東華大學圖書館 |

Physics-Informed Learning of Complex Systems with Sparse Data.

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Physics-Informed Learning of Complex Systems with Sparse Data./
作者:	Chen, Zhao.
出版者:	Ann Arbor : ProQuest Dissertations & Theses, : 2021,
面頁冊數:	179 p.
附註:	Source: Dissertations Abstracts International, Volume: 83-04, Section: B.
Contained By:	Dissertations Abstracts International83-04B.
標題:	Civil engineering. -
電子資源:	https://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=28717863
ISBN:	9798544281849

Physics-Informed Learning of Complex Systems with Sparse Data.
Chen, Zhao.

Physics-Informed Learning of Complex Systems with Sparse Data. - Ann Arbor : ProQuest Dissertations & Theses, 2021 - 179 p.

Source: Dissertations Abstracts International, Volume: 83-04, Section: B.

Thesis (Ph.D.)--Northeastern University, 2021.

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

Current practices on the modeling of complex dynamical systems have been mostly rooted in the use of ordinary and/or partial differential equations (ODEs, PDEs) that govern the system behaviors. Apart from governing equations obtained from rigorous first principles, there remain many real-world complex systems whose governing equations and properties are elusive or partially revealed. A novel perspective to analyze such unknown systems is to tackle the fundamental governing equations using symbolic regression that heavily relies on data quantity/quality in the current literature.As the synergistic advancement of machine learning theories, hardware power and sensing technologies, harnessing novel computational theories to analyze statistics patterns embedded in big data provide new opportunities to advance our understanding of complex physical systems. While bottom-up machine learning approaches have delivered super-human accuracy for visual recognition, language translation and even creating fine arts by digesting a huge amount data, their black-box nature renders it susceptible to generalization issues when the new data is statistically distinct from the training data or when the training data is less reliable (e.g. sparse and noisy).To further relax the strong dependence on quality/quantity of training data for symbolic system identification and leverage the horsepower of machine learning, in this dissertation we propose a series of physics-informed computational methods encoding rough domain knowledge into data-driven models, which address the aforementioned issues when machine learning is applied to symbolic system identification and state forecasting of spatio-temporal or dynamic systems (in the form of PDEs or ODEs). In particular, rough domain knowledge is embedded in machine learning models in such a way that by fitting to the training data, the physics mechanism of measurements is also learned and stored in the form of symbolic governing equations. Reciprocally, the constraint of domain knowledge refrains the data-driven model from being perturbed by noise and data scarcity. Therefore, by learning the underlying physics mechanism, the trained model is able to predict well for never-seen new data, overcoming the detrimental generalization issues faced by popular deep learning models. Furthermore, we can distill the symbolic governing equations from lower quality and quantity data than peer symbolic regression methods. The design and pruning of a novel physics representation have also been investigated to allow a more diverse and cost-effective functional search than current literature.Specifically, our contributions are as follows in the chapter order:When the governing equation is aware, we introduce a Bayesian learning with sensitivity analysis for model updating and sparse damage identification in various structural operational stages using scarce and noisy data;When the governing equation is unknown, we develop a sparsity-promoted physics-informed deep learning approach to discover governing laws for nonlinear spatio-temporal systems that achieves remarkable accuracy and robustness with data quality/quantity that is relatively less than popular peer methods;To alleviate dependency on prior knowledge in the quest for underlying system mechanism, we present a symbolic neural network architecture to create a more diverse functional search space using cost-effective trainable variables, which is verified on the symbolic identification of multiple mechanical and structural systems as well as other spatio-temporal systems with aid from deep neural networks;To conduct robust and interpretable forecasting for unknown dynamics, we design a Bayesian physics-encoded forecasting model for generalized multi-step-ahead forecasting of nonlinear/ chaotic dynamics with the consideration of the aleatory/epistemic uncertainty and the partial observability problem, which demonstrates superior performance over popular deep neural network models when the testing data is statistically different from the training data.In the end, we pinpoint caveats of our current methodologies such as the primitiveness of used neural networks and the lack of connections to the practicality, which lay paths for future work that aims for providing novel and efficient perspective for solving scientific and engineering challenges.

