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Deep Learning of Model Correction and Discontinuity Detection

Zhou, Zixu
http://rave.ohiolink.edu/etdc/view?acc_num=osu1646332839090501

Abstract Details

2022, Doctor of Philosophy, Ohio State University, Mathematics.
In this dissertation, we discuss our work on deep learning of model correction and discontinuity detection. Dynamical systems are widely used to model physical phenomena in science and engineering. The empirical models for those phenomena are often derived under restrictive assumptions for simplicity, leading to low accuracy that is often not enough for reliable prediction. It would be highly desirable to construct more accurate models based on measurement data and the empirical models as prior knowledge. In Chapter 2, we design a novel model correction method to improve prediction accuracy by using machine learning techniques. Given a low-fidelity prior model and some measurement data, we would like to correct the inaccurate prior model over time. When a sufficient amount of measurement data become available, the corrected model is expected to provide more accurate predictions without further need of data. Our Machine Learning idea was inspired by the data assimilation method. Data assimilation is one of the classic data correction methods, which assumes the prior model contains errors whose statistics evolve through time. Then it provides cor- rections to the forecast whenever measurement data arrives. The method has been widely used by atmospheric and oceanic communities and beyond. However, the standard data assimilation does not address the forecast model’s inherent modeling deficiencies: it is only effective at the times when the measurement data are available. Our method, on the other hand, is not only able to correct the forecast model when the measurements are available, but also able to make corrected predictions when measurements are unavailable. Now, we are explored a novel model correction method to overcome the standard data assimilation method’s deficiency. This method is not only corrects data as the data assimilation method, it derives a better model. So it is a model correction method. In the third chapter, we present a discontinuity detector constructed by deep neural networks. Using convolutional neural network (CNN) structure, we design a comprehensive set of synthetic training data. The data consist of randomly generated piecewise smooth functions evaluated at equidistance grids, with labels denoting trou- bled cells where discontinuities are present. Upon successful training of the network, the CNN based detection network is capable of accurately identifying discontinuities in newly given function data by correctly labeling the troubled cells. Even though all of our training data have fixed size, the constructed detector can be applied to function data of arbitrary size, so long as they are on equidistance grids. To increase the detection efficiency in two- and three-dimensional cases, we propose a two-level detection procedure, where the detector is applied to a coarsened grid first and then to the fine grids only at the troubled cells identified at the coarse level. Through an extensive set of numerical tests, we demonstrate that the developed detectors possess strong generalization capabilities, in the sense that they are able to accurately detect discontinuity with structures much more complex than those in the training data. The approach has being used in shock detector for numerical solution of conservation laws[31].
Dongbin Xiu (Advisor)
Yulong Xing (Committee Member)
Lo-bin Chang (Committee Member)
113 p.
Mathematics
data-driven modeling, Machine Learning, model correction

Recommended Citations

Citations

  • Zhou, Z. (2022). Deep Learning of Model Correction and Discontinuity Detection [Doctoral dissertation, Ohio State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=osu1646332839090501

    APA Style (7th edition)

  • Zhou, Zixu. Deep Learning of Model Correction and Discontinuity Detection. 2022. Ohio State University, Doctoral dissertation. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=osu1646332839090501.

    MLA Style (8th edition)

  • Zhou, Zixu. "Deep Learning of Model Correction and Discontinuity Detection." Doctoral dissertation, Ohio State University, 2022. http://rave.ohiolink.edu/etdc/view?acc_num=osu1646332839090501

    Chicago Manual of Style (17th edition)

osu1646332839090501
275
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This open access ETD is published by The Ohio State University and OhioLINK.