Concepedia

Koopman Neural Operator as a Mesh-Free Solver of Non-Linear Partial Differential Equations

Wei Xiong, Xiaomeng Huang, Ziyang Zhang, Ruixuan Deng, Pei Sun, Yang Tian

SSRN Electronic Journal · 2023 · 19 citations · 45 references

Open access

Concepts

Natural SciencesComputational EngineeringMathematicsComputational MechanicsDifferential EquationsFluid DynamicsBoundary ConditionsFinite Element FormulationNumerical Methods For Differential EquationsPartial Differential EquationsSystems Of Differential EquationsVariational FormulationDifferential Equation SolversDiscretization Of Partial Differential EquationsNonlinear Partial Differential EquationsNumerical Analysis Of Partial Differential EquationsNumerical Solutions Of Partial Differential EquationsPartial Differential Equation SolversPartial Differential Equation Systems

References

45

Deep Residual Learning for Image Recognition

Kaiming He, Xiangyu Zhang, Shaoqing Ren et al. · 2016 · 222.1K citations · Full text

Computing, Computer Science, Computer Vision +11

Going deeper with convolutions

Christian Szegedy, Wei Liu, Yangqing Jia et al. · 2015 · 46.8K citations

Computing, Computer Science, Artificial Intelligence +15

Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations

Maziar Raissi, Paris Perdikaris, George Em Karniadakis · Journal of Computational Physics · 2018 · 16.9K citations · Full text

Natural Sciences, Computer Science, Physics +16

Integrals of nonlinear equations of evolution and solitary waves

Peter D. Lax · Communications on Pure and Applied Mathematics · 1968 · 3.1K citations

Natural Sciences, Mathematics, Physics +14

Learning nonlinear operators via DeepONet based on the universal approximation theorem of operators

Nature Machine Intelligence · 2021 · 2.8K citations · Full text

Computing, Computer Science, Mathematics +10