### Physics-based and Data-Driven Reduced-Order Modeling for Engineering Systems

Course Title: SPTP: PHYS-BASD & DATA-DRIVEN

CRN: 55531 (PETE)

Time: 02:20 PM-05:10 PM, Thu

Location: 313 RICH

Credit Hours: 3

**Description**

This course covers the introduction to surrogate and reduced order modeling to speed up engineering workflows, including, but not limited to, multiphysics applications in engineering where reduced-order modeling can mitigate many expensive computations. Such examples include reservoir simulation, production optimization, complex multiphase flow simulation, neutron diffusion, coupled neutronics/thermal-hydraulics, nuclear heat transfer, and other pertinent areas. It is intended primarily for graduate students interested in any computational science/ engineering application. Model reduction, proxy modeling, and surrogate modeling and their variants are becoming indispensable tools for computational-based design and optimization, statistical analysis, embedded computing, and real-time optimal control. This course will present a survey on physics-based model reduction for large-scale dynamical systems and on data-driven modeling based on surrogate and machine learning techniques. The course material described below is complemented by a balanced set of theoretical, algorithmic, and MATLAB/Python computer programming homeworks and assignments. Invited lectures from researchers and professionals in model reduction will be given as time permits.

**Prerequisites**

Linear algebra, numerical computation, matrix computation. Basic numerical methods for Partial Differential Equations and Ordinary Differential Equations. Depending on the student’s area, some introductory material in reservoir simulation and reactor multi-physics will be given

**Learning Outcomes**

- Understand the limitations of current simulation models and why some form of model reduction/approximation is necessary.
- Develop a basic understanding of current approaches to reduced-order modeling of large-scale systems, and in particular, to problems arising in energy (e.g., porous media flow, neutron diffusion, heat transfer) engineering.
- Bridge the gap between theoretical foundations, mathematical modeling, simulation and practical implementations of the algorithms presented in the class to solve real world large-scale problems faced by scientists and energy engineers

**Textbook and/or Resource Materials**

The main source of material for the course will be a series of notes and slides handed out to the students

([GIL] and [RAG] notes). Complementary textbooks are:

- [GIL] Eduardo Gildin. Lecture Notes
- [RAG] Jean Ragusa. Lecture Notes
- [PYT1] Rick Muller. A Crash Course in Python for Scientists. https://nbviewer.jupyter.org/gist/rpmuller/5920182
- [PYT2] Hans Petter Langtangen. A Primer on Scientific Programming with Python. Springer 2016
- [MAT ] Cleve Moler. Numerical Computing with MATLAB. SIAM 2004.
- [MOR1] Model Reduction and Approximation: Theory and Algorithms edited by Peter Benner, Albert Cohen, Mario Ohlberger, Karen Willcox. SIAM 2017
- [MOR2] Athanasios C. Antoulas. Approximation of Large-Scale Dynamical Systems. SIAM 2006
- [MOR3] Daniel Wirtz. Model Reduction for Nonlinear Systems: Kernel Methods and Error Estimation. epubli GmbH, 2014.
- [MOR4] Model Reduction of Parametrized Systems. Edited by Peter Benner, Mario Ohlberger, Anthony Patera, Gianluigi Rozza, Karsten Urban. Springer, 2014.
- [MOR5] Reduced Order Methods for Modeling and Computational Reduction edited by Alfio Quarteroni, Gianluigi Rozza. Springer, 2014.
- [MOR 6] Steven L. Brunton and J. Nathan Kutz. Data-Driven Science and Engineering: Machine Learning, Dynamical Systems, and Control. 1st Edition, Cambridge University Press; 2019.
- [MOR 7] J. N. Kutz, S. L. Brunton, B. Brunton, J.L.Proctor. Dynamic Mode Decomposition: Data-Driven Modeling of Complex Systems. SIAM-Society for Industrial and Applied Mathematics, 2016
- [DD_SUR1] Nathan Kutz, Data-Driven Modeling & Scientific Computation: Methods for Complex Systems & Big Data. 1st Edition, OUP Oxford, 2013
- [DD_SUR2] A. I. J. Forrester, A. Sóbester, A. Keane, Engineering Design via Surrogate Modelling: A Practical Guide 1st Edition, 2008 John Wiley & Sons, Ltd
- [DD-SUR2] Andy Keane, Prasanth Nair. Computational Approaches for Aerospace Design: The Pursuit of Excellence

**Course Schedule (Tentative)**

Week | Topic | Suggested Reading |
---|---|---|

1 | Course Introduction; Large scale dynamical systems, Reservoir Simulation, Reactor Multiphysics | GIL, RAG, PYT1, PY2, MAT1 |

2 | Python/Matlab for numerical computing and machine learning | PYT1, PY2, MAT1 |

3 | General Approximation methods and surrogate modeling (kriging, response surface) | DD_SUR1, SS_SUR2, DD_SUR3 |

4 | Dimensionality reduction (Singular value decomposition, Fourier, Wavelets, Sparsity) | GIL, RAG, MOR1, MOR2 |

5-6 | Machine Learning/Neural Nets | GIL, RAG, MOR6 |

7-8 | Dynamical Systems. Controllability/Observability | MOR1, MOR2, MOR6 |

9-10 | Model Reduction Concepts/System Theory – Balanced Truncation | MOR1 through MOR6 |

11 | Nonlinear model order reduction – Proper Orthogonal Decomposition (POD)-based methods | GIL, RAG, MOR1, MOR2 |

12 | POD with Discrete Empirical Interpolation | GIL, RAG |

13 | Dynamic Mode Decomposition methods | GIL, RAG, MOR6 |

14 | Other reduced-order modeling in reservoir engineering and reactor multiphysics | GIL, RAG |