國立高雄大學圖資館 |

登入

回首頁

Data-Driven Approaches for Differential Equation Governing Systems.

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Data-Driven Approaches for Differential Equation Governing Systems.
作者:	Hu, Yihao.
出版者:	Ann Arbor : ProQuest Dissertations & Theses, 2022
面頁冊數:	130 p.
附註:	Source: Dissertations Abstracts International, Volume: 84-01, Section: B.
附註:	Advisor: Xu, Zhiliang.
Contained By:	Dissertations Abstracts International84-01B.
標題:	Applied mathematics.
電子資源:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=29164276
ISBN:	9798438799313

Data-Driven Approaches for Differential Equation Governing Systems.
Hu, Yihao.

Data-Driven Approaches for Differential Equation Governing Systems. - Ann Arbor : ProQuest Dissertations & Theses, 2022 - 130 p.

Source: Dissertations Abstracts International, Volume: 84-01, Section: B.

Thesis (Ph.D.)--University of Notre Dame, 2022.

This item must not be sold to any third party vendors.

Applying deep learning methods to solve high-dimensional and nonlinear differential equations(DE) has raised much attention recently. A goal of using machine learning in systems of differential equations is to train a surrogate model with prior physics information and generate predictions with stability and accuracy. However, training such models for high-dimensional/nonlinear multi-scale ODE or PDE systems with limited or labeled data is a grant challenge; and the proper design of the architecture of the neural network is still poorly understood.This dissertation explores data-driven methods in modeling and predicting differential equation governing systems. To tackle the training issue in learning switch systems with imbalanced scales, we propose a novel PINN-based neural network model that resolves the training issue of regular PINN in learning nonlinear switch systems. We explore and incorporate batch statistics in physics-constrained loss functions. The numerical results are demonstrated via three examples by semi-supervised learning and supervised learning algorithms with a small batch of the signal dataset.For learning the system of PDEs, a sequence to sequence supervised learning model for PDEs named Neural-PDE is proposed in this work. Unlike the conventional machine learning approaches for learning PDEs, such as CNN and MLP, which require a great number of parameters for model precision, the Neural-PDE utilizes an RNN based structure, which shares parameters among all-time steps. Thus the Neural-PDE considerably reduces computational complexity and leads to a fast learning algorithm. We showcase the prediction power of the Neural-PDE by applying it to problems from 1D PDEs to a multi-scale complex fluid system.Motivated by those innovative methodologies for learning systems of differential equations, we develop a machine learning framework for learning the dynamics of time-dependent oceanic variables across multiply detection sensors. The prediction accurately replicates complex signals and provides comparable performance to state-of-the-art benchmarks.

ISBN: 9798438799313Subjects--Topical Terms:

377601
Applied mathematics.
Subjects--Index Terms:

Differential equations

Data-Driven Approaches for Differential Equation Governing Systems.
LDR:03238nmm a2200373 4500 001 636104
005 20230501063900.5
006 m o d
007 cr#unu||||||||
008 230724s2022 ||||||||||||||||| ||eng d
020 $a 9798438799313
035 $a (MiAaPQ)AAI29164276
035 $a AAI29164276
040 $a MiAaPQ $c MiAaPQ
100 1 $a Hu, Yihao. $3 942417
245 1 0 $a Data-Driven Approaches for Differential Equation Governing Systems.
260 1 $a Ann Arbor : $b ProQuest Dissertations & Theses, $c 2022
300 $a 130 p.
500 $a Source: Dissertations Abstracts International, Volume: 84-01, Section: B.
500 $a Advisor: Xu, Zhiliang.
502 $a Thesis (Ph.D.)--University of Notre Dame, 2022.
506 $a This item must not be sold to any third party vendors.
520 $a Applying deep learning methods to solve high-dimensional and nonlinear differential equations(DE) has raised much attention recently. A goal of using machine learning in systems of differential equations is to train a surrogate model with prior physics information and generate predictions with stability and accuracy. However, training such models for high-dimensional/nonlinear multi-scale ODE or PDE systems with limited or labeled data is a grant challenge; and the proper design of the architecture of the neural network is still poorly understood.This dissertation explores data-driven methods in modeling and predicting differential equation governing systems. To tackle the training issue in learning switch systems with imbalanced scales, we propose a novel PINN-based neural network model that resolves the training issue of regular PINN in learning nonlinear switch systems. We explore and incorporate batch statistics in physics-constrained loss functions. The numerical results are demonstrated via three examples by semi-supervised learning and supervised learning algorithms with a small batch of the signal dataset.For learning the system of PDEs, a sequence to sequence supervised learning model for PDEs named Neural-PDE is proposed in this work. Unlike the conventional machine learning approaches for learning PDEs, such as CNN and MLP, which require a great number of parameters for model precision, the Neural-PDE utilizes an RNN based structure, which shares parameters among all-time steps. Thus the Neural-PDE considerably reduces computational complexity and leads to a fast learning algorithm. We showcase the prediction power of the Neural-PDE by applying it to problems from 1D PDEs to a multi-scale complex fluid system.Motivated by those innovative methodologies for learning systems of differential equations, we develop a machine learning framework for learning the dynamics of time-dependent oceanic variables across multiply detection sensors. The prediction accurately replicates complex signals and provides comparable performance to state-of-the-art benchmarks.
590 $a School code: 0165.
650 4 $a Applied mathematics. $3 377601
650 4 $a Statistics. $3 182057
650 4 $a Computer science. $3 199325
653 $a Differential equations
653 $a Machine learning
653 $a PINN
690 $a 0364
690 $a 0984
690 $a 0463
710 2 $a University of Notre Dame. $b Applied and Computational Mathematics and Statistics. $3 942418
773 0 $t Dissertations Abstracts International $g 84-01B.
790 $a 0165
791 $a Ph.D.
792 $a 2022
793 $a English
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=29164276