Physics-informed ConvNet: learning physical field from a shallow neural network
DOI10.1016/j.cnsns.2024.107911arXiv2201.10967OpenAlexW4391850501MaRDI QIDQ6199712
Zhi Zeng, Pengpeng Shi, Tianshou Liang
Publication date: 21 March 2024
Published in: Communications in Nonlinear Science and Numerical Simulation (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2201.10967
machine learningdata-driven scientific computingdenoising displaymulti-frequency fieldoperator estimatingphysics-informed ConvNet(PICN)
Learning and adaptive systems in artificial intelligence (68T05) Nonlinear ordinary differential equations and systems (34A34) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Large deviations (60F10) Numerical interpolation (65D05) NLS equations (nonlinear Schrödinger equations) (35Q55) Finite difference methods for boundary value problems involving PDEs (65N06) Series expansions (e.g., Taylor, Lidstone series, but not Fourier series) (41A58) Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems (65M99) PDEs in connection with classical thermodynamics and heat transfer (35Q79) Time-dependent Schrödinger equations and Dirac equations (35Q41) PDEs on graphs and networks (ramified or polygonal spaces) (35R02)
Cites Work
- Unnamed Item
- Solution of nonlinear ordinary differential equations by feedforward neural networks
- PhyCRNet: physics-informed convolutional-recurrent network for solving spatiotemporal PDEs
- Lift \& learn: physics-informed machine learning for large-scale nonlinear dynamical systems
- PhyGeoNet: physics-informed geometry-adaptive convolutional neural networks for solving parameterized steady-state PDEs on irregular domain
- Parallel physics-informed neural networks via domain decomposition
- Scientific machine learning through physics-informed neural networks: where we are and what's next
- Deep learning solver for solving advection-diffusion equation in comparison to finite difference methods
- Physics-constrained deep learning for high-dimensional surrogate modeling and uncertainty quantification without labeled data
- ConvPDE-UQ: convolutional neural networks with quantified uncertainty for heterogeneous elliptic partial differential equations on varied domains
- Modeling the dynamics of PDE systems with physics-constrained deep auto-regressive networks
- On the eigenvector bias of Fourier feature networks: from regression to solving multi-scale PDEs with physics-informed neural networks
- Conditional physics informed neural networks
- Physics-informed neural networks: a deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations
- Neural algorithm for solving differential equations
- Data-driven forward-inverse problems for Yajima-Oikawa system using deep learning with parameter regularization
- Machine learning: Trends, perspectives, and prospects
- Neural‐network‐based approximations for solving partial differential equations
- A Multigrid Tutorial, Second Edition
- Deep Hidden Physics Models: Deep Learning of Nonlinear Partial Differential Equations
- Hidden fluid mechanics: Learning velocity and pressure fields from flow visualizations
- Shallow neural networks for fluid flow reconstruction with limited sensors
- Physics-Informed Neural Networks with Hard Constraints for Inverse Design
- Dynamic analysis on optical pulses via modified PINNs: soliton solutions, rogue waves and parameter discovery of the CQ-NLSE
- Three ways to solve partial differential equations with neural networks — A review
- A study on data-driven identification and representation of nonlinear dynamical systems with a physics-integrated deep learning approach: Koopman operators and nonlinear normal modes
This page was built for publication: Physics-informed ConvNet: learning physical field from a shallow neural network
