Titlebook: Machine Learning in Modeling and Simulation; Methods and Applicat Timon Rabczuk,Klaus-Jürgen Bathe Book 2023 The Editor(s) (if applicable)

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Ilias Chamatidis,Manos Stoumpos,George Kazakis,Nikos Ath. Kallioras,Savvas Triantafyllou,Vagelis Pleta of ternary alloy systems. Reliable phase diagrams provide materials scientists and engineers with basic information important for fundamental research, development and optimization of materials. ...The often conflicting literature data have been critically evaluated by Materials Science Internati

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Tianyu Huang,Marisa Bisram,Yang Li,Hongyi Xu,Danielle Zeng,Xuming Su,Jian Cao,Wei Chentional scientists.Also available online in www.springerLink..The present volume in the New Series of Landolt-Börnstein provides critically evaluated data on phase diagrams, crystallographic and thermodynamic data of ternary alloy systems. Reliable phase diagrams provide materials scientists and engi

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Machine Learning in Computer Aided Engineering,s, improving or substituting many established approaches in Computer Aided Engineering (CAE), and also solving long-standing problems. In this chapter, we first review the ideas behind the most used ML approaches in CAE, and then discuss a variety of different applications which have been traditiona

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Gaussian Processes,h not reaching the same widespread usage as neural network-based technology, it is also considered a key methodology for the machine learning pratictioner. In this short chapter, a basic introduction to the approach will be provided; following which, several extensions to the fundamental Gaussian pr

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Physics-Informed Neural Networks: Theory and Applications,rks (PINNs) are among the earliest approaches, which attempt to employ the universal approximation property of artificial neural networks to represent the solution field. In this framework, solving the original differential equation can be seen as an optimization problem, where we seek to minimize t

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Physics-Informed Deep Neural Operator Networks,n an advection–diffusion reaction partial differential equation, or simply as a black box, e.g. a system-of-systems. The first neural operator was the Deep Operator Network (DeepONet) proposed in 2019 based on rigorous approximation theory. Since then, a few other less general operators have been pu

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Digital Twin for Dynamical Systems,n this chapter. While physics-based models allow better generalization, a purely physics-based digital twin is often not robust because of noise in the data. On the other hand, gray-box modeling-based digital twin allows seamless fusion of data and physics. One of the primary challenges associated w