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Free boundary problems appear naturally in numerous areas of mathematics, science and engineering.
The inverse Stefan problem for the heat equation in two space variables
David Colton · 1974
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Solidification of droplets on a cold surface
J Madejski · 1976
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Numerical computation of the free boundary for the two-dimensional Stefan problem by space-time finite elements
R Bonnerot and P Jamet · 1977
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Numerical solution of Stefan problems
AB Crowley · 1978
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A comparative study of numerical methods for moving boundary problems
RM Furzeland · 1980
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The numerical solution of the inverse Stefan problem
Peter Jochum · 1980
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Phase field methods for free boundary problems
George J Fix · 1982
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To the numerical solution of an inverse Stefan problem in two space variables
Peter Jochum · 1982
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The numerical solution of the inverse Stefan problem in two space variables
David Colton and Rembert Reemtsen · 1984
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A method for the numerical solution of the one-dimensional inverse Stefan problem
Rembert Reemtsen and Andreas Kirsch · 1984
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A Legendre spectral element method for the Stefan problem
Einar M Rønquist and Anthony T Patera · 1987
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An implicit enthalpy solution for phase change problems: with application to a binary alloy solidification
VR Voller · 1987
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A front-tracking method for multiphase free boundary problems
David E Womble · 1989
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Theoretical and numerical results on the two-phase Stefan problem
Enrico Magenes, Claudio Verdi, and A Visintin · 1989
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A mathematical model for the diffusion of tumour angiogenesis factor into the surrounding host tissue
MAJ Chaplain and AM Stuart · 1991
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An adaptive finite element method for two-phase Stefan problems in two space dimensions. i. stability and error estimates
RH Nochetto, M Paolini, and C Verdi · 1991
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A front-tracking method for viscous, incompressible, multi-fluid flows
Salih Ozen Unverdi and Grétar Tryggvason · 1992
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Novel strongly implicit enthalpy formulation for multidimensional Stefan problems
AW Date · 1992
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Inverse Stefan problem: tracking of the interface position from measurements on the solid phase
C Benard and A Afshari · 1992
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Stefan problem with kinetic condition arising in semiconductor processing
A Friedman and B Hu · 1995
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A front-tracking method for dendritic solidification
Damir Juric and Grétar Tryggvason · 1996
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Optimal stopping, free boundary, and american option in a jump-diffusion model
Huyên Pham · 1997
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A simple level set method for solving Stefan problems
S Chen, B Merriman, Smereka Osher, and P Smereka · 1997
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A stefan problem for a protocell model
Avner Friedman and Bei Hu · 1999
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Free boundary problems in science and technology
Avner Friedman · 2000
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A bibliography on moving-free boundary problems for the heat-diffusion equation
Domingo Alberto Tarzia et al · 2000
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An adaptive level set method for moving-boundary problems: application to droplet spreading and solidification
LL Zheng and H Zhang · 2000
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A free boundary problem arising in a model of wound healing
Xinfu Chen and Avner Friedman · 2000
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A front-tracking method for the computations of multiphase flow
Grétar Tryggvason, Bernard Bunner, Asghar Esmaeeli, Damir Juric, N Al-Rawahi, W Tauber, J Han, S Nas, and Y-J Jan · 2001
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A moving mesh finite element method for the solution of two-dimensional Stefan problems
DGM: A deep learning algorithm for solving partial differential equations
Justin Sirignano and Konstantinos Spiliopoulos · 2018
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Solving high-dimensional partial differential equations using deep learning
Jiequn Han, Arnulf Jentzen, and E Weinan · 2018
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Physics-informed deep generative models
Yibo Yang and Paris Perdikaris · 2018
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Learning parameters and constitutive relationships with physics informed deep neural networks
Alexandre M Tartakovsky, Carlos Ortiz Marrero, Paris Perdikaris, Guzel D Tartakovsky, and David Barajas-Solano · 2018
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Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations
Maziar Raissi, Paris Perdikaris, and George E Karniadakis · 2019
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G Beckett, John A Mackenzie, and ML Robertson · 2001
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A moving mesh method for the solution of the one-dimensional phase-field equations
JA Mackenzie and ML Robertson · 2002
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Level set methods and dynamic implicit surfaces
Stanley Osher, Ronald Fedkiw, and K Piechor · 2004
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A conservative level set method for two phase flow
Elin Olsson and Gunilla Kreiss · 2005
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A comparison of numerical models for one-dimensional Stefan problems
E Javierre, C Vuik, FJ Vermolen, and S Van der Zwaag · 2006
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Direct and inverse one-phase Stefan problem solved by the variational iteration method
Damian Słota · 2007
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Solving the inverse Stefan design problem using genetic algorithms
Damian Słota · 2008
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fpinns: Fractional physics-informed neural networks
Guofei Pang, Lu Lu, and George Em Karniadakis · 2019
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Adversarial uncertainty quantification in physics-informed neural networks
Yibo Yang and Paris Perdikaris · 2019
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Physics-constrained deep learning for high-dimensional surrogate modeling and uncertainty quantification without labeled data
Yinhao Zhu, Nicholas Zabaras, Phaedon-Stelios Koutsourelakis, and Paris Perdikaris · 2019
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Deep physical informed neural networks for metamaterial design
Zhiwei Fang and Justin Zhan · 2019
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Multi-fidelity physics-constrained neural network and its application in materials modeling
Dehao Liu and Yan Wang · 2019
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Deep learning of turbulent scalar mixing
Maziar Raissi, Hessam Babaee, and Peyman Givi · 2019
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Deep learning of vortex-induced vibrations
Maziar Raissi, Zhicheng Wang, Michael S Triantafyllou, and George Em Karniadakis · 2019
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Lu Lu, Pengzhan Jin, and George Em Karniadakis · 2019
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Understanding and mitigating gradient pathologies in physics-informed neural networks
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