Concepedia

Variational system identification of the partial differential equations governing microstructure evolution in materials: Inference over sparse and spatially unrelated data

Z. Wang, Xun Huan, Krishna Garikipati

Computer Methods in Applied Mechanics and Engineering · 2021 · 36 citations · 38 references

Concepts

EngineeringVariational AnalysisPhysicsNatural SciencesNumerical SimulationVariational System IdentificationSolid MechanicsMicrostructure EvolutionContinuum ModelingConstitutive ModelingPlasticityComputational MechanicsMaterial NonlinearitiesUnrelated DataMultiscale Modeling

References

38

Compressed sensing

David L. Donoho · IEEE Transactions on Information Theory · 2006 · 22.8K citations

Image Analysis, Engineering, Image Coding +11

Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information

Emmanuel J. Candès, Justin Romberg, Terence Tao · IEEE Transactions on Information Theory · 2006 · 15.6K citations

Statistical Signal Processing, Sparse Representation, Engineering +15

Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations

Maziar Raissi, Paris Perdikaris, George Em Karniadakis · Journal of Computational Physics · 2018 · 14.4K citations · Full text

Engineering, Pde-constrained Optimization, Deep Learning Framework +6

The chemical basis of morphogenesis

Alan Turing · Philosophical transactions of the Royal Society of London. Series B, Biological sciences · 1952 · 11.5K citations

Free Energy of a Nonuniform System. I. Interfacial Free Energy

John W. Cahn, J. E. Hilliard · The Journal of Chemical Physics · 1958 · 10K citations

Free Energy, Engineering, Energy Efficiency +16