Learning phase field mean curvature flows with neural networks
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Publication:2083658
DOI10.1016/j.jcp.2022.111579OpenAlexW4226070051WikidataQ114950918 ScholiaQ114950918MaRDI QIDQ2083658
Simon Masnou, Roland Denis, Garry Terii, Elie Bretin
Publication date: 11 October 2022
Published in: Journal of Computational Physics (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2112.07343
Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems (65Mxx) Parabolic equations and parabolic systems (35Kxx) Manifolds and measure-geometric topics (49Qxx)
Uses Software
Cites Work
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- Convergence of the thresholding scheme for multi-phase mean-curvature flow
- A numerical method for computing minimal surfaces in arbitrary dimension
- Motion of level sets by mean curvature. I
- On the parametric finite element approximation of evolving hypersurfaces in \(\mathbb R^3\)
- A contribution to the particle modeling of soap films
- Fronts propagating with curvature-dependent speed: Algorithms based on Hamilton-Jacobi formulations
- A contribution to the numerical approximation of minimal surfaces
- Efficient algorithms for diffusion-generated motion by mean curvature
- Threshold dynamics type approximation schemes for propagating fronts
- Quasi-optimal error estimates for the mean curvature flow with a forcing term
- Bayesian deep convolutional encoder-decoder networks for surrogate modeling and uncertainty quantification
- A phase-field approximation of the Steiner problem in dimension two
- The Deep Ritz Method: a deep learning-based numerical algorithm for solving variational problems
- Multiphase mean curvature flows with high mobility contrasts: a phase-field approach, with applications to nanowires
- On anisotropic order parameter models for multi-phase systems and their sharp interface limits
- Lectures on curvature flow of networks
- A physics-informed operator regression framework for extracting data-driven continuum models
- On motion by curvature of a network with a triple junction
- Model reduction and neural networks for parametric PDEs
- High order, semi-implicit, energy stable schemes for gradient flows
- A convex approach to the Gilbert-Steiner problem
- Physics-informed neural networks: a deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations
- Prediction of aerodynamic flow fields using convolutional neural networks
- A new phase field model for inhomogeneous minimal partitions, and applications to droplets dynamics
- Computing minimal surfaces via level set curvature flow
- A semi-analytical Fourier spectral method for the Allen-Cahn equation
- Phase field method for mean curvature flow with boundary constraints
- Lecture Notes on Mean Curvature Flow, Barriers and Singular Perturbations
- A modified phase field approximation for mean curvature flow with conservation of the volume
- Approximation of functional depending on jumps by elliptic functional via t-convergence
- Solution of the Plateau problem for đ-dimensional surfaces of varying topological type
- Large-Scale Machine Learning with Stochastic Gradient Descent
- The phase field method for geometric moving interfaces and their numerical approximations
- The Random Feature Model for Input-Output Maps between Banach Spaces
- Computation of geometric partial differential equations and mean curvature flow
- ALLENâCAHN SYSTEMS WITH VOLUME CONSTRAINTS
- Generation and Propagation of Interfaces in Reaction-Diffusion Systems
- The discrete Plateau Problem: Algorithm and numerics
- The discrete plateau problem: Convergence results
- Geometric Level Set Methods in Imaging, Vision, and Graphics
- Variational Approximation of Functionals Defined on 1-dimensional Connected Sets: The Planar Case
- Solving ill-posed inverse problems using iterative deep neural networks
- Volume Reconstruction from Slices
- Geometrical Evolution of Developed Interfaces
- Approximation of Partitions of Least Perimeter by Î-Convergence: Around Kelvinâs Conjecture
- A MultiPhase Field Concept: Numerical Simulations of Moving Phase Boundaries and Multiple Junctions
- Solving high-dimensional partial differential equations using deep learning
- Solving parametric PDE problems with artificial neural networks
- Variational approximation of size-mass energies fork-dimensional currents
- Physics-Informed Probabilistic Learning of Linear Embeddings of Nonlinear Dynamics with Guaranteed Stability
- Phase-field modelling and computing for a large number of phases
- Numerical approximation of the Steiner problem in dimension $2$ and $3$
- Threshold Dynamics for Networks with Arbitrary Surface Tensions
- Approximation of Length Minimization Problems Among Compact Connected Sets
- Learning Consistent Discretizations of the Total Variation
- Uniqueness and existence of viscosity solutions of generalized mean curvature flow equations
- Approximation by superpositions of a sigmoidal function
- Connections between numerical algorithms for PDEs and neural networks
