Recent advance in machine learning for partial differential equation
Explore this paper's citation graph
Summary
This paper discusses two newly developed machine learning based methods for solving partial differential equations, which are naturally derived from physical rules that describe some of phenomena.
- Type
- article
- Published
- 2021-08-20
- Cited by
- 13
- References
- 67
- OpenAlex
- https://openalex.org/W3194756493
- Semantic Scholar
- https://api.semanticscholar.org/CorpusID:238700851
Keywords
Computer science, Partial differential equation, Artificial intelligence, Task (project management), Machine learning
References
- Cluster analysis of multivariate data : efficiency versus interpretability of classifications
- Partial Differential Equations in Physics
- A logical calculus of the ideas immanent in nervous activity
- Identification of distributed parameter systems: A neural net based approach
- Feedforward Neural Network for Solving Partial Differential Equations
- Classification and regression trees
- Long Short-Term Memory
- Numerical methods for the navier-stokes equations. Applications to the simulation of compressible and incompressible viscous flows
- Support-Vector Networks
- Nonlinear principal component analysis using autoassociative neural networks
- Some methods for classification and analysis of multivariate observations
- Backpropagation Applied to Handwritten Zip Code Recognition
- Artificial neural networks for solving ordinary and partial differential equations
- Deep Residual Learning for Image Recognition
- SymPy: Symbolic computing in Python
- Accelerating Eulerian Fluid Simulation With Convolutional Networks
- Stable architectures for deep neural networks
- Deep Learning-Based Numerical Methods for High-Dimensional Parabolic Partial Differential Equations and Backward Stochastic Differential Equations
- Size estimates for fat inclusions in an isotropic Reissner–Mindlin plate
- DGM: A deep learning algorithm for solving partial differential equations
Cited by
- Scientific Machine Learning Through Physics–Informed Neural Networks: Where we are and What’s Next
- Data-driven method for identifying the expression of the Lyapunov exponent from discrete random data
- Physics-Informed Machine Learning: A Survey on Problems, Methods and Applications
- Data-driven identification for approximate analytical solution of first-passage problem
- A Deep Learning Method for Dynamic Process Modeling of Real Landslides Based on Fourier Neural Operator
- Exploring Physics-Informed Neural Networks: From Fundamentals to Applications in Complex Systems
- Diminishing spectral bias in physics-informed neural networks using spatially-adaptive Fourier feature encoding
- Physics-Informed Neural Networks for the Structural Analysis and Monitoring of Railway Bridges: A Systematic Review
- Open-Skull Post-Selection Misconduct versus Closed-Skull Sole-Learner
- Comparative performance evaluation of DeepONet architectures for dam-break hydrodynamic simulations
- Hybrid Numerical–Machine Learning Techniques for Solving Multi-Physics Nonlinear Partial Differential Equations
- Development of Natural and Artificial Intelligence
- A physics-informed multi-scale fourier neural operator framework for snow avalanche dynamics simulation
Related papers
- Multitask Learning Over Graphs: An Approach for Distributed, Streaming Machine Learning
- Physician-Friendly Machine Learning: A Case Study with Cardiovascular Disease Risk Prediction
- Learning to Multitask
- The Benefit of Multitask Representation Learning
- A Machine Learning Tutorial for Operational Meteorology, Part I: Traditional Machine Learning
- Breakdown of Machine Learning Algorithms
- Applications of nonstandard analysis to partial differential equations—I. the diffusion equation