article Open AccessTop 1% cited
An energy approach to the solution of partial differential equations in computational mechanics via machine learning: Concepts, implementation and applications
Computer Methods in Applied Mechanics and Engineering · 2020 · Vol. 362 · pp. 112790–112790
Esteban Samaniego(University of Cuenca)Cosmin Anitescu(Bauhaus-Universität Weimar)Somdatta Goswami(Bauhaus-Universität Weimar)Vien Minh Nguyen‐Thanh(Leibniz University Hannover)Hongwei Guo(Leibniz University Hannover)Khader M. Hamdia(Leibniz University Hannover)Xiaoying Zhuang(Leibniz University Hannover)Timon Rabczuk✉(Ton Duc Thang University)
Model Reduction and Neural NetworksAdvanced Numerical Analysis TechniquesNumerical methods in engineeringPartial differential equationDiscretizationComputer scienceFinite element methodComputational mechanicsCollocation (remote sensing)Function (biology)Mathematical optimizationFlexibility (engineering)Applied mathematics
Citations
1,823
FWCI
111.10
field-weighted impact
References
56
Percentile
100%
vs. same field & year
Citations per year
Cited by
Deep learning for topology optimization of 2D metamaterials
Materials & Design · 2020 · 337 citations
hp-VPINNs: Variational physics-informed neural networks with domain decomposition
Computer Methods in Applied Mechanics and Engineering · 2020 · 676 citations
References
A phase-field description of dynamic brittle fracture
Computer Methods in Applied Mechanics and Engineering · 2012 · 1,769 citations
Numerical experiments in revisited brittle fracture
Journal of the Mechanics and Physics of Solids · 2000 · 2,550 citations
Thermodynamically consistent phase‐field models of fracture: Variational principles and multi‐field FE implementations
International Journal for Numerical Methods in Engineering · 2010 · 2,633 citations
A phase field model for rate-independent crack propagation: Robust algorithmic implementation based on operator splits
Computer Methods in Applied Mechanics and Engineering · 2010 · 2,801 citations
Data-driven computational mechanics
Computer Methods in Applied Mechanics and Engineering · 2016 · 736 citations
The finite element method. Linear static and dynamic finite element analysis
Computer Methods in Applied Mechanics and Engineering · 1987 · 5,123 citations
A unified deep artificial neural network approach to partial differential equations in complex geometries
Neurocomputing · 2018 · 631 citations
Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations
Journal of Computational Physics · 2018 · 15,047 citations
Citation Network
How this paper connects to the literature. Drag to explore, click any node to open that paper.