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Parameter Estimation and Inference f...

Venkatraman, Sara Kokila.

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Parameter Estimation and Inference for Nonlinear Dynamical Systems.

Record Type:	Electronic resources : Monograph/item
Title/Author:	Parameter Estimation and Inference for Nonlinear Dynamical Systems./
Author:	Venkatraman, Sara Kokila.
Published:	Ann Arbor : ProQuest Dissertations & Theses, : 2024,
Description:	154 p.
Notes:	Source: Dissertations Abstracts International, Volume: 85-12, Section: B.
Contained By:	Dissertations Abstracts International85-12B.
Subject:	Statistics. -
Online resource:	https://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=31242634
ISBN:	9798382843551

Parameter Estimation and Inference for Nonlinear Dynamical Systems.
Venkatraman, Sara Kokila.

Parameter Estimation and Inference for Nonlinear Dynamical Systems. - Ann Arbor : ProQuest Dissertations & Theses, 2024 - 154 p.

Source: Dissertations Abstracts International, Volume: 85-12, Section: B.

Thesis (Ph.D.)--Cornell University, 2024.

Dynamical systems, expressed as differential equations, serve as fundamental tools across various scientific disciplines for describing the temporal or spatial dynamics of real-world processes. Despite the increasing abundance of data from such processes, deriving the underlying physical laws analytically has grown more challenging. Consequently, statisticians and applied mathematicians have turned to developing techniques to estimate the differential equations governing temporally or spatially evolving systems from time series data. This dissertation contributes to this field by presenting novel advancements in both parameter estimation for differential equations of a known functional form and equation discovery for systems of an unknown form.The first method introduced is a Bayesian regression algorithm tailored for fitting a specific system of differential equations to time-course gene expression data. Subsequently, the resulting model is utilized to cluster genes based on the similarity of their temporal behavior. Following this, a regularized regression-based approach is presented for recovering systems of ordinary differential equations from time series data. Notably, this method offers classical uncertainty estimates in the form of confidence intervals and hypothesis tests for each term in the reconstructed equation. This addresses a pertinent issue in the literature on data-driven dynamical system recovery, namely how to quantify uncertainty in a computationally efficient and interpretable manner. Finally, an extension of this methodology to partial differential equations recovered from spatiotemporal data is proposed and contextualized within the broader field of scientific machine learning. Detailed discussions on future extensions of the proposed methods are provided, and software packages implementing these methods are made publicly accessible.

ISBN: 9798382843551Subjects--Topical Terms:

517247
Statistics.
Subjects--Index Terms:

Dynamical systems

Parameter Estimation and Inference for Nonlinear Dynamical Systems.
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100 1 $a Venkatraman, Sara Kokila. $0 (orcid)0009-0006-1129-2397 $3 3770105
245 1 0 $a Parameter Estimation and Inference for Nonlinear Dynamical Systems.
260 1 $a Ann Arbor : $b ProQuest Dissertations & Theses, $c 2024
300 $a 154 p.
500 $a Source: Dissertations Abstracts International, Volume: 85-12, Section: B.
500 $a Advisor: Wells, Martin.
502 $a Thesis (Ph.D.)--Cornell University, 2024.
520 $a Dynamical systems, expressed as differential equations, serve as fundamental tools across various scientific disciplines for describing the temporal or spatial dynamics of real-world processes. Despite the increasing abundance of data from such processes, deriving the underlying physical laws analytically has grown more challenging. Consequently, statisticians and applied mathematicians have turned to developing techniques to estimate the differential equations governing temporally or spatially evolving systems from time series data. This dissertation contributes to this field by presenting novel advancements in both parameter estimation for differential equations of a known functional form and equation discovery for systems of an unknown form.The first method introduced is a Bayesian regression algorithm tailored for fitting a specific system of differential equations to time-course gene expression data. Subsequently, the resulting model is utilized to cluster genes based on the similarity of their temporal behavior. Following this, a regularized regression-based approach is presented for recovering systems of ordinary differential equations from time series data. Notably, this method offers classical uncertainty estimates in the form of confidence intervals and hypothesis tests for each term in the reconstructed equation. This addresses a pertinent issue in the literature on data-driven dynamical system recovery, namely how to quantify uncertainty in a computationally efficient and interpretable manner. Finally, an extension of this methodology to partial differential equations recovered from spatiotemporal data is proposed and contextualized within the broader field of scientific machine learning. Detailed discussions on future extensions of the proposed methods are provided, and software packages implementing these methods are made publicly accessible.
590 $a School code: 0058.
650 4 $a Statistics. $3 517247
650 4 $a Applied mathematics. $3 2122814
650 4 $a Systems science. $3 3168411
650 4 $a Computer science. $3 523869
653 $a Dynamical systems
653 $a Spatial statistics
653 $a Time series analysis
653 $a Parameter estimation
653 $a Differential equations
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690 $a 0790
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710 2 $a Cornell University. $b Statistics. $3 3169949
773 0 $t Dissertations Abstracts International $g 85-12B.
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792 $a 2024
793 $a English
856 4 0 $u https://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=31242634