國立高雄大學圖資館 |

登入

回首頁

Data-driven modelling and scientific machine learning in continuum physics

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Data-driven modelling and scientific machine learning in continuum physicsby Krishna Garikipati.
作者:	Garikipati, Krishna.
出版者:	Cham :Springer International Publishing :2024.
面頁冊數:	xiv, 230 p. :ill. (chiefly col.), digital ;24 cm.
Contained By:	Springer Nature eBook
標題:	Field theory (Physics)
電子資源:	https://doi.org/10.1007/978-3-031-62029-4
ISBN:	9783031620294$q(electronic bk.)

Data-driven modelling and scientific machine learning in continuum physics
Garikipati, Krishna.

Data-driven modelling and scientific machine learning in continuum physics[electronic resource] /by Krishna Garikipati. - Cham :Springer International Publishing :2024. - xiv, 230 p. :ill. (chiefly col.), digital ;24 cm. - Interdisciplinary applied mathematics,v. 602196-9973 ;. - Interdisciplinary applied mathematics ;v. 21..

Part I. Introduction and Background in Continuum Materials Physics -- Introduction -- Nonlinear Elasticity -- Phase Field Methods -- Part II. Solving Partial Differential Equations -- Finite Element Methods -- Part III. Data-driven Modelling and Scientific Machine Learning -- Reduced Order Models: Numerical Homogenization for the Elastic Response of Material Microstructures -- Surrogate Optimization -- Graph Theoretic Methods -- Scale Bridging -- Inverse Modeling and System Inference from Data -- Machine Learning Solvers of Partial Differential Equations -- An Outlook on Scientific Machine Learning in Continuum Physics -- References.

This monograph takes the reader through recent advances in data-driven methods and machine learning for problems in science-specifically in continuum physics. It develops the foundations and details a number of scientific machine learning approaches to enrich current computational models of continuum physics, or to use the data generated by these models to infer more information on these problems. The perspective presented here is drawn from recent research by the author and collaborators. Applications drawn from the physics of materials or from biophysics illustrate each topic. Some elements of the theoretical background in continuum physics that are essential to address these applications are developed first. These chapters focus on nonlinear elasticity and mass transport, with particular attention directed at descriptions of phase separation. This is followed by a brief treatment of the finite element method, since it is the most widely used approach to solve coupled partial differential equations in continuum physics. With these foundations established, the treatment proceeds to a number of recent developments in data-driven methods and scientific machine learning in the context of the continuum physics of materials and biosystems. This part of the monograph begins by addressing numerical homogenization of microstructural response using feed-forward as well as convolutional neural networks. Next is surrogate optimization using multifidelity learning for problems of phase evolution. Graph theory bears many equivalences to partial differential equations in its properties of representation and avenues for analysis as well as reduced-order descriptions--all ideas that offer fruitful opportunities for exploration. Neural networks, by their capacity for representation of high-dimensional functions, are powerful for scale bridging in physics--an idea on which we present a particular perspective in the context of alloys. One of the most compelling ideas in scientific machine learning is the identification of governing equations from dynamical data--another topic that we explore from the viewpoint of partial differential equations encoding mechanisms. This is followed by an examination of approaches to replace traditional, discretization-based solvers of partial differential equations with deterministic and probabilistic neural networks that generalize across boundary value problems. The monograph closes with a brief outlook on current emerging ideas in scientific machine learning.

ISBN: 9783031620294$q(electronic bk.)

