<mods:mods xmlns:mods="http://www.loc.gov/mods/v3" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:schemaLocation="http://www.loc.gov/mods/v3 http://www.loc.gov/standards/mods/v3/mods-3-7.xsd"><mods:titleInfo><mods:title>Stochastic Modeling of Data-driven Complex Systems Using Machine Learning Tools</mods:title></mods:titleInfo><mods:name type="personal"><mods:namePart>Zhang, Dongkun</mods:namePart><mods:role><mods:roleTerm type="text">creator</mods:roleTerm></mods:role></mods:name><mods:name type="personal"><mods:namePart>Karniadakis, George</mods:namePart><mods:role><mods:roleTerm type="text">Advisor</mods:roleTerm></mods:role></mods:name><mods:name type="personal"><mods:namePart>Wang, Hui</mods:namePart><mods:role><mods:roleTerm type="text">Reader</mods:roleTerm></mods:role></mods:name><mods:name type="personal"><mods:namePart>Sapsis, Themistoklis</mods:namePart><mods:role><mods:roleTerm type="text">Reader</mods:roleTerm></mods:role></mods:name><mods:name type="personal"><mods:namePart>Babaee, Hessam</mods:namePart><mods:role><mods:roleTerm type="text">Reader</mods:roleTerm></mods:role></mods:name><mods:name type="corporate"><mods:namePart>Brown University. Department of Applied Mathematics</mods:namePart><mods:role><mods:roleTerm type="text">sponsor</mods:roleTerm></mods:role></mods:name><mods:originInfo><mods:copyrightDate>2019</mods:copyrightDate></mods:originInfo><mods:physicalDescription><mods:extent>xvii, 169 p.</mods:extent><mods:digitalOrigin>born digital</mods:digitalOrigin></mods:physicalDescription><mods:note type="thesis">Thesis (Ph. D.)--Brown University, 2019</mods:note><mods:genre authority="aat">theses</mods:genre><mods:abstract>This dissertation is composed around the subject of modeling data-driven stochastic complex systems, where there are two challenges: information fusion and uncertainty quantification. In this dissertation, four models/frameworks are proposed to address these challenges, and they are supported by numerical examples.&#13;
The Stochastic Domain Decomposition via Moment Minimization method is developed to facilitate the uncertainty propagation between stochastic solvers that only work for partial domains. It serves as a general framework that takes the local random solvers as black boxes, and can be used to solve problems involving multi-scale phenomena and hybrid stochastic systems.&#13;
The Domain Decomposition with Gaussian Process Regression method is designed to infer solutions in the global domain by assimilating information of both the physical laws and the data. The Data-domain is synchronized with the PDE-domain via a Schwarz alternative process, which also propagates the uncertainty quantified using the numerical Gaussian Process regression method. In a scenario where multi-fidelity data are present, a combination of cheap low-fidelity data and expensive high-fidelity data contributes to more accurate predictions.&#13;
The NN-aPC method is designed for solving both the model inference and model identification problems. A set of arbitrary polynomial basis are generated based on sensor data, and the modal functions of the arbitrary polynomial chaos expansion are learned using the Physics-Informed Neural Networks (PINNs), i.e., DNNs that encode the underlying stochastic differential equation. Two types of uncertainties are quantified: the parametric uncertainty due to the stochastic differential equation, as well as the approximation uncertainty of neural networks.&#13;
Also based on PINNs, the NN-DO/BO methods focus on time-dependent stochastic problems where the bases in both physical and stochastic spaces evolve with time according to the development of the system's stochasticity. To capture the bases dynamics, the Dynamically Orthogonal/Bi-Orthogonal conditions are imposed seamlessly to PINNs by making the best use of the flexibility in designing the loss functions, thus avoiding making addition assumptions about the stochastic behavior of the solution. The NN-DO/BO methods are readily applied to solving time-dependent stochastic inverse problems.</mods:abstract><mods:subject><mods:topic>Machine Learning</mods:topic></mods:subject><mods:subject><mods:topic>Data-Driven Scientific Computing</mods:topic></mods:subject><mods:subject><mods:topic>Uncertainty Quantification</mods:topic></mods:subject><mods:language><mods:languageTerm authority="iso639-2b">English</mods:languageTerm></mods:language><mods:recordInfo><mods:recordContentSource authority="marcorg">RPB</mods:recordContentSource><mods:recordCreationDate encoding="iso8601">20190603</mods:recordCreationDate></mods:recordInfo><mods:identifier type="doi">10.26300/s8tf-dp92</mods:identifier><mods:accessCondition type="rights statement" xlink:href="http://rightsstatements.org/vocab/InC/1.0/">In Copyright</mods:accessCondition><mods:accessCondition type="restriction on access">All rights reserved. Collection is open to the Brown community for research.</mods:accessCondition><mods:typeOfResource authority="primo">dissertations</mods:typeOfResource></mods:mods>