Machine learning materials physics: integrable deep neural networks enable scale bridging by learning free energy functions

DOI10.1016/j.cma.2019.05.019zbMath1441.82021arXiv1901.00081OpenAlexW2907233076WikidataQ127818186 ScholiaQ127818186MaRDI QIDQ1988102

Ad H. G. S. van der Ven, Krishna Garikipati, Gregory H. Teichert, A. R. Natarajan

Publication date: 16 April 2020

Published in: Computer Methods in Applied Mechanics and Engineering (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1901.00081

zbMATH Keywords

chemical potentialphase fielddeep neural networksmultiscale physics

Mathematics Subject Classification ID

Neural nets applied to problems in time-dependent statistical mechanics (82C32) Neural nets and related approaches to inference from stochastic processes (62M45) Numerical methods for functional equations (65Q20)

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Uses Software

• PETSc
• PetIGA
• ImageNet
• AlexNet

Cites Work

• Machine learning strategies for systems with invariance properties
• Linking the electronic structure of solids to their thermodynamic and kinetic properties
• Triple-junction motion for an Allen-Cahn/Cahn-Hilliard system
• Machine learning materials physics: surrogate optimization and multi-fidelity algorithms predict precipitate morphology in an alternative to phase field dynamics
• PetIGA: a framework for high-performance isogeometric analysis
• Unconditionally stable, second-order accurate schemes for solid state phase transformations driven by mechano-chemical spinodal decomposition
• On calculating with B-splines
• Finite Element Approximation of a Degenerate Allen--Cahn/Cahn--Hilliard System
• Isogeometric Analysis
• An Introduction to Numerical Analysis
• Free Energy of a Nonuniform System. I. Interfacial Free Energy
• The Numerical Evaluation of B-Splines
• Approximation by superpositions of a sigmoidal function
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