojtkiewicz S.F. "Model Falsification in a Bayesian Framework'', ASCE Engineering Mechanics Institute Conference, 2017, University of California, San Diego, CA, USA.
  10. De, S., Yu, T., Johnson, E.A. and, Wojtkiewicz S.F. "Model Validation of a 4 Story Base Isolated Building using Seismic Shake-Table Experiments'', 11th U.S.~National Conference on Earthquake Engineering, 2018, Los Angeles, CA, USA.
  11. De, S., Johnson, E.A. and, Wojtkiewicz S.F. "Uncertainty Quantification of Locally Nonlinear Dynamical Systems using Polynomial Chaos Expansion", SIAM Conference on Uncertainty Quantification (UQ18), 2018, Hyatt Regency Orange County, Garden Grove, CA, USA.
  12. De, S., Dasgupta, A., Johnson, E.A. and, Wojtkiewicz S.F. "Probabilistic Model Validation of Large-Scale Systems using Reduced Order Models", SIAM Conference on Uncertainty Quantification (UQ18), 2018, Hyatt Regency Orange County, Garden Grove, CA, USA.
  13. De, S., Yu, T., Dasgupta, A., Johnson, E.A. and, Wojtkiewicz S.F. "Probabilistic Model Validation of the Isolation layer of a Full-Scale Four-Story Base-Isolated Building", ASCE Engineering Mechanics Institute Conference, , 2018, Massachusetts Institute of Technology, Cambridge, MA, USA.
  14. Dasgupta A., De, S., Yu, T., Johnson, E.A. and, Wojtkiewicz S.F. "Probabilistic validation of material models", ASCE Engineering Mechanics Institute Conference, , 2018, Massachusetts Institute of Technology, Cambridge, MA, USA.
  15. De, S., Maute, K. and, Doostan, A. "Topology Optimization under Uncertainty using Stochastic Gradients", Topology Optimization Roundtable,, 2019, Albuquerque Marriot, Albuquerque, NM, USA.
  16. De, S., Maute, K. and, Doostan, A. "Optimization under Uncertainty Using Stochastic Gradients", 15th U.S. Congress on Computational Mechanics, 2019, Austin, TX, USA.
  17. De, S., Johnson, E.A. and, Wojtkiewicz S.F. "Efficient Evidence Estimation for Bayesian Model Selection", ASCE Engineering Mechanics Institute Conference, , 2019, California Institute of Technology, Pasadena, CA, USA.
  18. Glaws, A., King, R, Reynolds, M., Doostan, A. and, De, S. "Physics-informed Deep Learning for Multi-fidelity Uncertainty Quantification", Workshop on Research Challenges and Opportunities at the interface of Machine Learning and Uncertainty Quantification, 2019, Los Angeles, CA, USA.
  19. De, S., Britton, J., Reynolds, M. and, Doostan, A. "Neural Network Training using Bi-fidelity Data for Uncertainty Quantification", SIAM Conference on Uncertainty Quantification (UQ20),,2020, Munich, Germany (cancelled due to COVID-19).
  20. De, S., Britton, J., Reynolds, M. and, Doostan, A. "Ultrasonic guided wave-based structural health monitoring system in fluid-solid and their interface", 10th European Workshop on Structural Health Monitoring (EWSHM 2020),,2020, Palermo, Italy (postponed due to COVID-19).
  21. De, S. and, Doostan, A. "Multi-fidelity methods for deep neural network surrogates", SIAM Conference on Computational Science and Engineering (CSE21),,2021, Fort Worth, Texas, USA.
  22. De, S., Maute, K. and, Doostan, A. "Topology Optimization in the Presence of Microscale Uncertainty", ASCE Engineering Mechanics Institute Conference,,2021, New York, USA.
  23. De, S., Maute, K. and, Doostan, A. "Use of Stochastic Gradient Descent for Topology Optimization under Reliability Constraints", 16th U.S. Congress on Computational Mechanics,,2021, Chicago, USA.
  24. De, S., Maute, K. and, Doostan, A. "Microscale Uncertainty in Macroscale Topology Optimization", 14th World Congress of Structural and Multidisciplinary Optimization (WCSMO-14),,2021, Boulder, USA.
  25. Maute, K., De, S. and, Doostan, A. "Shape and Material Optimization of Problems with Dynamically Evolving Interfaces", 14th World Congress of Structural and Multidisciplinary Optimization (WCSMO-14),,2021, Boulder, USA.
  26. De, S. and, Doostan, A. "Bi-fidelity Training of Neural Networks Using l1-Regularization", SIAM Conference on Uncertainty Quantification (UQ22),,2022, Atlanta, USA.

Codes

Transfer Learning of Neural Networks

Stochastic Gradient Descent Algorithms

Data-driven Model Falsification Methods

Tutorials

Neural Networks and Backpropagation

Mechanics of Deformable Bodies

Probability and Statistics for Engineers

Model Validation:

Introduction to Statistics using Python:

Invited Talks:



Visitors from unique locations (since May 2021):


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