Fundamental solution neural networks for solving inverse Cauchy problems for the Laplace and biharmonic equations
Xin Li, Fajie Wang, Renhao Wang, Shengdong Zhao, Daigeng Yang
Topics & Concepts
Biharmonic equationMathematicsArtificial neural networkLaplace transformCauchy distributionInverse problemInverseBoundary (topology)Function (biology)Method of fundamental solutionsBoundary value problemLaplace's equationCoordinate systemApplied mathematicsMathematical analysisInterval (graph theory)Variable (mathematics)Numerical analysisGreen's function for the three-variable Laplace equationPoint (geometry)Cauchy problemMathematical optimizationAlgorithmInverse scattering problemDistribution (mathematics)Inverse Laplace transformRegularized meshless methodPartial differential equationSpherical coordinate systemLaplace transform applied to differential equationsNumerical integrationCoordinate descentNumerical methods in inverse problemsModel Reduction and Neural NetworksImage and Signal Denoising Methods