Learning nonlinear operators via DeepONet based on the universal approximation theorem of operators
Lu Lu, Pengzhan Jin, Guofei Pang, Zhongqiang Zhang, George Em Karniadakis
Topics & Concepts
GeneralizationArtificial neural networkFunction approximationNonlinear systemOperator (biology)MathematicsOperator theoryDeep learningComputer scienceEncoding (memory)Function (biology)Domain (mathematical analysis)Continuous function (set theory)Spectral theoremSpace (punctuation)Approximation propertyArtificial intelligenceDifferential operatorFunction spaceHilbert spaceApplied mathematicsDifferentiable functionTopology (electrical circuits)Approximation errorRecurrent neural networkModel Reduction and Neural NetworksStochastic Gradient Optimization TechniquesNeural Networks and Applications