Standard No.: 10.1007/978-3-031-62029-4doiSubjects--Topical Terms:

208085
Field theory (Physics)

LC Class. No.: QC173.7 / .G37 2024

Dewey Class. No.: 530.14

Data-driven modelling and scientific machine learning in continuum physics
LDR:04317nmm a2200361 a 4500 001 667226
003 DE-He213
005 20240730130220.0
006 m d
007 cr nn 008maaau
008 250107s2024 sz s 0 eng d
020 $a 9783031620294$q(electronic bk.)
020 $a 9783031620287$q(paper)
024 7 $a 10.1007/978-3-031-62029-4 $2 doi
035 $a 978-3-031-62029-4
040 $a GP $c GP
041 0 $a eng
050 4 $a QC173.7 $b .G37 2024
072 7 $a PBWH $2 bicssc
072 7 $a TBJ $2 bicssc
072 7 $a MAT003000 $2 bisacsh
072 7 $a PBWH $2 thema
072 7 $a TBJ $2 thema
082 0 4 $a 530.14 $2 23
090 $a QC173.7 $b .G232 2024
100 1 $a Garikipati, Krishna. $3 455682
245 1 0 $a Data-driven modelling and scientific machine learning in continuum physics $h [electronic resource] / $c by Krishna Garikipati.
260 $a Cham : $b Springer International Publishing : $b Imprint: Springer, $c 2024.
300 $a xiv, 230 p. : $b ill. (chiefly col.), digital ; $c 24 cm.
490 1 $a Interdisciplinary applied mathematics, $x 2196-9973 ; $v v. 60
505 0 $a Part I. Introduction and Background in Continuum Materials Physics -- Introduction -- Nonlinear Elasticity -- Phase Field Methods -- Part II. Solving Partial Differential Equations -- Finite Element Methods -- Part III. Data-driven Modelling and Scientific Machine Learning -- Reduced Order Models: Numerical Homogenization for the Elastic Response of Material Microstructures -- Surrogate Optimization -- Graph Theoretic Methods -- Scale Bridging -- Inverse Modeling and System Inference from Data -- Machine Learning Solvers of Partial Differential Equations -- An Outlook on Scientific Machine Learning in Continuum Physics -- References.
520 $a This monograph takes the reader through recent advances in data-driven methods and machine learning for problems in science-specifically in continuum physics. It develops the foundations and details a number of scientific machine learning approaches to enrich current computational models of continuum physics, or to use the data generated by these models to infer more information on these problems. The perspective presented here is drawn from recent research by the author and collaborators. Applications drawn from the physics of materials or from biophysics illustrate each topic. Some elements of the theoretical background in continuum physics that are essential to address these applications are developed first. These chapters focus on nonlinear elasticity and mass transport, with particular attention directed at descriptions of phase separation. This is followed by a brief treatment of the finite element method, since it is the most widely used approach to solve coupled partial differential equations in continuum physics. With these foundations established, the treatment proceeds to a number of recent developments in data-driven methods and scientific machine learning in the context of the continuum physics of materials and biosystems. This part of the monograph begins by addressing numerical homogenization of microstructural response using feed-forward as well as convolutional neural networks. Next is surrogate optimization using multifidelity learning for problems of phase evolution. Graph theory bears many equivalences to partial differential equations in its properties of representation and avenues for analysis as well as reduced-order descriptions--all ideas that offer fruitful opportunities for exploration. Neural networks, by their capacity for representation of high-dimensional functions, are powerful for scale bridging in physics--an idea on which we present a particular perspective in the context of alloys. One of the most compelling ideas in scientific machine learning is the identification of governing equations from dynamical data--another topic that we explore from the viewpoint of partial differential equations encoding mechanisms. This is followed by an examination of approaches to replace traditional, discretization-based solvers of partial differential equations with deterministic and probabilistic neural networks that generalize across boundary value problems. The monograph closes with a brief outlook on current emerging ideas in scientific machine learning.
650 0 $a Field theory (Physics) $3 208085
650 0 $a Machine learning. $3 188639
650 1 4 $a Mathematical Modeling and Industrial Mathematics. $3 274070
650 2 4 $a Data Science. $3 913495
650 2 4 $a Machine Learning. $3 833608
710 2 $a SpringerLink (Online service) $3 273601
773 0 $t Springer Nature eBook
830 0 $a Interdisciplinary applied mathematics ; $v v. 21. $3 440074
856 4 0 $u https://doi.org/10.1007/978-3-031-62029-4
950 $a Mathematics and Statistics (SpringerNature-11649)