東華大學圖書館 |

語系: 繁體中文

說明(常見問題)

回圖書館首頁

手機版館藏查詢

登入

回首頁

切換: 標籤 | MARC模式 | ISBD

Formal Methods for Partial Different...

Penedo Alvarez, Francisco.

FindBook

Google Book

Amazon

博客來

Formal Methods for Partial Differential Equations.

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Formal Methods for Partial Differential Equations./
作者:	Penedo Alvarez, Francisco.
出版者:	Ann Arbor : ProQuest Dissertations & Theses, : 2020,
面頁冊數:	110 p.
附註:	Source: Dissertations Abstracts International, Volume: 81-11.
Contained By:	Dissertations Abstracts International81-11.
標題:	Systems science. -
電子資源:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=27963691
ISBN:	9798645448509

Formal Methods for Partial Differential Equations.
Penedo Alvarez, Francisco.

Formal Methods for Partial Differential Equations. - Ann Arbor : ProQuest Dissertations & Theses, 2020 - 110 p.

Source: Dissertations Abstracts International, Volume: 81-11.

Thesis (Ph.D.)--Boston University, 2020.

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

Partial differential equations (PDEs) model nearly all of the physical systems and processes of interest to scientists and engineers. The analysis of PDEs has had a tremendous impact on society by enabling our understanding of thermal, electrical, fluidic and mechanical processes. However, the study of PDEs is often approached with methods that do not allow for rigorous guarantees that a system satisfies complex design objectives. In contrast, formal methods have recently been developed to allow the formal statement of specifications, while also developing analysis techniques that can guarantee their satisfaction by design. In this dissertation new design methodologies are introduced that enable the systematic creation of structures whose mechanical properties, shape and functionality can be time-varying.A formal methods formulation and solution to the tunable fields problem is first introduced, where a prescribed time evolution of the displacement field for different spatial regions of the structure is to be achieved using boundary control inputs. A spatial and temporal logic is defined that allows the specification of interesting properties in a user-friendly fashion and can provide a satisfaction score for the designed inputs. This score is used to formulate an optimization procedure based on Mixed Integer Programming (MIP) to find the best design.In the second part, a sampling based assumption mining algorithm is introduced, which is the first step towards a divide and conquer strategy to solve the tunable fields problem using assume-guarantee contracts. The algorithm produces a temporal logic formula that represents initial conditions and external inputs of a system that satisfy a goal given as a temporal logic formula over its state. An online supervised learning algorithm is presented, based on decision tree learning, that is used to produce a temporal logic formula from assumption samples.The third part focuses on the tunable constitutive properties problem, where the goal is to create structures satisfying a stress-strain response by designing their geometry. The goal is represented as a logic formula that captures the allowed deviation from a reference and provides a satisfaction score. An optimization procedure is used to obtain the best geometric design.

ISBN: 9798645448509Subjects--Topical Terms:

3168411
Systems science.
Subjects--Index Terms:

Partial differential equations

Formal Methods for Partial Differential Equations.
LDR:03377nmm a2200349 4500 001 2270151
005 20200921070638.5
008 220629s2020 ||||||||||||||||| ||eng d
020 $a 9798645448509
035 $a (MiAaPQ)AAI27963691
035 $a AAI27963691
040 $a MiAaPQ $c MiAaPQ
100 1 $a Penedo Alvarez, Francisco. $3 3547521
245 1 0 $a Formal Methods for Partial Differential Equations.
260 1 $a Ann Arbor : $b ProQuest Dissertations & Theses, $c 2020
300 $a 110 p.
500 $a Source: Dissertations Abstracts International, Volume: 81-11.
500 $a Advisor: Belta, Calin.
502 $a Thesis (Ph.D.)--Boston University, 2020.
506 $a This item must not be sold to any third party vendors.
520 $a Partial differential equations (PDEs) model nearly all of the physical systems and processes of interest to scientists and engineers. The analysis of PDEs has had a tremendous impact on society by enabling our understanding of thermal, electrical, fluidic and mechanical processes. However, the study of PDEs is often approached with methods that do not allow for rigorous guarantees that a system satisfies complex design objectives. In contrast, formal methods have recently been developed to allow the formal statement of specifications, while also developing analysis techniques that can guarantee their satisfaction by design. In this dissertation new design methodologies are introduced that enable the systematic creation of structures whose mechanical properties, shape and functionality can be time-varying.A formal methods formulation and solution to the tunable fields problem is first introduced, where a prescribed time evolution of the displacement field for different spatial regions of the structure is to be achieved using boundary control inputs. A spatial and temporal logic is defined that allows the specification of interesting properties in a user-friendly fashion and can provide a satisfaction score for the designed inputs. This score is used to formulate an optimization procedure based on Mixed Integer Programming (MIP) to find the best design.In the second part, a sampling based assumption mining algorithm is introduced, which is the first step towards a divide and conquer strategy to solve the tunable fields problem using assume-guarantee contracts. The algorithm produces a temporal logic formula that represents initial conditions and external inputs of a system that satisfy a goal given as a temporal logic formula over its state. An online supervised learning algorithm is presented, based on decision tree learning, that is used to produce a temporal logic formula from assumption samples.The third part focuses on the tunable constitutive properties problem, where the goal is to create structures satisfying a stress-strain response by designing their geometry. The goal is represented as a logic formula that captures the allowed deviation from a reference and provides a satisfaction score. An optimization procedure is used to obtain the best geometric design.
590 $a School code: 0017.
650 4 $a Systems science. $3 3168411
650 4 $a Computer science. $3 523869
650 4 $a Materials science. $3 543314
653 $a Partial differential equations
653 $a Mixed integer programming
653 $a Tunable fields
690 $a 0790
690 $a 0794
690 $a 0984
710 2 $a Boston University. $b Systems Engineering ENG. $3 3277612
773 0 $t Dissertations Abstracts International $g 81-11.
790 $a 0017
791 $a Ph.D.
792 $a 2020
793 $a English
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=27963691