Physics-based machine learning and data-driven reduced-order modeling

This thesis considers the task of learning efficient low-dimensional models for dynamical systems. To be effective in an engineering setting, these models must be predictive -- that is, they must yield reliable predictions for conditions outside the data used to train them. These models must also be able to make predictions that enforce physical constraints. Achieving these tasks is particularly challenging for the case of systems governed by partial differential equations, where generating data (either from high-fidelity simulations or from physical experiments) is expensive. We address this challenge by developing learning approaches that embed physical constraints. We propose two physics-based approaches for generating low-dimensional predictive models. The first leverages the proper orthogonal decomposition (POD) to represent high-dimensional simulation data with a low-dimensional physics-based parameterization in combination with machine learning methods to construct a map from model inputs to POD coefficients. A comparison of four machine learning methods is provided through an application of predicting flow around an airfoil. This framework also provides a way to enforce a number of linear constraints by modifying the data with a particular solution. The results help to highlight the importance of including physics knowledge when learning from small amounts of data. We also apply a data-driven approach to learning the operators of low-dimensional models. This method provides an avenue for constructing low-dimensional models of systems where the operators of discretized governing equations are unknown or too complex, while also having the ability to enforce physical constraints. The methodology is applied to a two-dimensional combustion problem, where discretized model operators are unavailable. The results show that the method is able to accurately make predictions and enforce important physical constraints.

Name thesis:degree_name

Master

Department dc:contributor.department

Massachusetts Institute of Technology. Computation for Design and Optimization Program

Grantor dc:publisher

Massachusetts Institute of Technology

Year dc:date.issued

2019

Author dc:creator

• Swischuk, Renee C.(Renee Copland)

Advisor dc:contributor.advisor

• Karen Willcox and Boris Kramer.

• Computation for Design and Optimization Program.

Statement dc:rights

• MIT theses are protected by copyright. They may be viewed, downloaded, or printed from this source but further reproduction or distribution in any format is prohibited without written permission.

Licence dc:rights.uri

• http://dspace.mit.edu/handle/1721.1/7582

Language dc:language.iso

eng

Handle dc:identifier.uri

https://hdl.handle.net/1721.1/122682

OAI identifier oai:identifier

oai:dspace.mit.edu:1721.1/122682