ISBN: 9798544281849Subjects--Topical Terms:

860360
Civil engineering.
Subjects--Index Terms:

Partial differential equations

Physics-Informed Learning of Complex Systems with Sparse Data.
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100 1 $a Chen, Zhao. $3 1938350
245 1 0 $a Physics-Informed Learning of Complex Systems with Sparse Data.
260 1 $a Ann Arbor : $b ProQuest Dissertations & Theses, $c 2021
300 $a 179 p.
500 $a Source: Dissertations Abstracts International, Volume: 83-04, Section: B.
500 $a Advisor: Sun, Hao.
502 $a Thesis (Ph.D.)--Northeastern University, 2021.
506 $a This item must not be sold to any third party vendors.
520 $a Current practices on the modeling of complex dynamical systems have been mostly rooted in the use of ordinary and/or partial differential equations (ODEs, PDEs) that govern the system behaviors. Apart from governing equations obtained from rigorous first principles, there remain many real-world complex systems whose governing equations and properties are elusive or partially revealed. A novel perspective to analyze such unknown systems is to tackle the fundamental governing equations using symbolic regression that heavily relies on data quantity/quality in the current literature.As the synergistic advancement of machine learning theories, hardware power and sensing technologies, harnessing novel computational theories to analyze statistics patterns embedded in big data provide new opportunities to advance our understanding of complex physical systems. While bottom-up machine learning approaches have delivered super-human accuracy for visual recognition, language translation and even creating fine arts by digesting a huge amount data, their black-box nature renders it susceptible to generalization issues when the new data is statistically distinct from the training data or when the training data is less reliable (e.g. sparse and noisy).To further relax the strong dependence on quality/quantity of training data for symbolic system identification and leverage the horsepower of machine learning, in this dissertation we propose a series of physics-informed computational methods encoding rough domain knowledge into data-driven models, which address the aforementioned issues when machine learning is applied to symbolic system identification and state forecasting of spatio-temporal or dynamic systems (in the form of PDEs or ODEs). In particular, rough domain knowledge is embedded in machine learning models in such a way that by fitting to the training data, the physics mechanism of measurements is also learned and stored in the form of symbolic governing equations. Reciprocally, the constraint of domain knowledge refrains the data-driven model from being perturbed by noise and data scarcity. Therefore, by learning the underlying physics mechanism, the trained model is able to predict well for never-seen new data, overcoming the detrimental generalization issues faced by popular deep learning models. Furthermore, we can distill the symbolic governing equations from lower quality and quantity data than peer symbolic regression methods. The design and pruning of a novel physics representation have also been investigated to allow a more diverse and cost-effective functional search than current literature.Specifically, our contributions are as follows in the chapter order:When the governing equation is aware, we introduce a Bayesian learning with sensitivity analysis for model updating and sparse damage identification in various structural operational stages using scarce and noisy data;When the governing equation is unknown, we develop a sparsity-promoted physics-informed deep learning approach to discover governing laws for nonlinear spatio-temporal systems that achieves remarkable accuracy and robustness with data quality/quantity that is relatively less than popular peer methods;To alleviate dependency on prior knowledge in the quest for underlying system mechanism, we present a symbolic neural network architecture to create a more diverse functional search space using cost-effective trainable variables, which is verified on the symbolic identification of multiple mechanical and structural systems as well as other spatio-temporal systems with aid from deep neural networks;To conduct robust and interpretable forecasting for unknown dynamics, we design a Bayesian physics-encoded forecasting model for generalized multi-step-ahead forecasting of nonlinear/ chaotic dynamics with the consideration of the aleatory/epistemic uncertainty and the partial observability problem, which demonstrates superior performance over popular deep neural network models when the testing data is statistically different from the training data.In the end, we pinpoint caveats of our current methodologies such as the primitiveness of used neural networks and the lack of connections to the practicality, which lay paths for future work that aims for providing novel and efficient perspective for solving scientific and engineering challenges.
590 $a School code: 0160.
650 4 $a Civil engineering. $3 860360
653 $a Partial differential equations
653 $a Machine learning
653 $a Complex dynamical systems
690 $a 0543
710 2 $a Northeastern University. $b Civil and Environmental Engineering. $3 1035254
773 0 $t Dissertations Abstracts International $g 83-04B.
790 $a 0160
791 $a Ph.D.
792 $a 2021
793 $a English
856 4 0 $u https://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=28717863