Physics-Informed Neural Networks for Solving Dynamic Two-Phase Interface Problems
DOI10.1137/22m1517081zbMath1528.35105arXiv2207.10725MaRDI QIDQ6068803
Pengtao Sun, Xiaozhe Hu, Xingwen Zhu
Publication date: 15 December 2023
Published in: SIAM Journal on Scientific Computing (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2207.10725
meshfree methodapproximation accuracydeep neural network (DNN)physics-informed neural networks (PINNs)fluid-structure interaction problem (FSI)least-squares (LS) loss functionaltwo-phase flow interface problem
Computational learning theory (68Q32) Artificial neural networks and deep learning (68T07) Numerical optimization and variational techniques (65K10) Navier-Stokes equations for incompressible viscous fluids (76D05) Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.) (74F10) Navier-Stokes equations (35Q30) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Neural nets applied to problems in time-dependent statistical mechanics (82C32) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15) Numerical methods for partial differential equations, boundary value problems (65N99) Liquid-liquid two component flows (76T06)
Cites Work
- Unnamed Item
- Unnamed Item
- Weak Galerkin methods for second order elliptic interface problems
- Stabilized space-time computation of wind-turbine rotor aerodynamics
- A finite element method for interface problems in domains with smooth boundaries and interfaces
- A sharp interface finite volume method for elliptic equations on Cartesian grids
- A Nitsche-based cut finite element method for a fluid-structure interaction problem
- Least-squares finite element methods
- Finite element methods and their convergence for elliptic and parabolic interface problems
- An interface-fitted mesh generator and virtual element methods for elliptic interface problems
- An overview of the immersed interface method and its applications
- An unfitted finite element method, based on Nitsche's method, for elliptic interface problems.
- A boundary condition capturing method for Poisson's equation on irregular domains
- A consistent spatially adaptive smoothed particle hydrodynamics method for fluid-structure interactions
- A spatially adaptive high-order meshless method for fluid-structure interactions
- DGM: a deep learning algorithm for solving partial differential equations
- \textit{hp}-VPINNs: variational physics-informed neural networks with domain decomposition
- Self-adaptive physics-informed neural networks
- Deep least-squares methods: an unsupervised learning-based numerical method for solving elliptic PDEs
- Deep learning of free boundary and Stefan problems
- Parallel physics-informed neural networks via domain decomposition
- When and why PINNs fail to train: a neural tangent kernel perspective
- A mesh-free method using piecewise deep neural network for elliptic interface problems
- Physics-informed neural networks for inverse problems in supersonic flows
- Conservative physics-informed neural networks on discrete domains for conservation laws: applications to forward and inverse problems
- A mesh-free method for interface problems using the deep learning approach
- Adaptive activation functions accelerate convergence in deep and physics-informed neural networks
- On the meshfree particle methods for fluid-structure interaction problems
- Modeling and simulations for fluid and rotating structure interactions
- An energy approach to the solution of partial differential equations in computational mechanics via machine learning: concepts, implementation and applications
- Physics-informed neural networks: a deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations
- High order matched interface and boundary method for elliptic equations with discontinuous coefficients and singular sources
- The finite element method for elliptic equations with discontinuous coefficients
- Extended Finite Element Method
- CutFEM: Discretizing geometry and partial differential equations
- An Overview on Meshfree Methods: For Computational Solid Mechanics
- Numerical Simulation and Benchmarking of a Monolithic Multigrid Solver for Fluid-Structure Interaction Problems with Application to Hemodynamics
- The extended/generalized finite element method: An overview of the method and its applications
- Discontinuous Galerkin Finite Element Methods for Interface Problems: A Priori and A Posteriori Error Estimations
- Relu Deep Neural Networks and Linear Finite Elements
- The immersed boundary method
- Proposal for Numerical Benchmarking of Fluid-Structure Interaction between an Elastic Object and Laminar Incompressible Flow
- A Second-Order Cartesian Grid Finite Volume Technique for Elliptic Interface Problems
- Neural‐network‐based approximations for solving partial differential equations
- The Immersed Interface Method for Elliptic Equations with Discontinuous Coefficients and Singular Sources
- Meshfree Methods: A Comprehensive Review of Applications
- An Unfitted Discontinuous Galerkin Method Applied to Elliptic Interface Problems
- Understanding and Mitigating Gradient Flow Pathologies in Physics-Informed Neural Networks
- Solving high-dimensional partial differential equations using deep learning
- When Do Extended Physics-Informed Neural Networks (XPINNs) Improve Generalization?
- Estimates on the generalization error of physics-informed neural networks for approximating a class of inverse problems for PDEs
- DeepXDE: A Deep Learning Library for Solving Differential Equations
- Locally adaptive activation functions with slope recovery for deep and physics-informed neural networks
- Extended Physics-Informed Neural Networks (XPINNs): A Generalized Space-Time Domain Decomposition Based Deep Learning Framework for Nonlinear Partial Differential Equations
- Partially Penalized Immersed Finite Element Methods For Elliptic Interface Problems
- A Stochastic Approximation Method
- The immersed interface method for the Navier-Stokes equations with singular forces
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