000 05269nam a22005655i 4500
001 978-3-031-62029-4
003 DE-He213
005 20251030112658.0
007 cr nn 008mamaa
008 240730s2024 sz | s |||| 0|eng d
020 _a9783031620294
_9978-3-031-62029-4
024 7 _a10.1007/978-3-031-62029-4
_2doi
050 4 _aTA342-343
072 7 _aPBWH
_2bicssc
072 7 _aTBJ
_2bicssc
072 7 _aMAT003000
_2bisacsh
072 7 _aPBWH
_2thema
072 7 _aTBJ
_2thema
100 1 _aGarikipati, Krishna.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
_981534
245 1 0 _aData-driven Modelling and Scientific Machine Learning in Continuum Physics
_h[electronic resource] /
_cby Krishna Garikipati.
250 _a1st ed. 2024.
264 1 _aCham :
_bSpringer International Publishing :
_bImprint: Springer,
_c2024.
300 _aXIV, 230 p. 75 illus., 70 illus. in color.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aInterdisciplinary Applied Mathematics,
_x2196-9973 ;
_v60
505 0 _aPart 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 _aThis 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 _aMathematical models.
_966910
650 0 _aArtificial intelligence
_xData processing.
650 0 _aMachine learning.
_955059
650 1 4 _aMathematical Modeling and Industrial Mathematics.
_966912
650 2 4 _aData Science.
650 2 4 _aMachine Learning.
_955059
710 2 _aSpringerLink (Online service)
773 0 _tSpringer Nature eBook
776 0 8 _iPrinted edition:
_z9783031620287
776 0 8 _iPrinted edition:
_z9783031620300
776 0 8 _iPrinted edition:
_z9783031633645
830 0 _aInterdisciplinary Applied Mathematics,
_x2196-9973 ;
_v60
_970741
856 4 0 _uhttps://doi.org/10.1007/978-3-031-62029-4
912 _aZDB-2-SMA
912 _aZDB-2-SXMS
999 _c62044
_d62044